%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU266+1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 10:43:44 AM UTC 2026
% Result : Theorem 218.46s 36.66s
% Output : CNFRefutation 218.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 38
% Syntax : Number of formulae : 563 ( 355 unt; 0 typ; 0 def)
% Number of atoms : 3186 (1026 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 6061 ( 913 ~; 874 |; 52 &;4169 @)
% ( 17 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 30 usr; 9 con; 0-3 aty)
% Number of variables : 1358 ( 0 ^;1346 !; 12 ?;1358 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
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_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_of2,type,
relation_of2: $i > $i > $i > $o ).
thf(tp_relation_of2_as_subset,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_relation_rng_as_subset,type,
relation_rng_as_subset: $i > $i > $i > $i ).
thf(tp_sK10_B,type,
sK10_B: $i > $i ).
thf(tp_sK11_C,type,
sK11_C: $i > $i > $i ).
thf(tp_sK12_D,type,
sK12_D: $i > $i > $i > $i ).
thf(tp_sK13_C,type,
sK13_C: $i > $i > $i ).
thf(tp_sK14_SY78,type,
sK14_SY78: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY67,type,
sK2_SY67: $i ).
thf(tp_sK3_SY71,type,
sK3_SY71: $i ).
thf(tp_sK4_SY75,type,
sK4_SY75: $i > $i ).
thf(tp_sK5_SY74,type,
sK5_SY74: $i ).
thf(tp_sK6_C,type,
sK6_C: $i > $i > $i ).
thf(tp_sK7_A,type,
sK7_A: $i ).
thf(tp_sK8_A,type,
sK8_A: $i ).
thf(tp_sK9_C,type,
sK9_C: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(3,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ B @ ( relation_rng @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(11,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( relation_rng_as_subset @ A @ B @ C )
= ( relation_rng @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).
thf(14,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(15,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(16,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(17,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(18,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(19,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(20,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(22,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(23,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_rng_as_subset @ A @ B @ C ) @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relset_1) ).
thf(25,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(26,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(27,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(28,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(29,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(30,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(31,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(32,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(34,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(38,conjecture,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
~ ( in @ ( ordered_pair @ E @ D ) @ C ) )
<=> ( ( relation_rng_as_subset @ A @ B @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_relset_1) ).
thf(39,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
~ ( in @ ( ordered_pair @ E @ D ) @ C ) )
<=> ( ( relation_rng_as_subset @ A @ B @ C )
= B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[38]) ).
thf(40,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
~ ( in @ ( ordered_pair @ E @ D ) @ C ) )
<=> ( ( relation_rng_as_subset @ A @ B @ C )
= B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[39]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(42,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(43,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(44,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(45,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(46,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(47,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(48,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(49,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)],[9]) ).
thf(50,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(51,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(52,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(53,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( relation_rng_as_subset @ A @ B @ C )
= ( relation_rng @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(54,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(55,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(56,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(57,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(59,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(60,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(61,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(62,plain,
$true = $true,
inference(unfold_def,[status(thm)],[22]) ).
thf(63,plain,
$true = $true,
inference(unfold_def,[status(thm)],[23]) ).
thf(64,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_rng_as_subset @ A @ B @ C ) @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(65,plain,
$true = $true,
inference(unfold_def,[status(thm)],[25]) ).
thf(66,plain,
$true = $true,
inference(unfold_def,[status(thm)],[26]) ).
thf(67,plain,
$true = $true,
inference(unfold_def,[status(thm)],[27]) ).
thf(68,plain,
$true = $true,
inference(unfold_def,[status(thm)],[28]) ).
thf(69,plain,
$true = $true,
inference(unfold_def,[status(thm)],[29]) ).
thf(70,plain,
$true = $true,
inference(unfold_def,[status(thm)],[30]) ).
thf(71,plain,
$true = $true,
inference(unfold_def,[status(thm)],[31]) ).
thf(72,plain,
$true = $true,
inference(unfold_def,[status(thm)],[32]) ).
thf(73,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(74,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)],[34]) ).
thf(75,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(76,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(77,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(78,plain,
( ( ! [SY67: $i,SY68: $i] :
( ( relation_of2_as_subset @ SY68 @ sK1_A @ SY67 )
=> ( ! [D: $i] :
~ ( ( in @ D @ SY67 )
& ! [E: $i] :
~ ( in @ ( ordered_pair @ E @ D ) @ SY68 ) )
<=> ( ( relation_rng_as_subset @ sK1_A @ SY67 @ SY68 )
= SY67 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(79,plain,
( ( ! [SY71: $i] :
( ( relation_of2_as_subset @ SY71 @ sK1_A @ sK2_SY67 )
=> ( ! [SY72: $i] :
~ ( ( in @ SY72 @ sK2_SY67 )
& ! [E: $i] :
~ ( in @ ( ordered_pair @ E @ SY72 ) @ SY71 ) )
<=> ( ( relation_rng_as_subset @ sK1_A @ sK2_SY67 @ SY71 )
= sK2_SY67 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[78]) ).
thf(80,plain,
( ( ( relation_of2_as_subset @ sK3_SY71 @ sK1_A @ sK2_SY67 )
=> ( ! [SY74: $i] :
~ ( ( in @ SY74 @ sK2_SY67 )
& ! [SY75: $i] :
~ ( in @ ( ordered_pair @ SY75 @ SY74 ) @ sK3_SY71 ) )
<=> ( ( relation_rng_as_subset @ sK1_A @ sK2_SY67 @ sK3_SY71 )
= sK2_SY67 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[79]) ).
thf(81,plain,
( ( relation_of2_as_subset @ sK3_SY71 @ sK1_A @ sK2_SY67 )
= $true ),
inference(standard_cnf,[status(thm)],[80]) ).
thf(82,plain,
( ( ! [SY74: $i] :
~ ( ( in @ SY74 @ sK2_SY67 )
& ! [SY75: $i] :
~ ( in @ ( ordered_pair @ SY75 @ SY74 ) @ sK3_SY71 ) )
<=> ( ( relation_rng_as_subset @ sK1_A @ sK2_SY67 @ sK3_SY71 )
= sK2_SY67 ) )
= $false ),
inference(standard_cnf,[status(thm)],[80]) ).
thf(83,plain,
( ( ! [SY74: $i] :
~ ( ( in @ SY74 @ sK2_SY67 )
& ! [SY75: $i] :
~ ( in @ ( ordered_pair @ SY75 @ SY74 ) @ sK3_SY71 ) )
=> ( ( relation_rng_as_subset @ sK1_A @ sK2_SY67 @ sK3_SY71 )
= sK2_SY67 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[82]) ).
thf(84,plain,
( ( ( ( relation_rng_as_subset @ sK1_A @ sK2_SY67 @ sK3_SY71 )
= sK2_SY67 )
=> ! [SY74: $i] :
~ ( ( in @ SY74 @ sK2_SY67 )
& ! [SY75: $i] :
~ ( in @ ( ordered_pair @ SY75 @ SY74 ) @ sK3_SY71 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[82]) ).
thf(85,plain,
( ( ~ ( ! [SY74: $i] :
~ ( ( in @ SY74 @ sK2_SY67 )
& ! [SY75: $i] :
~ ( in @ ( ordered_pair @ SY75 @ SY74 ) @ sK3_SY71 ) )
=> ( ( relation_rng_as_subset @ sK1_A @ sK2_SY67 @ sK3_SY71 )
= sK2_SY67 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[83]) ).
thf(86,plain,
( ( ~ ( ( ( relation_rng_as_subset @ sK1_A @ sK2_SY67 @ sK3_SY71 )
= sK2_SY67 )
=> ! [SY74: $i] :
~ ( ( in @ SY74 @ sK2_SY67 )
& ! [SY75: $i] :
~ ( in @ ( ordered_pair @ SY75 @ SY74 ) @ sK3_SY71 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[84]) ).
thf(87,plain,
( ( ! [SY74: $i] :
( ( in @ ( ordered_pair @ ( sK4_SY75 @ SY74 ) @ SY74 ) @ sK3_SY71 )
| ~ ( in @ SY74 @ sK2_SY67 ) )
& ( ( relation_rng_as_subset @ sK1_A @ sK2_SY67 @ sK3_SY71 )
!= sK2_SY67 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(88,plain,
( ( ( ( relation_rng_as_subset @ sK1_A @ sK2_SY67 @ sK3_SY71 )
= sK2_SY67 )
& ! [SY76: $i] :
~ ( in @ ( ordered_pair @ SY76 @ sK5_SY74 ) @ sK3_SY71 )
& ( in @ sK5_SY74 @ sK2_SY67 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[86]) ).
thf(89,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(90,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(91,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(92,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(93,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(94,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(95,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK6_C @ B @ A ) @ A )
| ~ ( in @ ( sK6_C @ B @ A ) @ B ) )
& ( ( in @ ( sK6_C @ B @ A ) @ A )
| ( in @ ( sK6_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(97,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_dom @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_rng @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(98,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(99,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(100,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(101,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( ( relation_rng_as_subset @ A @ B @ C )
= ( relation_rng @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(102,plain,
( ( ~ ( empty @ sK7_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(103,plain,
( ( empty @ sK8_A )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(104,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK9_C @ B @ A ) @ A @ B ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(105,plain,
( ( ! [A: $i] : ( element @ ( sK10_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(106,plain,
( ( ! [A: $i,B: $i] : ( relation_of2 @ ( sK11_C @ B @ A ) @ A @ B ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(107,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(108,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( element @ ( relation_rng_as_subset @ A @ B @ C ) @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(109,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY77: $i] :
~ ( in @ ( ordered_pair @ SY77 @ ( sK13_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK13_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK14_SY78 @ B @ A ) @ ( sK13_C @ B @ A ) ) @ A )
| ( in @ ( sK13_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ ( sK12_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(110,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[76]) ).
thf(111,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[77]) ).
thf(112,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(113,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(114,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(115,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY77: $i] :
~ ( in @ ( ordered_pair @ SY77 @ ( sK13_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK13_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK14_SY78 @ B @ A ) @ ( sK13_C @ B @ A ) ) @ A )
| ( in @ ( sK13_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ ( sK12_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(116,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(117,plain,
$true = $true,
inference(copy,[status(thm)],[72]) ).
thf(118,plain,
$true = $true,
inference(copy,[status(thm)],[71]) ).
thf(119,plain,
$true = $true,
inference(copy,[status(thm)],[70]) ).
thf(120,plain,
$true = $true,
inference(copy,[status(thm)],[69]) ).
thf(121,plain,
$true = $true,
inference(copy,[status(thm)],[68]) ).
thf(122,plain,
$true = $true,
inference(copy,[status(thm)],[67]) ).
thf(123,plain,
$true = $true,
inference(copy,[status(thm)],[66]) ).
thf(124,plain,
$true = $true,
inference(copy,[status(thm)],[65]) ).
thf(125,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( element @ ( relation_rng_as_subset @ A @ B @ C ) @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(126,plain,
$true = $true,
inference(copy,[status(thm)],[63]) ).
thf(127,plain,
$true = $true,
inference(copy,[status(thm)],[62]) ).
thf(128,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(129,plain,
( ( ! [A: $i,B: $i] : ( relation_of2 @ ( sK11_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(130,plain,
( ( ! [A: $i] : ( element @ ( sK10_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(131,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK9_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(132,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(133,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(134,plain,
( ( empty @ sK8_A )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(135,plain,
( ( ~ ( empty @ sK7_A ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(136,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( ( relation_rng_as_subset @ A @ B @ C )
= ( relation_rng @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(137,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(138,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(139,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(140,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_dom @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_rng @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(141,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(142,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK6_C @ B @ A ) @ A )
| ~ ( in @ ( sK6_C @ B @ A ) @ B ) )
& ( ( in @ ( sK6_C @ B @ A ) @ A )
| ( in @ ( sK6_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(143,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(144,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(145,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(146,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(147,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(148,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(149,plain,
( ( relation_of2_as_subset @ sK3_SY71 @ sK1_A @ sK2_SY67 )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(150,plain,
( ( ! [SY74: $i] :
( ( in @ ( ordered_pair @ ( sK4_SY75 @ SY74 ) @ SY74 ) @ sK3_SY71 )
| ~ ( in @ SY74 @ sK2_SY67 ) )
& ( ( relation_rng_as_subset @ sK1_A @ sK2_SY67 @ sK3_SY71 )
!= sK2_SY67 ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(151,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ SX2 @ ( sK13_C @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SX1 @ SX0 ) @ ( sK13_C @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_rng @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(152,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( relation_of2 @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(153,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(154,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( ordered_pair @ ( sK4_SY75 @ SX0 ) @ SX0 ) @ sK3_SY71 )
| ~ ( in @ SX0 @ sK2_SY67 ) )
| ~ ( ( ( relation_rng_as_subset @ sK1_A @ sK2_SY67 @ sK3_SY71 )
!= sK2_SY67 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(155,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(156,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ ( relation_dom @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ ( relation_rng @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(157,plain,
! [SV1: $i] :
( ( ! [SY79: $i] :
( ~ ( in @ SV1 @ SY79 )
| ~ ( in @ SY79 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(158,plain,
! [SV2: $i] :
( ( ! [SY80: $i,SY81: $i] :
( ~ ( element @ SY81 @ ( powerset @ ( cartesian_product2 @ SV2 @ SY80 ) ) )
| ( relation @ SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(159,plain,
! [SV3: $i] :
( ( ! [SY82: $i] :
( ( unordered_pair @ SV3 @ SY82 )
= ( unordered_pair @ SY82 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(160,plain,
! [SV4: $i] :
( ( ! [SY83: $i] :
( ( ordered_pair @ SV4 @ SY83 )
= ( unordered_pair @ ( unordered_pair @ SV4 @ SY83 ) @ ( singleton @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(161,plain,
! [SV5: $i] :
( ( ! [SY84: $i,SY85: $i] :
( ~ ( relation_of2 @ SY85 @ SV5 @ SY84 )
| ( element @ ( relation_rng_as_subset @ SV5 @ SY84 @ SY85 ) @ ( powerset @ SY84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(162,plain,
! [SV6: $i] :
( ( ! [SY86: $i,SY87: $i] :
( ~ ( relation_of2_as_subset @ SY87 @ SV6 @ SY86 )
| ( element @ SY87 @ ( powerset @ ( cartesian_product2 @ SV6 @ SY86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(163,plain,
! [SV7: $i] :
( ( ! [SY88: $i] : ( relation_of2 @ ( sK11_C @ SY88 @ SV7 ) @ SV7 @ SY88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(164,plain,
! [SV8: $i] :
( ( element @ ( sK10_B @ SV8 ) @ SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(165,plain,
! [SV9: $i] :
( ( ! [SY89: $i] : ( relation_of2_as_subset @ ( sK9_C @ SY89 @ SV9 ) @ SV9 @ SY89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(166,plain,
! [SV10: $i] :
( ( ! [SY90: $i] :
~ ( empty @ ( ordered_pair @ SV10 @ SY90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(167,plain,
( ( empty @ sK7_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(168,plain,
! [SV11: $i] :
( ( ! [SY91: $i,SY92: $i] :
( ~ ( relation_of2 @ SY92 @ SV11 @ SY91 )
| ( ( relation_rng_as_subset @ SV11 @ SY91 @ SY92 )
= ( relation_rng @ SY92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(169,plain,
! [SV12: $i] :
( ( subset @ SV12 @ SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(170,plain,
! [SV13: $i] :
( ( ! [SY93: $i] :
( ~ ( in @ SV13 @ SY93 )
| ( element @ SV13 @ SY93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(171,plain,
! [SV14: $i] :
( ( ! [SY94: $i] :
( ~ ( element @ SV14 @ SY94 )
| ( empty @ SY94 )
| ( in @ SV14 @ SY94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(172,plain,
! [SV15: $i] :
( ( ! [SY95: $i,SY96: $i] :
( ~ ( element @ SY95 @ ( powerset @ SY96 ) )
| ~ ( in @ SV15 @ SY95 )
| ( element @ SV15 @ SY96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(173,plain,
! [SV16: $i] :
( ( ! [SY97: $i,SY98: $i] :
( ~ ( element @ SY97 @ ( powerset @ SY98 ) )
| ~ ( in @ SV16 @ SY97 )
| ~ ( empty @ SY98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(174,plain,
! [SV17: $i] :
( ( ~ ( empty @ SV17 )
| ( SV17 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(175,plain,
! [SV18: $i] :
( ( ! [SY99: $i] :
( ~ ( empty @ SY99 )
| ~ ( in @ SV18 @ SY99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(176,plain,
! [SV19: $i] :
( ( ! [SY100: $i] :
( ( SV19 = SY100 )
| ~ ( empty @ SV19 )
| ~ ( empty @ SY100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(177,plain,
! [SV20: $i] :
( ( ~ ( relation @ SV20 )
| ~ ( ~ ! [SY101: $i] :
( ~ ( ~ ( ! [SY102: $i] :
~ ( in @ ( ordered_pair @ SY102 @ ( sK13_C @ SY101 @ SV20 ) ) @ SV20 )
| ~ ( in @ ( sK13_C @ SY101 @ SV20 ) @ SY101 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SY101 @ SV20 ) @ ( sK13_C @ SY101 @ SV20 ) ) @ SV20 )
| ( in @ ( sK13_C @ SY101 @ SV20 ) @ SY101 ) ) )
| ( SY101
= ( relation_rng @ SV20 ) ) )
| ~ ! [SY103: $i] :
( ( SY103
!= ( relation_rng @ SV20 ) )
| ~ ( ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( in @ ( ordered_pair @ SY105 @ SY104 ) @ SV20 )
| ( in @ SY104 @ SY103 ) )
| ~ ! [SY106: $i] :
( ~ ( in @ SY106 @ SY103 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY106 @ SY103 @ SV20 ) @ SY106 ) @ SV20 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(178,plain,
! [SV21: $i] :
( ( ~ ( ~ ! [SY107: $i,SY108: $i] :
( ~ ( relation_of2 @ SY108 @ SV21 @ SY107 )
| ( relation_of2_as_subset @ SY108 @ SV21 @ SY107 ) )
| ~ ! [SY109: $i,SY110: $i] :
( ~ ( relation_of2_as_subset @ SY110 @ SV21 @ SY109 )
| ( relation_of2 @ SY110 @ SV21 @ SY109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(179,plain,
! [SV22: $i] :
( ( ! [SY111: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_C @ SY111 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK6_C @ SY111 @ SV22 ) @ SY111 ) )
| ~ ( ( in @ ( sK6_C @ SY111 @ SV22 ) @ SV22 )
| ( in @ ( sK6_C @ SY111 @ SV22 ) @ SY111 ) ) )
| ( SV22 = SY111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(180,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( ordered_pair @ ( sK4_SY75 @ SX0 ) @ SX0 ) @ sK3_SY71 )
| ~ ( in @ SX0 @ sK2_SY67 ) )
| ~ ( ( ( relation_rng_as_subset @ sK1_A @ sK2_SY67 @ sK3_SY71 )
!= sK2_SY67 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(181,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(182,plain,
! [SV23: $i] :
( ( ~ ( ~ ! [SY112: $i,SY113: $i] :
( ~ ( relation @ SY113 )
| ~ ( in @ ( ordered_pair @ SV23 @ SY112 ) @ SY113 )
| ( in @ SV23 @ ( relation_dom @ SY113 ) ) )
| ~ ! [SY114: $i,SY115: $i] :
( ~ ( relation @ SY115 )
| ~ ( in @ ( ordered_pair @ SV23 @ SY114 ) @ SY115 )
| ( in @ SY114 @ ( relation_rng @ SY115 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(183,plain,
! [SV24: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV24 )
| ~ ( in @ SV24 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(184,plain,
! [SV25: $i,SV2: $i] :
( ( ! [SY116: $i] :
( ~ ( element @ SY116 @ ( powerset @ ( cartesian_product2 @ SV2 @ SV25 ) ) )
| ( relation @ SY116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(185,plain,
! [SV26: $i,SV3: $i] :
( ( ( unordered_pair @ SV3 @ SV26 )
= ( unordered_pair @ SV26 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(186,plain,
! [SV27: $i,SV4: $i] :
( ( ( ordered_pair @ SV4 @ SV27 )
= ( unordered_pair @ ( unordered_pair @ SV4 @ SV27 ) @ ( singleton @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(187,plain,
! [SV28: $i,SV5: $i] :
( ( ! [SY117: $i] :
( ~ ( relation_of2 @ SY117 @ SV5 @ SV28 )
| ( element @ ( relation_rng_as_subset @ SV5 @ SV28 @ SY117 ) @ ( powerset @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(188,plain,
! [SV29: $i,SV6: $i] :
( ( ! [SY118: $i] :
( ~ ( relation_of2_as_subset @ SY118 @ SV6 @ SV29 )
| ( element @ SY118 @ ( powerset @ ( cartesian_product2 @ SV6 @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(189,plain,
! [SV7: $i,SV30: $i] :
( ( relation_of2 @ ( sK11_C @ SV30 @ SV7 ) @ SV7 @ SV30 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(190,plain,
! [SV9: $i,SV31: $i] :
( ( relation_of2_as_subset @ ( sK9_C @ SV31 @ SV9 ) @ SV9 @ SV31 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(191,plain,
! [SV32: $i,SV10: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV10 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(192,plain,
! [SV33: $i,SV11: $i] :
( ( ! [SY119: $i] :
( ~ ( relation_of2 @ SY119 @ SV11 @ SV33 )
| ( ( relation_rng_as_subset @ SV11 @ SV33 @ SY119 )
= ( relation_rng @ SY119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(193,plain,
! [SV34: $i,SV13: $i] :
( ( ~ ( in @ SV13 @ SV34 )
| ( element @ SV13 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(194,plain,
! [SV35: $i,SV14: $i] :
( ( ~ ( element @ SV14 @ SV35 )
| ( empty @ SV35 )
| ( in @ SV14 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(195,plain,
! [SV15: $i,SV36: $i] :
( ( ! [SY120: $i] :
( ~ ( element @ SV36 @ ( powerset @ SY120 ) )
| ~ ( in @ SV15 @ SV36 )
| ( element @ SV15 @ SY120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(196,plain,
! [SV16: $i,SV37: $i] :
( ( ! [SY121: $i] :
( ~ ( element @ SV37 @ ( powerset @ SY121 ) )
| ~ ( in @ SV16 @ SV37 )
| ~ ( empty @ SY121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(197,plain,
! [SV17: $i] :
( ( ( ~ ( empty @ SV17 ) )
= $true )
| ( ( SV17 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(198,plain,
! [SV18: $i,SV38: $i] :
( ( ~ ( empty @ SV38 )
| ~ ( in @ SV18 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(199,plain,
! [SV39: $i,SV19: $i] :
( ( ( SV19 = SV39 )
| ~ ( empty @ SV19 )
| ~ ( empty @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(200,plain,
! [SV20: $i] :
( ( ( ~ ( relation @ SV20 ) )
= $true )
| ( ( ~ ( ~ ! [SY101: $i] :
( ~ ( ~ ( ! [SY102: $i] :
~ ( in @ ( ordered_pair @ SY102 @ ( sK13_C @ SY101 @ SV20 ) ) @ SV20 )
| ~ ( in @ ( sK13_C @ SY101 @ SV20 ) @ SY101 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SY101 @ SV20 ) @ ( sK13_C @ SY101 @ SV20 ) ) @ SV20 )
| ( in @ ( sK13_C @ SY101 @ SV20 ) @ SY101 ) ) )
| ( SY101
= ( relation_rng @ SV20 ) ) )
| ~ ! [SY103: $i] :
( ( SY103
!= ( relation_rng @ SV20 ) )
| ~ ( ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( in @ ( ordered_pair @ SY105 @ SY104 ) @ SV20 )
| ( in @ SY104 @ SY103 ) )
| ~ ! [SY106: $i] :
( ~ ( in @ SY106 @ SY103 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY106 @ SY103 @ SV20 ) @ SY106 ) @ SV20 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(201,plain,
! [SV21: $i] :
( ( ~ ! [SY107: $i,SY108: $i] :
( ~ ( relation_of2 @ SY108 @ SV21 @ SY107 )
| ( relation_of2_as_subset @ SY108 @ SV21 @ SY107 ) )
| ~ ! [SY109: $i,SY110: $i] :
( ~ ( relation_of2_as_subset @ SY110 @ SV21 @ SY109 )
| ( relation_of2 @ SY110 @ SV21 @ SY109 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(202,plain,
! [SV22: $i,SV40: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV40 ) )
| ~ ( ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV22 )
| ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV40 ) ) )
| ( SV22 = SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(203,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( ordered_pair @ ( sK4_SY75 @ SX0 ) @ SX0 ) @ sK3_SY71 )
| ~ ( in @ SX0 @ sK2_SY67 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(204,plain,
( ( ~ ( ( ( relation_rng_as_subset @ sK1_A @ sK2_SY67 @ sK3_SY71 )
!= sK2_SY67 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(205,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(206,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(207,plain,
! [SV23: $i] :
( ( ~ ! [SY112: $i,SY113: $i] :
( ~ ( relation @ SY113 )
| ~ ( in @ ( ordered_pair @ SV23 @ SY112 ) @ SY113 )
| ( in @ SV23 @ ( relation_dom @ SY113 ) ) )
| ~ ! [SY114: $i,SY115: $i] :
( ~ ( relation @ SY115 )
| ~ ( in @ ( ordered_pair @ SV23 @ SY114 ) @ SY115 )
| ( in @ SY114 @ ( relation_rng @ SY115 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(208,plain,
! [SV24: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV24 ) )
= $true )
| ( ( ~ ( in @ SV24 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(209,plain,
! [SV25: $i,SV2: $i,SV41: $i] :
( ( ~ ( element @ SV41 @ ( powerset @ ( cartesian_product2 @ SV2 @ SV25 ) ) )
| ( relation @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(210,plain,
! [SV28: $i,SV5: $i,SV42: $i] :
( ( ~ ( relation_of2 @ SV42 @ SV5 @ SV28 )
| ( element @ ( relation_rng_as_subset @ SV5 @ SV28 @ SV42 ) @ ( powerset @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(211,plain,
! [SV29: $i,SV6: $i,SV43: $i] :
( ( ~ ( relation_of2_as_subset @ SV43 @ SV6 @ SV29 )
| ( element @ SV43 @ ( powerset @ ( cartesian_product2 @ SV6 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(212,plain,
! [SV32: $i,SV10: $i] :
( ( empty @ ( ordered_pair @ SV10 @ SV32 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(213,plain,
! [SV33: $i,SV11: $i,SV44: $i] :
( ( ~ ( relation_of2 @ SV44 @ SV11 @ SV33 )
| ( ( relation_rng_as_subset @ SV11 @ SV33 @ SV44 )
= ( relation_rng @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(214,plain,
! [SV34: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV34 ) )
= $true )
| ( ( element @ SV13 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(215,plain,
! [SV35: $i,SV14: $i] :
( ( ( ~ ( element @ SV14 @ SV35 ) )
= $true )
| ( ( ( empty @ SV35 )
| ( in @ SV14 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(216,plain,
! [SV15: $i,SV45: $i,SV36: $i] :
( ( ~ ( element @ SV36 @ ( powerset @ SV45 ) )
| ~ ( in @ SV15 @ SV36 )
| ( element @ SV15 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(217,plain,
! [SV16: $i,SV46: $i,SV37: $i] :
( ( ~ ( element @ SV37 @ ( powerset @ SV46 ) )
| ~ ( in @ SV16 @ SV37 )
| ~ ( empty @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(218,plain,
! [SV17: $i] :
( ( ( empty @ SV17 )
= $false )
| ( ( SV17 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(219,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ( empty @ SV38 ) )
= $true )
| ( ( ~ ( in @ SV18 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(220,plain,
! [SV39: $i,SV19: $i] :
( ( ( ( SV19 = SV39 )
| ~ ( empty @ SV19 ) )
= $true )
| ( ( ~ ( empty @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(221,plain,
! [SV20: $i] :
( ( ( relation @ SV20 )
= $false )
| ( ( ~ ( ~ ! [SY101: $i] :
( ~ ( ~ ( ! [SY102: $i] :
~ ( in @ ( ordered_pair @ SY102 @ ( sK13_C @ SY101 @ SV20 ) ) @ SV20 )
| ~ ( in @ ( sK13_C @ SY101 @ SV20 ) @ SY101 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SY101 @ SV20 ) @ ( sK13_C @ SY101 @ SV20 ) ) @ SV20 )
| ( in @ ( sK13_C @ SY101 @ SV20 ) @ SY101 ) ) )
| ( SY101
= ( relation_rng @ SV20 ) ) )
| ~ ! [SY103: $i] :
( ( SY103
!= ( relation_rng @ SV20 ) )
| ~ ( ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( in @ ( ordered_pair @ SY105 @ SY104 ) @ SV20 )
| ( in @ SY104 @ SY103 ) )
| ~ ! [SY106: $i] :
( ~ ( in @ SY106 @ SY103 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY106 @ SY103 @ SV20 ) @ SY106 ) @ SV20 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(222,plain,
! [SV21: $i] :
( ( ~ ! [SY107: $i,SY108: $i] :
( ~ ( relation_of2 @ SY108 @ SV21 @ SY107 )
| ( relation_of2_as_subset @ SY108 @ SV21 @ SY107 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(223,plain,
! [SV21: $i] :
( ( ~ ! [SY109: $i,SY110: $i] :
( ~ ( relation_of2_as_subset @ SY110 @ SV21 @ SY109 )
| ( relation_of2 @ SY110 @ SV21 @ SY109 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(224,plain,
! [SV22: $i,SV40: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV40 ) )
| ~ ( ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV22 )
| ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV40 ) ) ) )
= $true )
| ( ( SV22 = SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(225,plain,
( ( ! [SX0: $i] :
( ( in @ ( ordered_pair @ ( sK4_SY75 @ SX0 ) @ SX0 ) @ sK3_SY71 )
| ~ ( in @ SX0 @ sK2_SY67 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(226,plain,
( ( ( relation_rng_as_subset @ sK1_A @ sK2_SY67 @ sK3_SY71 )
!= sK2_SY67 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(227,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(228,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(229,plain,
! [SV23: $i] :
( ( ~ ! [SY112: $i,SY113: $i] :
( ~ ( relation @ SY113 )
| ~ ( in @ ( ordered_pair @ SV23 @ SY112 ) @ SY113 )
| ( in @ SV23 @ ( relation_dom @ SY113 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(230,plain,
! [SV23: $i] :
( ( ~ ! [SY114: $i,SY115: $i] :
( ~ ( relation @ SY115 )
| ~ ( in @ ( ordered_pair @ SV23 @ SY114 ) @ SY115 )
| ( in @ SY114 @ ( relation_rng @ SY115 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(231,plain,
! [SV24: $i,SV1: $i] :
( ( ( in @ SV1 @ SV24 )
= $false )
| ( ( ~ ( in @ SV24 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(232,plain,
! [SV25: $i,SV2: $i,SV41: $i] :
( ( ( ~ ( element @ SV41 @ ( powerset @ ( cartesian_product2 @ SV2 @ SV25 ) ) ) )
= $true )
| ( ( relation @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(233,plain,
! [SV28: $i,SV5: $i,SV42: $i] :
( ( ( ~ ( relation_of2 @ SV42 @ SV5 @ SV28 ) )
= $true )
| ( ( element @ ( relation_rng_as_subset @ SV5 @ SV28 @ SV42 ) @ ( powerset @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(234,plain,
! [SV29: $i,SV6: $i,SV43: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV43 @ SV6 @ SV29 ) )
= $true )
| ( ( element @ SV43 @ ( powerset @ ( cartesian_product2 @ SV6 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(235,plain,
! [SV33: $i,SV11: $i,SV44: $i] :
( ( ( ~ ( relation_of2 @ SV44 @ SV11 @ SV33 ) )
= $true )
| ( ( ( relation_rng_as_subset @ SV11 @ SV33 @ SV44 )
= ( relation_rng @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(236,plain,
! [SV34: $i,SV13: $i] :
( ( ( in @ SV13 @ SV34 )
= $false )
| ( ( element @ SV13 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(237,plain,
! [SV35: $i,SV14: $i] :
( ( ( element @ SV14 @ SV35 )
= $false )
| ( ( ( empty @ SV35 )
| ( in @ SV14 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(238,plain,
! [SV15: $i,SV45: $i,SV36: $i] :
( ( ( ~ ( element @ SV36 @ ( powerset @ SV45 ) )
| ~ ( in @ SV15 @ SV36 ) )
= $true )
| ( ( element @ SV15 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(239,plain,
! [SV16: $i,SV46: $i,SV37: $i] :
( ( ( ~ ( element @ SV37 @ ( powerset @ SV46 ) )
| ~ ( in @ SV16 @ SV37 ) )
= $true )
| ( ( ~ ( empty @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(240,plain,
! [SV18: $i,SV38: $i] :
( ( ( empty @ SV38 )
= $false )
| ( ( ~ ( in @ SV18 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(241,plain,
! [SV39: $i,SV19: $i] :
( ( ( SV19 = SV39 )
= $true )
| ( ( ~ ( empty @ SV19 ) )
= $true )
| ( ( ~ ( empty @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(242,plain,
! [SV20: $i] :
( ( ( ~ ! [SY101: $i] :
( ~ ( ~ ( ! [SY102: $i] :
~ ( in @ ( ordered_pair @ SY102 @ ( sK13_C @ SY101 @ SV20 ) ) @ SV20 )
| ~ ( in @ ( sK13_C @ SY101 @ SV20 ) @ SY101 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SY101 @ SV20 ) @ ( sK13_C @ SY101 @ SV20 ) ) @ SV20 )
| ( in @ ( sK13_C @ SY101 @ SV20 ) @ SY101 ) ) )
| ( SY101
= ( relation_rng @ SV20 ) ) )
| ~ ! [SY103: $i] :
( ( SY103
!= ( relation_rng @ SV20 ) )
| ~ ( ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( in @ ( ordered_pair @ SY105 @ SY104 ) @ SV20 )
| ( in @ SY104 @ SY103 ) )
| ~ ! [SY106: $i] :
( ~ ( in @ SY106 @ SY103 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY106 @ SY103 @ SV20 ) @ SY106 ) @ SV20 ) ) ) ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(243,plain,
! [SV21: $i] :
( ( ! [SY107: $i,SY108: $i] :
( ~ ( relation_of2 @ SY108 @ SV21 @ SY107 )
| ( relation_of2_as_subset @ SY108 @ SV21 @ SY107 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(244,plain,
! [SV21: $i] :
( ( ! [SY109: $i,SY110: $i] :
( ~ ( relation_of2_as_subset @ SY110 @ SV21 @ SY109 )
| ( relation_of2 @ SY110 @ SV21 @ SY109 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(245,plain,
! [SV22: $i,SV40: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV40 ) )
| ~ ( ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV22 )
| ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV40 ) ) )
= $false )
| ( ( SV22 = SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(246,plain,
! [SV47: $i] :
( ( ( in @ ( ordered_pair @ ( sK4_SY75 @ SV47 ) @ SV47 ) @ sK3_SY71 )
| ~ ( in @ SV47 @ sK2_SY67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(247,plain,
( ( ( relation_rng_as_subset @ sK1_A @ sK2_SY67 @ sK3_SY71 )
= sK2_SY67 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(248,plain,
! [SV48: $i] :
( ( ! [SY122: $i] :
( ~ ( element @ SV48 @ ( powerset @ SY122 ) )
| ( subset @ SV48 @ SY122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(249,plain,
! [SV49: $i] :
( ( ! [SY123: $i] :
( ~ ( subset @ SV49 @ SY123 )
| ( element @ SV49 @ ( powerset @ SY123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(250,plain,
! [SV23: $i] :
( ( ! [SY112: $i,SY113: $i] :
( ~ ( relation @ SY113 )
| ~ ( in @ ( ordered_pair @ SV23 @ SY112 ) @ SY113 )
| ( in @ SV23 @ ( relation_dom @ SY113 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(251,plain,
! [SV23: $i] :
( ( ! [SY114: $i,SY115: $i] :
( ~ ( relation @ SY115 )
| ~ ( in @ ( ordered_pair @ SV23 @ SY114 ) @ SY115 )
| ( in @ SY114 @ ( relation_rng @ SY115 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(252,plain,
! [SV1: $i,SV24: $i] :
( ( ( in @ SV24 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(253,plain,
! [SV25: $i,SV2: $i,SV41: $i] :
( ( ( element @ SV41 @ ( powerset @ ( cartesian_product2 @ SV2 @ SV25 ) ) )
= $false )
| ( ( relation @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(254,plain,
! [SV28: $i,SV5: $i,SV42: $i] :
( ( ( relation_of2 @ SV42 @ SV5 @ SV28 )
= $false )
| ( ( element @ ( relation_rng_as_subset @ SV5 @ SV28 @ SV42 ) @ ( powerset @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(255,plain,
! [SV29: $i,SV6: $i,SV43: $i] :
( ( ( relation_of2_as_subset @ SV43 @ SV6 @ SV29 )
= $false )
| ( ( element @ SV43 @ ( powerset @ ( cartesian_product2 @ SV6 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(256,plain,
! [SV33: $i,SV11: $i,SV44: $i] :
( ( ( relation_of2 @ SV44 @ SV11 @ SV33 )
= $false )
| ( ( ( relation_rng_as_subset @ SV11 @ SV33 @ SV44 )
= ( relation_rng @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(257,plain,
! [SV14: $i,SV35: $i] :
( ( ( empty @ SV35 )
= $true )
| ( ( in @ SV14 @ SV35 )
= $true )
| ( ( element @ SV14 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(258,plain,
! [SV15: $i,SV45: $i,SV36: $i] :
( ( ( ~ ( element @ SV36 @ ( powerset @ SV45 ) ) )
= $true )
| ( ( ~ ( in @ SV15 @ SV36 ) )
= $true )
| ( ( element @ SV15 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(259,plain,
! [SV16: $i,SV46: $i,SV37: $i] :
( ( ( ~ ( element @ SV37 @ ( powerset @ SV46 ) ) )
= $true )
| ( ( ~ ( in @ SV16 @ SV37 ) )
= $true )
| ( ( ~ ( empty @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(260,plain,
! [SV38: $i,SV18: $i] :
( ( ( in @ SV18 @ SV38 )
= $false )
| ( ( empty @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(261,plain,
! [SV39: $i,SV19: $i] :
( ( ( empty @ SV19 )
= $false )
| ( ( SV19 = SV39 )
= $true )
| ( ( ~ ( empty @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(262,plain,
! [SV20: $i] :
( ( ( ~ ! [SY101: $i] :
( ~ ( ~ ( ! [SY102: $i] :
~ ( in @ ( ordered_pair @ SY102 @ ( sK13_C @ SY101 @ SV20 ) ) @ SV20 )
| ~ ( in @ ( sK13_C @ SY101 @ SV20 ) @ SY101 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SY101 @ SV20 ) @ ( sK13_C @ SY101 @ SV20 ) ) @ SV20 )
| ( in @ ( sK13_C @ SY101 @ SV20 ) @ SY101 ) ) )
| ( SY101
= ( relation_rng @ SV20 ) ) ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(263,plain,
! [SV20: $i] :
( ( ( ~ ! [SY103: $i] :
( ( SY103
!= ( relation_rng @ SV20 ) )
| ~ ( ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( in @ ( ordered_pair @ SY105 @ SY104 ) @ SV20 )
| ( in @ SY104 @ SY103 ) )
| ~ ! [SY106: $i] :
( ~ ( in @ SY106 @ SY103 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY106 @ SY103 @ SV20 ) @ SY106 ) @ SV20 ) ) ) ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(264,plain,
! [SV50: $i,SV21: $i] :
( ( ! [SY124: $i] :
( ~ ( relation_of2 @ SY124 @ SV21 @ SV50 )
| ( relation_of2_as_subset @ SY124 @ SV21 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(265,plain,
! [SV51: $i,SV21: $i] :
( ( ! [SY125: $i] :
( ~ ( relation_of2_as_subset @ SY125 @ SV21 @ SV51 )
| ( relation_of2 @ SY125 @ SV21 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(266,plain,
! [SV22: $i,SV40: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV40 ) ) )
= $false )
| ( ( SV22 = SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[245]) ).
thf(267,plain,
! [SV22: $i,SV40: $i] :
( ( ( ~ ( ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV22 )
| ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV40 ) ) )
= $false )
| ( ( SV22 = SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[245]) ).
thf(268,plain,
! [SV47: $i] :
( ( ( in @ ( ordered_pair @ ( sK4_SY75 @ SV47 ) @ SV47 ) @ sK3_SY71 )
= $true )
| ( ( ~ ( in @ SV47 @ sK2_SY67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(269,plain,
! [SV52: $i,SV48: $i] :
( ( ~ ( element @ SV48 @ ( powerset @ SV52 ) )
| ( subset @ SV48 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(270,plain,
! [SV53: $i,SV49: $i] :
( ( ~ ( subset @ SV49 @ SV53 )
| ( element @ SV49 @ ( powerset @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(271,plain,
! [SV54: $i,SV23: $i] :
( ( ! [SY126: $i] :
( ~ ( relation @ SY126 )
| ~ ( in @ ( ordered_pair @ SV23 @ SV54 ) @ SY126 )
| ( in @ SV23 @ ( relation_dom @ SY126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(272,plain,
! [SV55: $i,SV23: $i] :
( ( ! [SY127: $i] :
( ~ ( relation @ SY127 )
| ~ ( in @ ( ordered_pair @ SV23 @ SV55 ) @ SY127 )
| ( in @ SV55 @ ( relation_rng @ SY127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(273,plain,
! [SV15: $i,SV45: $i,SV36: $i] :
( ( ( element @ SV36 @ ( powerset @ SV45 ) )
= $false )
| ( ( ~ ( in @ SV15 @ SV36 ) )
= $true )
| ( ( element @ SV15 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(274,plain,
! [SV16: $i,SV46: $i,SV37: $i] :
( ( ( element @ SV37 @ ( powerset @ SV46 ) )
= $false )
| ( ( ~ ( in @ SV16 @ SV37 ) )
= $true )
| ( ( ~ ( empty @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(275,plain,
! [SV19: $i,SV39: $i] :
( ( ( empty @ SV39 )
= $false )
| ( ( SV19 = SV39 )
= $true )
| ( ( empty @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(276,plain,
! [SV20: $i] :
( ( ( ! [SY101: $i] :
( ~ ( ~ ( ! [SY102: $i] :
~ ( in @ ( ordered_pair @ SY102 @ ( sK13_C @ SY101 @ SV20 ) ) @ SV20 )
| ~ ( in @ ( sK13_C @ SY101 @ SV20 ) @ SY101 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SY101 @ SV20 ) @ ( sK13_C @ SY101 @ SV20 ) ) @ SV20 )
| ( in @ ( sK13_C @ SY101 @ SV20 ) @ SY101 ) ) )
| ( SY101
= ( relation_rng @ SV20 ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(277,plain,
! [SV20: $i] :
( ( ( ! [SY103: $i] :
( ( SY103
!= ( relation_rng @ SV20 ) )
| ~ ( ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( in @ ( ordered_pair @ SY105 @ SY104 ) @ SV20 )
| ( in @ SY104 @ SY103 ) )
| ~ ! [SY106: $i] :
( ~ ( in @ SY106 @ SY103 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY106 @ SY103 @ SV20 ) @ SY106 ) @ SV20 ) ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(278,plain,
! [SV50: $i,SV21: $i,SV56: $i] :
( ( ~ ( relation_of2 @ SV56 @ SV21 @ SV50 )
| ( relation_of2_as_subset @ SV56 @ SV21 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(279,plain,
! [SV51: $i,SV21: $i,SV57: $i] :
( ( ~ ( relation_of2_as_subset @ SV57 @ SV21 @ SV51 )
| ( relation_of2 @ SV57 @ SV21 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(280,plain,
! [SV22: $i,SV40: $i] :
( ( ( ~ ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV40 ) )
= $true )
| ( ( SV22 = SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(281,plain,
! [SV22: $i,SV40: $i] :
( ( ( ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV22 )
| ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV40 ) )
= $true )
| ( ( SV22 = SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(282,plain,
! [SV47: $i] :
( ( ( in @ SV47 @ sK2_SY67 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK4_SY75 @ SV47 ) @ SV47 ) @ sK3_SY71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(283,plain,
! [SV52: $i,SV48: $i] :
( ( ( ~ ( element @ SV48 @ ( powerset @ SV52 ) ) )
= $true )
| ( ( subset @ SV48 @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(284,plain,
! [SV53: $i,SV49: $i] :
( ( ( ~ ( subset @ SV49 @ SV53 ) )
= $true )
| ( ( element @ SV49 @ ( powerset @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(285,plain,
! [SV54: $i,SV23: $i,SV58: $i] :
( ( ~ ( relation @ SV58 )
| ~ ( in @ ( ordered_pair @ SV23 @ SV54 ) @ SV58 )
| ( in @ SV23 @ ( relation_dom @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(286,plain,
! [SV55: $i,SV23: $i,SV59: $i] :
( ( ~ ( relation @ SV59 )
| ~ ( in @ ( ordered_pair @ SV23 @ SV55 ) @ SV59 )
| ( in @ SV55 @ ( relation_rng @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(287,plain,
! [SV45: $i,SV36: $i,SV15: $i] :
( ( ( in @ SV15 @ SV36 )
= $false )
| ( ( element @ SV36 @ ( powerset @ SV45 ) )
= $false )
| ( ( element @ SV15 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(288,plain,
! [SV46: $i,SV37: $i,SV16: $i] :
( ( ( in @ SV16 @ SV37 )
= $false )
| ( ( element @ SV37 @ ( powerset @ SV46 ) )
= $false )
| ( ( ~ ( empty @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(289,plain,
! [SV20: $i,SV60: $i] :
( ( ( ~ ( ~ ( ! [SY128: $i] :
~ ( in @ ( ordered_pair @ SY128 @ ( sK13_C @ SV60 @ SV20 ) ) @ SV20 )
| ~ ( in @ ( sK13_C @ SV60 @ SV20 ) @ SV60 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SV60 @ SV20 ) @ ( sK13_C @ SV60 @ SV20 ) ) @ SV20 )
| ( in @ ( sK13_C @ SV60 @ SV20 ) @ SV60 ) ) )
| ( SV60
= ( relation_rng @ SV20 ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(290,plain,
! [SV20: $i,SV61: $i] :
( ( ( ( SV61
!= ( relation_rng @ SV20 ) )
| ~ ( ~ ! [SY129: $i] :
( ! [SY105: $i] :
~ ( in @ ( ordered_pair @ SY105 @ SY129 ) @ SV20 )
| ( in @ SY129 @ SV61 ) )
| ~ ! [SY131: $i] :
( ~ ( in @ SY131 @ SV61 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY131 @ SV61 @ SV20 ) @ SY131 ) @ SV20 ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(291,plain,
! [SV50: $i,SV21: $i,SV56: $i] :
( ( ( ~ ( relation_of2 @ SV56 @ SV21 @ SV50 ) )
= $true )
| ( ( relation_of2_as_subset @ SV56 @ SV21 @ SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(292,plain,
! [SV51: $i,SV21: $i,SV57: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV57 @ SV21 @ SV51 ) )
= $true )
| ( ( relation_of2 @ SV57 @ SV21 @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(293,plain,
! [SV22: $i,SV40: $i] :
( ( ( ~ ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV22 ) )
= $true )
| ( ( ~ ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV40 ) )
= $true )
| ( ( SV22 = SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(294,plain,
! [SV22: $i,SV40: $i] :
( ( ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV22 )
= $true )
| ( ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV40 )
= $true )
| ( ( SV22 = SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(295,plain,
! [SV52: $i,SV48: $i] :
( ( ( element @ SV48 @ ( powerset @ SV52 ) )
= $false )
| ( ( subset @ SV48 @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(296,plain,
! [SV53: $i,SV49: $i] :
( ( ( subset @ SV49 @ SV53 )
= $false )
| ( ( element @ SV49 @ ( powerset @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(297,plain,
! [SV54: $i,SV23: $i,SV58: $i] :
( ( ( ~ ( relation @ SV58 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV23 @ SV54 ) @ SV58 )
| ( in @ SV23 @ ( relation_dom @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(298,plain,
! [SV55: $i,SV23: $i,SV59: $i] :
( ( ( ~ ( relation @ SV59 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV23 @ SV55 ) @ SV59 )
| ( in @ SV55 @ ( relation_rng @ SV59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(299,plain,
! [SV16: $i,SV37: $i,SV46: $i] :
( ( ( empty @ SV46 )
= $false )
| ( ( element @ SV37 @ ( powerset @ SV46 ) )
= $false )
| ( ( in @ SV16 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(300,plain,
! [SV20: $i,SV60: $i] :
( ( ( ~ ( ~ ( ! [SY128: $i] :
~ ( in @ ( ordered_pair @ SY128 @ ( sK13_C @ SV60 @ SV20 ) ) @ SV20 )
| ~ ( in @ ( sK13_C @ SV60 @ SV20 ) @ SV60 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SV60 @ SV20 ) @ ( sK13_C @ SV60 @ SV20 ) ) @ SV20 )
| ( in @ ( sK13_C @ SV60 @ SV20 ) @ SV60 ) ) ) )
= $true )
| ( ( SV60
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(301,plain,
! [SV20: $i,SV61: $i] :
( ( ( SV61
!= ( relation_rng @ SV20 ) )
= $true )
| ( ( ~ ( ~ ! [SY129: $i] :
( ! [SY105: $i] :
~ ( in @ ( ordered_pair @ SY105 @ SY129 ) @ SV20 )
| ( in @ SY129 @ SV61 ) )
| ~ ! [SY131: $i] :
( ~ ( in @ SY131 @ SV61 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY131 @ SV61 @ SV20 ) @ SY131 ) @ SV20 ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(302,plain,
! [SV50: $i,SV21: $i,SV56: $i] :
( ( ( relation_of2 @ SV56 @ SV21 @ SV50 )
= $false )
| ( ( relation_of2_as_subset @ SV56 @ SV21 @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(303,plain,
! [SV51: $i,SV21: $i,SV57: $i] :
( ( ( relation_of2_as_subset @ SV57 @ SV21 @ SV51 )
= $false )
| ( ( relation_of2 @ SV57 @ SV21 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(304,plain,
! [SV22: $i,SV40: $i] :
( ( ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV22 )
= $false )
| ( ( ~ ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV40 ) )
= $true )
| ( ( SV22 = SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(305,plain,
! [SV54: $i,SV23: $i,SV58: $i] :
( ( ( relation @ SV58 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV23 @ SV54 ) @ SV58 )
| ( in @ SV23 @ ( relation_dom @ SV58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(306,plain,
! [SV55: $i,SV23: $i,SV59: $i] :
( ( ( relation @ SV59 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV23 @ SV55 ) @ SV59 )
| ( in @ SV55 @ ( relation_rng @ SV59 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(307,plain,
! [SV20: $i,SV60: $i] :
( ( ( ~ ( ! [SY128: $i] :
~ ( in @ ( ordered_pair @ SY128 @ ( sK13_C @ SV60 @ SV20 ) ) @ SV20 )
| ~ ( in @ ( sK13_C @ SV60 @ SV20 ) @ SV60 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SV60 @ SV20 ) @ ( sK13_C @ SV60 @ SV20 ) ) @ SV20 )
| ( in @ ( sK13_C @ SV60 @ SV20 ) @ SV60 ) ) )
= $false )
| ( ( SV60
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(308,plain,
! [SV20: $i,SV61: $i] :
( ( ( SV61
= ( relation_rng @ SV20 ) )
= $false )
| ( ( ~ ( ~ ! [SY129: $i] :
( ! [SY105: $i] :
~ ( in @ ( ordered_pair @ SY105 @ SY129 ) @ SV20 )
| ( in @ SY129 @ SV61 ) )
| ~ ! [SY131: $i] :
( ~ ( in @ SY131 @ SV61 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY131 @ SV61 @ SV20 ) @ SY131 ) @ SV20 ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(309,plain,
! [SV22: $i,SV40: $i] :
( ( ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV40 )
= $false )
| ( ( in @ ( sK6_C @ SV40 @ SV22 ) @ SV22 )
= $false )
| ( ( SV22 = SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(310,plain,
! [SV58: $i,SV54: $i,SV23: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV23 @ SV54 ) @ SV58 ) )
= $true )
| ( ( in @ SV23 @ ( relation_dom @ SV58 ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(311,plain,
! [SV59: $i,SV55: $i,SV23: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV23 @ SV55 ) @ SV59 ) )
= $true )
| ( ( in @ SV55 @ ( relation_rng @ SV59 ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(312,plain,
! [SV20: $i,SV60: $i] :
( ( ( ~ ( ! [SY128: $i] :
~ ( in @ ( ordered_pair @ SY128 @ ( sK13_C @ SV60 @ SV20 ) ) @ SV20 )
| ~ ( in @ ( sK13_C @ SV60 @ SV20 ) @ SV60 ) ) )
= $false )
| ( ( SV60
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(313,plain,
! [SV20: $i,SV60: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SV60 @ SV20 ) @ ( sK13_C @ SV60 @ SV20 ) ) @ SV20 )
| ( in @ ( sK13_C @ SV60 @ SV20 ) @ SV60 ) ) )
= $false )
| ( ( SV60
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(314,plain,
! [SV61: $i,SV20: $i] :
( ( ( ~ ! [SY129: $i] :
( ! [SY105: $i] :
~ ( in @ ( ordered_pair @ SY105 @ SY129 ) @ SV20 )
| ( in @ SY129 @ SV61 ) )
| ~ ! [SY131: $i] :
( ~ ( in @ SY131 @ SV61 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY131 @ SV61 @ SV20 ) @ SY131 ) @ SV20 ) ) )
= $false )
| ( ( SV61
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(315,plain,
! [SV58: $i,SV54: $i,SV23: $i] :
( ( ( in @ ( ordered_pair @ SV23 @ SV54 ) @ SV58 )
= $false )
| ( ( in @ SV23 @ ( relation_dom @ SV58 ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(316,plain,
! [SV59: $i,SV55: $i,SV23: $i] :
( ( ( in @ ( ordered_pair @ SV23 @ SV55 ) @ SV59 )
= $false )
| ( ( in @ SV55 @ ( relation_rng @ SV59 ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(317,plain,
! [SV20: $i,SV60: $i] :
( ( ( ! [SY128: $i] :
~ ( in @ ( ordered_pair @ SY128 @ ( sK13_C @ SV60 @ SV20 ) ) @ SV20 )
| ~ ( in @ ( sK13_C @ SV60 @ SV20 ) @ SV60 ) )
= $true )
| ( ( SV60
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(318,plain,
! [SV20: $i,SV60: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SV60 @ SV20 ) @ ( sK13_C @ SV60 @ SV20 ) ) @ SV20 )
| ( in @ ( sK13_C @ SV60 @ SV20 ) @ SV60 ) )
= $true )
| ( ( SV60
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(319,plain,
! [SV61: $i,SV20: $i] :
( ( ( ~ ! [SY129: $i] :
( ! [SY105: $i] :
~ ( in @ ( ordered_pair @ SY105 @ SY129 ) @ SV20 )
| ( in @ SY129 @ SV61 ) ) )
= $false )
| ( ( SV61
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[314]) ).
thf(320,plain,
! [SV20: $i,SV61: $i] :
( ( ( ~ ! [SY131: $i] :
( ~ ( in @ SY131 @ SV61 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY131 @ SV61 @ SV20 ) @ SY131 ) @ SV20 ) ) )
= $false )
| ( ( SV61
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[314]) ).
thf(321,plain,
! [SV20: $i,SV60: $i] :
( ( ( ! [SY128: $i] :
~ ( in @ ( ordered_pair @ SY128 @ ( sK13_C @ SV60 @ SV20 ) ) @ SV20 ) )
= $true )
| ( ( ~ ( in @ ( sK13_C @ SV60 @ SV20 ) @ SV60 ) )
= $true )
| ( ( SV60
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(322,plain,
! [SV20: $i,SV60: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SV60 @ SV20 ) @ ( sK13_C @ SV60 @ SV20 ) ) @ SV20 )
= $true )
| ( ( in @ ( sK13_C @ SV60 @ SV20 ) @ SV60 )
= $true )
| ( ( SV60
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(323,plain,
! [SV61: $i,SV20: $i] :
( ( ( ! [SY129: $i] :
( ! [SY105: $i] :
~ ( in @ ( ordered_pair @ SY105 @ SY129 ) @ SV20 )
| ( in @ SY129 @ SV61 ) ) )
= $true )
| ( ( SV61
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[319]) ).
thf(324,plain,
! [SV20: $i,SV61: $i] :
( ( ( ! [SY131: $i] :
( ~ ( in @ SY131 @ SV61 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY131 @ SV61 @ SV20 ) @ SY131 ) @ SV20 ) ) )
= $true )
| ( ( SV61
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(325,plain,
! [SV20: $i,SV60: $i,SV62: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV62 @ ( sK13_C @ SV60 @ SV20 ) ) @ SV20 ) )
= $true )
| ( ( ~ ( in @ ( sK13_C @ SV60 @ SV20 ) @ SV60 ) )
= $true )
| ( ( SV60
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(326,plain,
! [SV61: $i,SV20: $i,SV63: $i] :
( ( ( ! [SY132: $i] :
~ ( in @ ( ordered_pair @ SY132 @ SV63 ) @ SV20 )
| ( in @ SV63 @ SV61 ) )
= $true )
| ( ( SV61
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(327,plain,
! [SV20: $i,SV61: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ SV61 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV64 @ SV61 @ SV20 ) @ SV64 ) @ SV20 ) )
= $true )
| ( ( SV61
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(328,plain,
! [SV20: $i,SV60: $i,SV62: $i] :
( ( ( in @ ( ordered_pair @ SV62 @ ( sK13_C @ SV60 @ SV20 ) ) @ SV20 )
= $false )
| ( ( ~ ( in @ ( sK13_C @ SV60 @ SV20 ) @ SV60 ) )
= $true )
| ( ( SV60
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(329,plain,
! [SV61: $i,SV20: $i,SV63: $i] :
( ( ( ! [SY132: $i] :
~ ( in @ ( ordered_pair @ SY132 @ SV63 ) @ SV20 ) )
= $true )
| ( ( in @ SV63 @ SV61 )
= $true )
| ( ( SV61
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(330,plain,
! [SV20: $i,SV61: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ SV61 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK12_D @ SV64 @ SV61 @ SV20 ) @ SV64 ) @ SV20 )
= $true )
| ( ( SV61
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(331,plain,
! [SV62: $i,SV20: $i,SV60: $i] :
( ( ( in @ ( sK13_C @ SV60 @ SV20 ) @ SV60 )
= $false )
| ( ( in @ ( ordered_pair @ SV62 @ ( sK13_C @ SV60 @ SV20 ) ) @ SV20 )
= $false )
| ( ( SV60
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(332,plain,
! [SV61: $i,SV20: $i,SV63: $i,SV65: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV65 @ SV63 ) @ SV20 ) )
= $true )
| ( ( in @ SV63 @ SV61 )
= $true )
| ( ( SV61
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(333,plain,
! [SV20: $i,SV61: $i,SV64: $i] :
( ( ( in @ SV64 @ SV61 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK12_D @ SV64 @ SV61 @ SV20 ) @ SV64 ) @ SV20 )
= $true )
| ( ( SV61
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(334,plain,
! [SV61: $i,SV20: $i,SV63: $i,SV65: $i] :
( ( ( in @ ( ordered_pair @ SV65 @ SV63 ) @ SV20 )
= $false )
| ( ( in @ SV63 @ SV61 )
= $true )
| ( ( SV61
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(335,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[117,334,333,331,322,316,315,309,303,302,299,296,295,294,287,282,275,260,257,256,255,254,253,252,247,236,218,212,190,189,186,185,169,167,164,149,134,132,127,126,124,123,122,121,120,119,118]) ).
thf(336,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(337,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(338,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(339,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY77: $i] :
~ ( in @ ( ordered_pair @ SY77 @ ( sK13_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK13_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK14_SY78 @ B @ A ) @ ( sK13_C @ B @ A ) ) @ A )
| ( in @ ( sK13_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ ( sK12_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(340,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(341,plain,
$true = $true,
inference(copy,[status(thm)],[72]) ).
thf(342,plain,
$true = $true,
inference(copy,[status(thm)],[71]) ).
thf(343,plain,
$true = $true,
inference(copy,[status(thm)],[70]) ).
thf(344,plain,
$true = $true,
inference(copy,[status(thm)],[69]) ).
thf(345,plain,
$true = $true,
inference(copy,[status(thm)],[68]) ).
thf(346,plain,
$true = $true,
inference(copy,[status(thm)],[67]) ).
thf(347,plain,
$true = $true,
inference(copy,[status(thm)],[66]) ).
thf(348,plain,
$true = $true,
inference(copy,[status(thm)],[65]) ).
thf(349,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( element @ ( relation_rng_as_subset @ A @ B @ C ) @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(350,plain,
$true = $true,
inference(copy,[status(thm)],[63]) ).
thf(351,plain,
$true = $true,
inference(copy,[status(thm)],[62]) ).
thf(352,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(353,plain,
( ( ! [A: $i,B: $i] : ( relation_of2 @ ( sK11_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(354,plain,
( ( ! [A: $i] : ( element @ ( sK10_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(355,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK9_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(356,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(357,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(358,plain,
( ( empty @ sK8_A )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(359,plain,
( ( ~ ( empty @ sK7_A ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(360,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( ( relation_rng_as_subset @ A @ B @ C )
= ( relation_rng @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(361,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(362,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(363,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(364,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_dom @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_rng @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(365,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(366,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK6_C @ B @ A ) @ A )
| ~ ( in @ ( sK6_C @ B @ A ) @ B ) )
& ( ( in @ ( sK6_C @ B @ A ) @ A )
| ( in @ ( sK6_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(367,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(368,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(369,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(370,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(371,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(372,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(373,plain,
( ( relation_of2_as_subset @ sK3_SY71 @ sK1_A @ sK2_SY67 )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(374,plain,
( ( ( ( relation_rng_as_subset @ sK1_A @ sK2_SY67 @ sK3_SY71 )
= sK2_SY67 )
& ! [SY76: $i] :
~ ( in @ ( ordered_pair @ SY76 @ sK5_SY74 ) @ sK3_SY71 )
& ( in @ sK5_SY74 @ sK2_SY67 ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(375,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(376,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( relation_of2 @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(377,plain,
( ( ~ ( ( ( relation_rng_as_subset @ sK1_A @ sK2_SY67 @ sK3_SY71 )
!= sK2_SY67 )
| ~ ~ ( ~ ! [SX0: $i] :
~ ( in @ ( ordered_pair @ SX0 @ sK5_SY74 ) @ sK3_SY71 )
| ~ ( in @ sK5_SY74 @ sK2_SY67 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(378,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ SX2 @ ( sK13_C @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SX1 @ SX0 ) @ ( sK13_C @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_rng @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(379,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(380,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ ( relation_dom @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ ( relation_rng @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(381,plain,
! [SV66: $i] :
( ( ! [SY133: $i] :
( ~ ( in @ SV66 @ SY133 )
| ~ ( in @ SY133 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(382,plain,
! [SV67: $i] :
( ( ! [SY134: $i,SY135: $i] :
( ~ ( element @ SY135 @ ( powerset @ ( cartesian_product2 @ SV67 @ SY134 ) ) )
| ( relation @ SY135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(383,plain,
! [SV68: $i] :
( ( ! [SY136: $i] :
( ( unordered_pair @ SV68 @ SY136 )
= ( unordered_pair @ SY136 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(384,plain,
! [SV69: $i] :
( ( ! [SY137: $i] :
( ( ordered_pair @ SV69 @ SY137 )
= ( unordered_pair @ ( unordered_pair @ SV69 @ SY137 ) @ ( singleton @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(385,plain,
! [SV70: $i] :
( ( ! [SY138: $i,SY139: $i] :
( ~ ( relation_of2 @ SY139 @ SV70 @ SY138 )
| ( element @ ( relation_rng_as_subset @ SV70 @ SY138 @ SY139 ) @ ( powerset @ SY138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(386,plain,
! [SV71: $i] :
( ( ! [SY140: $i,SY141: $i] :
( ~ ( relation_of2_as_subset @ SY141 @ SV71 @ SY140 )
| ( element @ SY141 @ ( powerset @ ( cartesian_product2 @ SV71 @ SY140 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(387,plain,
! [SV72: $i] :
( ( ! [SY142: $i] : ( relation_of2 @ ( sK11_C @ SY142 @ SV72 ) @ SV72 @ SY142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(388,plain,
! [SV73: $i] :
( ( element @ ( sK10_B @ SV73 ) @ SV73 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(389,plain,
! [SV74: $i] :
( ( ! [SY143: $i] : ( relation_of2_as_subset @ ( sK9_C @ SY143 @ SV74 ) @ SV74 @ SY143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(390,plain,
! [SV75: $i] :
( ( ! [SY144: $i] :
~ ( empty @ ( ordered_pair @ SV75 @ SY144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(391,plain,
( ( empty @ sK7_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(392,plain,
! [SV76: $i] :
( ( ! [SY145: $i,SY146: $i] :
( ~ ( relation_of2 @ SY146 @ SV76 @ SY145 )
| ( ( relation_rng_as_subset @ SV76 @ SY145 @ SY146 )
= ( relation_rng @ SY146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(393,plain,
! [SV77: $i] :
( ( subset @ SV77 @ SV77 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(394,plain,
! [SV78: $i] :
( ( ! [SY147: $i] :
( ~ ( in @ SV78 @ SY147 )
| ( element @ SV78 @ SY147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(395,plain,
! [SV79: $i] :
( ( ! [SY148: $i] :
( ~ ( element @ SV79 @ SY148 )
| ( empty @ SY148 )
| ( in @ SV79 @ SY148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(396,plain,
! [SV80: $i] :
( ( ! [SY149: $i,SY150: $i] :
( ~ ( element @ SY149 @ ( powerset @ SY150 ) )
| ~ ( in @ SV80 @ SY149 )
| ( element @ SV80 @ SY150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(397,plain,
! [SV81: $i] :
( ( ! [SY151: $i,SY152: $i] :
( ~ ( element @ SY151 @ ( powerset @ SY152 ) )
| ~ ( in @ SV81 @ SY151 )
| ~ ( empty @ SY152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(398,plain,
! [SV82: $i] :
( ( ~ ( empty @ SV82 )
| ( SV82 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(399,plain,
! [SV83: $i] :
( ( ! [SY153: $i] :
( ~ ( empty @ SY153 )
| ~ ( in @ SV83 @ SY153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(400,plain,
! [SV84: $i] :
( ( ! [SY154: $i] :
( ( SV84 = SY154 )
| ~ ( empty @ SV84 )
| ~ ( empty @ SY154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(401,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(402,plain,
! [SV85: $i] :
( ( ~ ( ~ ! [SY155: $i,SY156: $i] :
( ~ ( relation_of2 @ SY156 @ SV85 @ SY155 )
| ( relation_of2_as_subset @ SY156 @ SV85 @ SY155 ) )
| ~ ! [SY157: $i,SY158: $i] :
( ~ ( relation_of2_as_subset @ SY158 @ SV85 @ SY157 )
| ( relation_of2 @ SY158 @ SV85 @ SY157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(403,plain,
( ( ( ( relation_rng_as_subset @ sK1_A @ sK2_SY67 @ sK3_SY71 )
!= sK2_SY67 )
| ~ ~ ( ~ ! [SX0: $i] :
~ ( in @ ( ordered_pair @ SX0 @ sK5_SY74 ) @ sK3_SY71 )
| ~ ( in @ sK5_SY74 @ sK2_SY67 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(404,plain,
! [SV86: $i] :
( ( ~ ( relation @ SV86 )
| ~ ( ~ ! [SY159: $i] :
( ~ ( ~ ( ! [SY160: $i] :
~ ( in @ ( ordered_pair @ SY160 @ ( sK13_C @ SY159 @ SV86 ) ) @ SV86 )
| ~ ( in @ ( sK13_C @ SY159 @ SV86 ) @ SY159 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SY159 @ SV86 ) @ ( sK13_C @ SY159 @ SV86 ) ) @ SV86 )
| ( in @ ( sK13_C @ SY159 @ SV86 ) @ SY159 ) ) )
| ( SY159
= ( relation_rng @ SV86 ) ) )
| ~ ! [SY161: $i] :
( ( SY161
!= ( relation_rng @ SV86 ) )
| ~ ( ~ ! [SY162: $i] :
( ! [SY163: $i] :
~ ( in @ ( ordered_pair @ SY163 @ SY162 ) @ SV86 )
| ( in @ SY162 @ SY161 ) )
| ~ ! [SY164: $i] :
( ~ ( in @ SY164 @ SY161 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY164 @ SY161 @ SV86 ) @ SY164 ) @ SV86 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(405,plain,
! [SV87: $i] :
( ( ! [SY165: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_C @ SY165 @ SV87 ) @ SV87 )
| ~ ( in @ ( sK6_C @ SY165 @ SV87 ) @ SY165 ) )
| ~ ( ( in @ ( sK6_C @ SY165 @ SV87 ) @ SV87 )
| ( in @ ( sK6_C @ SY165 @ SV87 ) @ SY165 ) ) )
| ( SV87 = SY165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(406,plain,
! [SV88: $i] :
( ( ~ ( ~ ! [SY166: $i,SY167: $i] :
( ~ ( relation @ SY167 )
| ~ ( in @ ( ordered_pair @ SV88 @ SY166 ) @ SY167 )
| ( in @ SV88 @ ( relation_dom @ SY167 ) ) )
| ~ ! [SY168: $i,SY169: $i] :
( ~ ( relation @ SY169 )
| ~ ( in @ ( ordered_pair @ SV88 @ SY168 ) @ SY169 )
| ( in @ SY168 @ ( relation_rng @ SY169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(407,plain,
! [SV89: $i,SV66: $i] :
( ( ~ ( in @ SV66 @ SV89 )
| ~ ( in @ SV89 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(408,plain,
! [SV90: $i,SV67: $i] :
( ( ! [SY170: $i] :
( ~ ( element @ SY170 @ ( powerset @ ( cartesian_product2 @ SV67 @ SV90 ) ) )
| ( relation @ SY170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(409,plain,
! [SV91: $i,SV68: $i] :
( ( ( unordered_pair @ SV68 @ SV91 )
= ( unordered_pair @ SV91 @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(410,plain,
! [SV92: $i,SV69: $i] :
( ( ( ordered_pair @ SV69 @ SV92 )
= ( unordered_pair @ ( unordered_pair @ SV69 @ SV92 ) @ ( singleton @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(411,plain,
! [SV93: $i,SV70: $i] :
( ( ! [SY171: $i] :
( ~ ( relation_of2 @ SY171 @ SV70 @ SV93 )
| ( element @ ( relation_rng_as_subset @ SV70 @ SV93 @ SY171 ) @ ( powerset @ SV93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(412,plain,
! [SV94: $i,SV71: $i] :
( ( ! [SY172: $i] :
( ~ ( relation_of2_as_subset @ SY172 @ SV71 @ SV94 )
| ( element @ SY172 @ ( powerset @ ( cartesian_product2 @ SV71 @ SV94 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(413,plain,
! [SV72: $i,SV95: $i] :
( ( relation_of2 @ ( sK11_C @ SV95 @ SV72 ) @ SV72 @ SV95 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(414,plain,
! [SV74: $i,SV96: $i] :
( ( relation_of2_as_subset @ ( sK9_C @ SV96 @ SV74 ) @ SV74 @ SV96 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(415,plain,
! [SV97: $i,SV75: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV75 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(416,plain,
! [SV98: $i,SV76: $i] :
( ( ! [SY173: $i] :
( ~ ( relation_of2 @ SY173 @ SV76 @ SV98 )
| ( ( relation_rng_as_subset @ SV76 @ SV98 @ SY173 )
= ( relation_rng @ SY173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(417,plain,
! [SV99: $i,SV78: $i] :
( ( ~ ( in @ SV78 @ SV99 )
| ( element @ SV78 @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(418,plain,
! [SV100: $i,SV79: $i] :
( ( ~ ( element @ SV79 @ SV100 )
| ( empty @ SV100 )
| ( in @ SV79 @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(419,plain,
! [SV80: $i,SV101: $i] :
( ( ! [SY174: $i] :
( ~ ( element @ SV101 @ ( powerset @ SY174 ) )
| ~ ( in @ SV80 @ SV101 )
| ( element @ SV80 @ SY174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(420,plain,
! [SV81: $i,SV102: $i] :
( ( ! [SY175: $i] :
( ~ ( element @ SV102 @ ( powerset @ SY175 ) )
| ~ ( in @ SV81 @ SV102 )
| ~ ( empty @ SY175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(421,plain,
! [SV82: $i] :
( ( ( ~ ( empty @ SV82 ) )
= $true )
| ( ( SV82 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[398]) ).
thf(422,plain,
! [SV83: $i,SV103: $i] :
( ( ~ ( empty @ SV103 )
| ~ ( in @ SV83 @ SV103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(423,plain,
! [SV104: $i,SV84: $i] :
( ( ( SV84 = SV104 )
| ~ ( empty @ SV84 )
| ~ ( empty @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(424,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[401]) ).
thf(425,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[401]) ).
thf(426,plain,
! [SV85: $i] :
( ( ~ ! [SY155: $i,SY156: $i] :
( ~ ( relation_of2 @ SY156 @ SV85 @ SY155 )
| ( relation_of2_as_subset @ SY156 @ SV85 @ SY155 ) )
| ~ ! [SY157: $i,SY158: $i] :
( ~ ( relation_of2_as_subset @ SY158 @ SV85 @ SY157 )
| ( relation_of2 @ SY158 @ SV85 @ SY157 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(427,plain,
( ( ( relation_rng_as_subset @ sK1_A @ sK2_SY67 @ sK3_SY71 )
!= sK2_SY67 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(428,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
~ ( in @ ( ordered_pair @ SX0 @ sK5_SY74 ) @ sK3_SY71 )
| ~ ( in @ sK5_SY74 @ sK2_SY67 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(429,plain,
! [SV86: $i] :
( ( ( ~ ( relation @ SV86 ) )
= $true )
| ( ( ~ ( ~ ! [SY159: $i] :
( ~ ( ~ ( ! [SY160: $i] :
~ ( in @ ( ordered_pair @ SY160 @ ( sK13_C @ SY159 @ SV86 ) ) @ SV86 )
| ~ ( in @ ( sK13_C @ SY159 @ SV86 ) @ SY159 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SY159 @ SV86 ) @ ( sK13_C @ SY159 @ SV86 ) ) @ SV86 )
| ( in @ ( sK13_C @ SY159 @ SV86 ) @ SY159 ) ) )
| ( SY159
= ( relation_rng @ SV86 ) ) )
| ~ ! [SY161: $i] :
( ( SY161
!= ( relation_rng @ SV86 ) )
| ~ ( ~ ! [SY162: $i] :
( ! [SY163: $i] :
~ ( in @ ( ordered_pair @ SY163 @ SY162 ) @ SV86 )
| ( in @ SY162 @ SY161 ) )
| ~ ! [SY164: $i] :
( ~ ( in @ SY164 @ SY161 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY164 @ SY161 @ SV86 ) @ SY164 ) @ SV86 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(430,plain,
! [SV87: $i,SV105: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV87 )
| ~ ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV105 ) )
| ~ ( ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV87 )
| ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV105 ) ) )
| ( SV87 = SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(431,plain,
! [SV88: $i] :
( ( ~ ! [SY166: $i,SY167: $i] :
( ~ ( relation @ SY167 )
| ~ ( in @ ( ordered_pair @ SV88 @ SY166 ) @ SY167 )
| ( in @ SV88 @ ( relation_dom @ SY167 ) ) )
| ~ ! [SY168: $i,SY169: $i] :
( ~ ( relation @ SY169 )
| ~ ( in @ ( ordered_pair @ SV88 @ SY168 ) @ SY169 )
| ( in @ SY168 @ ( relation_rng @ SY169 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(432,plain,
! [SV89: $i,SV66: $i] :
( ( ( ~ ( in @ SV66 @ SV89 ) )
= $true )
| ( ( ~ ( in @ SV89 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(433,plain,
! [SV90: $i,SV67: $i,SV106: $i] :
( ( ~ ( element @ SV106 @ ( powerset @ ( cartesian_product2 @ SV67 @ SV90 ) ) )
| ( relation @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(434,plain,
! [SV93: $i,SV70: $i,SV107: $i] :
( ( ~ ( relation_of2 @ SV107 @ SV70 @ SV93 )
| ( element @ ( relation_rng_as_subset @ SV70 @ SV93 @ SV107 ) @ ( powerset @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(435,plain,
! [SV94: $i,SV71: $i,SV108: $i] :
( ( ~ ( relation_of2_as_subset @ SV108 @ SV71 @ SV94 )
| ( element @ SV108 @ ( powerset @ ( cartesian_product2 @ SV71 @ SV94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(436,plain,
! [SV97: $i,SV75: $i] :
( ( empty @ ( ordered_pair @ SV75 @ SV97 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(437,plain,
! [SV98: $i,SV76: $i,SV109: $i] :
( ( ~ ( relation_of2 @ SV109 @ SV76 @ SV98 )
| ( ( relation_rng_as_subset @ SV76 @ SV98 @ SV109 )
= ( relation_rng @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(438,plain,
! [SV99: $i,SV78: $i] :
( ( ( ~ ( in @ SV78 @ SV99 ) )
= $true )
| ( ( element @ SV78 @ SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(439,plain,
! [SV100: $i,SV79: $i] :
( ( ( ~ ( element @ SV79 @ SV100 ) )
= $true )
| ( ( ( empty @ SV100 )
| ( in @ SV79 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(440,plain,
! [SV80: $i,SV110: $i,SV101: $i] :
( ( ~ ( element @ SV101 @ ( powerset @ SV110 ) )
| ~ ( in @ SV80 @ SV101 )
| ( element @ SV80 @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(441,plain,
! [SV81: $i,SV111: $i,SV102: $i] :
( ( ~ ( element @ SV102 @ ( powerset @ SV111 ) )
| ~ ( in @ SV81 @ SV102 )
| ~ ( empty @ SV111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(442,plain,
! [SV82: $i] :
( ( ( empty @ SV82 )
= $false )
| ( ( SV82 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(443,plain,
! [SV83: $i,SV103: $i] :
( ( ( ~ ( empty @ SV103 ) )
= $true )
| ( ( ~ ( in @ SV83 @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(444,plain,
! [SV104: $i,SV84: $i] :
( ( ( ( SV84 = SV104 )
| ~ ( empty @ SV84 ) )
= $true )
| ( ( ~ ( empty @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(445,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[424]) ).
thf(446,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[425]) ).
thf(447,plain,
! [SV85: $i] :
( ( ~ ! [SY155: $i,SY156: $i] :
( ~ ( relation_of2 @ SY156 @ SV85 @ SY155 )
| ( relation_of2_as_subset @ SY156 @ SV85 @ SY155 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[426]) ).
thf(448,plain,
! [SV85: $i] :
( ( ~ ! [SY157: $i,SY158: $i] :
( ~ ( relation_of2_as_subset @ SY158 @ SV85 @ SY157 )
| ( relation_of2 @ SY158 @ SV85 @ SY157 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[426]) ).
thf(449,plain,
( ( ( relation_rng_as_subset @ sK1_A @ sK2_SY67 @ sK3_SY71 )
= sK2_SY67 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(450,plain,
( ( ~ ( ~ ! [SX0: $i] :
~ ( in @ ( ordered_pair @ SX0 @ sK5_SY74 ) @ sK3_SY71 )
| ~ ( in @ sK5_SY74 @ sK2_SY67 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(451,plain,
! [SV86: $i] :
( ( ( relation @ SV86 )
= $false )
| ( ( ~ ( ~ ! [SY159: $i] :
( ~ ( ~ ( ! [SY160: $i] :
~ ( in @ ( ordered_pair @ SY160 @ ( sK13_C @ SY159 @ SV86 ) ) @ SV86 )
| ~ ( in @ ( sK13_C @ SY159 @ SV86 ) @ SY159 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SY159 @ SV86 ) @ ( sK13_C @ SY159 @ SV86 ) ) @ SV86 )
| ( in @ ( sK13_C @ SY159 @ SV86 ) @ SY159 ) ) )
| ( SY159
= ( relation_rng @ SV86 ) ) )
| ~ ! [SY161: $i] :
( ( SY161
!= ( relation_rng @ SV86 ) )
| ~ ( ~ ! [SY162: $i] :
( ! [SY163: $i] :
~ ( in @ ( ordered_pair @ SY163 @ SY162 ) @ SV86 )
| ( in @ SY162 @ SY161 ) )
| ~ ! [SY164: $i] :
( ~ ( in @ SY164 @ SY161 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY164 @ SY161 @ SV86 ) @ SY164 ) @ SV86 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(452,plain,
! [SV87: $i,SV105: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV87 )
| ~ ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV105 ) )
| ~ ( ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV87 )
| ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV105 ) ) ) )
= $true )
| ( ( SV87 = SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(453,plain,
! [SV88: $i] :
( ( ~ ! [SY166: $i,SY167: $i] :
( ~ ( relation @ SY167 )
| ~ ( in @ ( ordered_pair @ SV88 @ SY166 ) @ SY167 )
| ( in @ SV88 @ ( relation_dom @ SY167 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[431]) ).
thf(454,plain,
! [SV88: $i] :
( ( ~ ! [SY168: $i,SY169: $i] :
( ~ ( relation @ SY169 )
| ~ ( in @ ( ordered_pair @ SV88 @ SY168 ) @ SY169 )
| ( in @ SY168 @ ( relation_rng @ SY169 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[431]) ).
thf(455,plain,
! [SV89: $i,SV66: $i] :
( ( ( in @ SV66 @ SV89 )
= $false )
| ( ( ~ ( in @ SV89 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(456,plain,
! [SV90: $i,SV67: $i,SV106: $i] :
( ( ( ~ ( element @ SV106 @ ( powerset @ ( cartesian_product2 @ SV67 @ SV90 ) ) ) )
= $true )
| ( ( relation @ SV106 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(457,plain,
! [SV93: $i,SV70: $i,SV107: $i] :
( ( ( ~ ( relation_of2 @ SV107 @ SV70 @ SV93 ) )
= $true )
| ( ( element @ ( relation_rng_as_subset @ SV70 @ SV93 @ SV107 ) @ ( powerset @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(458,plain,
! [SV94: $i,SV71: $i,SV108: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV108 @ SV71 @ SV94 ) )
= $true )
| ( ( element @ SV108 @ ( powerset @ ( cartesian_product2 @ SV71 @ SV94 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(459,plain,
! [SV98: $i,SV76: $i,SV109: $i] :
( ( ( ~ ( relation_of2 @ SV109 @ SV76 @ SV98 ) )
= $true )
| ( ( ( relation_rng_as_subset @ SV76 @ SV98 @ SV109 )
= ( relation_rng @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(460,plain,
! [SV99: $i,SV78: $i] :
( ( ( in @ SV78 @ SV99 )
= $false )
| ( ( element @ SV78 @ SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(461,plain,
! [SV100: $i,SV79: $i] :
( ( ( element @ SV79 @ SV100 )
= $false )
| ( ( ( empty @ SV100 )
| ( in @ SV79 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(462,plain,
! [SV80: $i,SV110: $i,SV101: $i] :
( ( ( ~ ( element @ SV101 @ ( powerset @ SV110 ) )
| ~ ( in @ SV80 @ SV101 ) )
= $true )
| ( ( element @ SV80 @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(463,plain,
! [SV81: $i,SV111: $i,SV102: $i] :
( ( ( ~ ( element @ SV102 @ ( powerset @ SV111 ) )
| ~ ( in @ SV81 @ SV102 ) )
= $true )
| ( ( ~ ( empty @ SV111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(464,plain,
! [SV83: $i,SV103: $i] :
( ( ( empty @ SV103 )
= $false )
| ( ( ~ ( in @ SV83 @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(465,plain,
! [SV104: $i,SV84: $i] :
( ( ( SV84 = SV104 )
= $true )
| ( ( ~ ( empty @ SV84 ) )
= $true )
| ( ( ~ ( empty @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(466,plain,
! [SV112: $i] :
( ( ! [SY176: $i] :
( ~ ( element @ SV112 @ ( powerset @ SY176 ) )
| ( subset @ SV112 @ SY176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(467,plain,
! [SV113: $i] :
( ( ! [SY177: $i] :
( ~ ( subset @ SV113 @ SY177 )
| ( element @ SV113 @ ( powerset @ SY177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(468,plain,
! [SV85: $i] :
( ( ! [SY155: $i,SY156: $i] :
( ~ ( relation_of2 @ SY156 @ SV85 @ SY155 )
| ( relation_of2_as_subset @ SY156 @ SV85 @ SY155 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(469,plain,
! [SV85: $i] :
( ( ! [SY157: $i,SY158: $i] :
( ~ ( relation_of2_as_subset @ SY158 @ SV85 @ SY157 )
| ( relation_of2 @ SY158 @ SV85 @ SY157 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(470,plain,
( ( ~ ! [SX0: $i] :
~ ( in @ ( ordered_pair @ SX0 @ sK5_SY74 ) @ sK3_SY71 )
| ~ ( in @ sK5_SY74 @ sK2_SY67 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(471,plain,
! [SV86: $i] :
( ( ( ~ ! [SY159: $i] :
( ~ ( ~ ( ! [SY160: $i] :
~ ( in @ ( ordered_pair @ SY160 @ ( sK13_C @ SY159 @ SV86 ) ) @ SV86 )
| ~ ( in @ ( sK13_C @ SY159 @ SV86 ) @ SY159 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SY159 @ SV86 ) @ ( sK13_C @ SY159 @ SV86 ) ) @ SV86 )
| ( in @ ( sK13_C @ SY159 @ SV86 ) @ SY159 ) ) )
| ( SY159
= ( relation_rng @ SV86 ) ) )
| ~ ! [SY161: $i] :
( ( SY161
!= ( relation_rng @ SV86 ) )
| ~ ( ~ ! [SY162: $i] :
( ! [SY163: $i] :
~ ( in @ ( ordered_pair @ SY163 @ SY162 ) @ SV86 )
| ( in @ SY162 @ SY161 ) )
| ~ ! [SY164: $i] :
( ~ ( in @ SY164 @ SY161 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY164 @ SY161 @ SV86 ) @ SY164 ) @ SV86 ) ) ) ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(472,plain,
! [SV87: $i,SV105: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV87 )
| ~ ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV105 ) )
| ~ ( ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV87 )
| ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV105 ) ) )
= $false )
| ( ( SV87 = SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(473,plain,
! [SV88: $i] :
( ( ! [SY166: $i,SY167: $i] :
( ~ ( relation @ SY167 )
| ~ ( in @ ( ordered_pair @ SV88 @ SY166 ) @ SY167 )
| ( in @ SV88 @ ( relation_dom @ SY167 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[453]) ).
thf(474,plain,
! [SV88: $i] :
( ( ! [SY168: $i,SY169: $i] :
( ~ ( relation @ SY169 )
| ~ ( in @ ( ordered_pair @ SV88 @ SY168 ) @ SY169 )
| ( in @ SY168 @ ( relation_rng @ SY169 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[454]) ).
thf(475,plain,
! [SV66: $i,SV89: $i] :
( ( ( in @ SV89 @ SV66 )
= $false )
| ( ( in @ SV66 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(476,plain,
! [SV90: $i,SV67: $i,SV106: $i] :
( ( ( element @ SV106 @ ( powerset @ ( cartesian_product2 @ SV67 @ SV90 ) ) )
= $false )
| ( ( relation @ SV106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(477,plain,
! [SV93: $i,SV70: $i,SV107: $i] :
( ( ( relation_of2 @ SV107 @ SV70 @ SV93 )
= $false )
| ( ( element @ ( relation_rng_as_subset @ SV70 @ SV93 @ SV107 ) @ ( powerset @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(478,plain,
! [SV94: $i,SV71: $i,SV108: $i] :
( ( ( relation_of2_as_subset @ SV108 @ SV71 @ SV94 )
= $false )
| ( ( element @ SV108 @ ( powerset @ ( cartesian_product2 @ SV71 @ SV94 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(479,plain,
! [SV98: $i,SV76: $i,SV109: $i] :
( ( ( relation_of2 @ SV109 @ SV76 @ SV98 )
= $false )
| ( ( ( relation_rng_as_subset @ SV76 @ SV98 @ SV109 )
= ( relation_rng @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(480,plain,
! [SV79: $i,SV100: $i] :
( ( ( empty @ SV100 )
= $true )
| ( ( in @ SV79 @ SV100 )
= $true )
| ( ( element @ SV79 @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(481,plain,
! [SV80: $i,SV110: $i,SV101: $i] :
( ( ( ~ ( element @ SV101 @ ( powerset @ SV110 ) ) )
= $true )
| ( ( ~ ( in @ SV80 @ SV101 ) )
= $true )
| ( ( element @ SV80 @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(482,plain,
! [SV81: $i,SV111: $i,SV102: $i] :
( ( ( ~ ( element @ SV102 @ ( powerset @ SV111 ) ) )
= $true )
| ( ( ~ ( in @ SV81 @ SV102 ) )
= $true )
| ( ( ~ ( empty @ SV111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(483,plain,
! [SV103: $i,SV83: $i] :
( ( ( in @ SV83 @ SV103 )
= $false )
| ( ( empty @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(484,plain,
! [SV104: $i,SV84: $i] :
( ( ( empty @ SV84 )
= $false )
| ( ( SV84 = SV104 )
= $true )
| ( ( ~ ( empty @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(485,plain,
! [SV114: $i,SV112: $i] :
( ( ~ ( element @ SV112 @ ( powerset @ SV114 ) )
| ( subset @ SV112 @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(486,plain,
! [SV115: $i,SV113: $i] :
( ( ~ ( subset @ SV113 @ SV115 )
| ( element @ SV113 @ ( powerset @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(487,plain,
! [SV116: $i,SV85: $i] :
( ( ! [SY178: $i] :
( ~ ( relation_of2 @ SY178 @ SV85 @ SV116 )
| ( relation_of2_as_subset @ SY178 @ SV85 @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(488,plain,
! [SV117: $i,SV85: $i] :
( ( ! [SY179: $i] :
( ~ ( relation_of2_as_subset @ SY179 @ SV85 @ SV117 )
| ( relation_of2 @ SY179 @ SV85 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(489,plain,
( ( ~ ! [SX0: $i] :
~ ( in @ ( ordered_pair @ SX0 @ sK5_SY74 ) @ sK3_SY71 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(490,plain,
( ( ~ ( in @ sK5_SY74 @ sK2_SY67 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(491,plain,
! [SV86: $i] :
( ( ( ~ ! [SY159: $i] :
( ~ ( ~ ( ! [SY160: $i] :
~ ( in @ ( ordered_pair @ SY160 @ ( sK13_C @ SY159 @ SV86 ) ) @ SV86 )
| ~ ( in @ ( sK13_C @ SY159 @ SV86 ) @ SY159 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SY159 @ SV86 ) @ ( sK13_C @ SY159 @ SV86 ) ) @ SV86 )
| ( in @ ( sK13_C @ SY159 @ SV86 ) @ SY159 ) ) )
| ( SY159
= ( relation_rng @ SV86 ) ) ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[471]) ).
thf(492,plain,
! [SV86: $i] :
( ( ( ~ ! [SY161: $i] :
( ( SY161
!= ( relation_rng @ SV86 ) )
| ~ ( ~ ! [SY162: $i] :
( ! [SY163: $i] :
~ ( in @ ( ordered_pair @ SY163 @ SY162 ) @ SV86 )
| ( in @ SY162 @ SY161 ) )
| ~ ! [SY164: $i] :
( ~ ( in @ SY164 @ SY161 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY164 @ SY161 @ SV86 ) @ SY164 ) @ SV86 ) ) ) ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[471]) ).
thf(493,plain,
! [SV87: $i,SV105: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV87 )
| ~ ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV105 ) ) )
= $false )
| ( ( SV87 = SV105 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[472]) ).
thf(494,plain,
! [SV87: $i,SV105: $i] :
( ( ( ~ ( ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV87 )
| ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV105 ) ) )
= $false )
| ( ( SV87 = SV105 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[472]) ).
thf(495,plain,
! [SV118: $i,SV88: $i] :
( ( ! [SY180: $i] :
( ~ ( relation @ SY180 )
| ~ ( in @ ( ordered_pair @ SV88 @ SV118 ) @ SY180 )
| ( in @ SV88 @ ( relation_dom @ SY180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(496,plain,
! [SV119: $i,SV88: $i] :
( ( ! [SY181: $i] :
( ~ ( relation @ SY181 )
| ~ ( in @ ( ordered_pair @ SV88 @ SV119 ) @ SY181 )
| ( in @ SV119 @ ( relation_rng @ SY181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(497,plain,
! [SV80: $i,SV110: $i,SV101: $i] :
( ( ( element @ SV101 @ ( powerset @ SV110 ) )
= $false )
| ( ( ~ ( in @ SV80 @ SV101 ) )
= $true )
| ( ( element @ SV80 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(498,plain,
! [SV81: $i,SV111: $i,SV102: $i] :
( ( ( element @ SV102 @ ( powerset @ SV111 ) )
= $false )
| ( ( ~ ( in @ SV81 @ SV102 ) )
= $true )
| ( ( ~ ( empty @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(499,plain,
! [SV84: $i,SV104: $i] :
( ( ( empty @ SV104 )
= $false )
| ( ( SV84 = SV104 )
= $true )
| ( ( empty @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(500,plain,
! [SV114: $i,SV112: $i] :
( ( ( ~ ( element @ SV112 @ ( powerset @ SV114 ) ) )
= $true )
| ( ( subset @ SV112 @ SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(501,plain,
! [SV115: $i,SV113: $i] :
( ( ( ~ ( subset @ SV113 @ SV115 ) )
= $true )
| ( ( element @ SV113 @ ( powerset @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[486]) ).
thf(502,plain,
! [SV116: $i,SV85: $i,SV120: $i] :
( ( ~ ( relation_of2 @ SV120 @ SV85 @ SV116 )
| ( relation_of2_as_subset @ SV120 @ SV85 @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(503,plain,
! [SV117: $i,SV85: $i,SV121: $i] :
( ( ~ ( relation_of2_as_subset @ SV121 @ SV85 @ SV117 )
| ( relation_of2 @ SV121 @ SV85 @ SV117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(504,plain,
( ( ! [SX0: $i] :
~ ( in @ ( ordered_pair @ SX0 @ sK5_SY74 ) @ sK3_SY71 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[489]) ).
thf(505,plain,
( ( in @ sK5_SY74 @ sK2_SY67 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[490]) ).
thf(506,plain,
! [SV86: $i] :
( ( ( ! [SY159: $i] :
( ~ ( ~ ( ! [SY160: $i] :
~ ( in @ ( ordered_pair @ SY160 @ ( sK13_C @ SY159 @ SV86 ) ) @ SV86 )
| ~ ( in @ ( sK13_C @ SY159 @ SV86 ) @ SY159 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SY159 @ SV86 ) @ ( sK13_C @ SY159 @ SV86 ) ) @ SV86 )
| ( in @ ( sK13_C @ SY159 @ SV86 ) @ SY159 ) ) )
| ( SY159
= ( relation_rng @ SV86 ) ) ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[491]) ).
thf(507,plain,
! [SV86: $i] :
( ( ( ! [SY161: $i] :
( ( SY161
!= ( relation_rng @ SV86 ) )
| ~ ( ~ ! [SY162: $i] :
( ! [SY163: $i] :
~ ( in @ ( ordered_pair @ SY163 @ SY162 ) @ SV86 )
| ( in @ SY162 @ SY161 ) )
| ~ ! [SY164: $i] :
( ~ ( in @ SY164 @ SY161 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY164 @ SY161 @ SV86 ) @ SY164 ) @ SV86 ) ) ) ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[492]) ).
thf(508,plain,
! [SV87: $i,SV105: $i] :
( ( ( ~ ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV87 )
| ~ ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV105 ) )
= $true )
| ( ( SV87 = SV105 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[493]) ).
thf(509,plain,
! [SV87: $i,SV105: $i] :
( ( ( ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV87 )
| ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV105 ) )
= $true )
| ( ( SV87 = SV105 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(510,plain,
! [SV118: $i,SV88: $i,SV122: $i] :
( ( ~ ( relation @ SV122 )
| ~ ( in @ ( ordered_pair @ SV88 @ SV118 ) @ SV122 )
| ( in @ SV88 @ ( relation_dom @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(511,plain,
! [SV119: $i,SV88: $i,SV123: $i] :
( ( ~ ( relation @ SV123 )
| ~ ( in @ ( ordered_pair @ SV88 @ SV119 ) @ SV123 )
| ( in @ SV119 @ ( relation_rng @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(512,plain,
! [SV110: $i,SV101: $i,SV80: $i] :
( ( ( in @ SV80 @ SV101 )
= $false )
| ( ( element @ SV101 @ ( powerset @ SV110 ) )
= $false )
| ( ( element @ SV80 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(513,plain,
! [SV111: $i,SV102: $i,SV81: $i] :
( ( ( in @ SV81 @ SV102 )
= $false )
| ( ( element @ SV102 @ ( powerset @ SV111 ) )
= $false )
| ( ( ~ ( empty @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(514,plain,
! [SV114: $i,SV112: $i] :
( ( ( element @ SV112 @ ( powerset @ SV114 ) )
= $false )
| ( ( subset @ SV112 @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(515,plain,
! [SV115: $i,SV113: $i] :
( ( ( subset @ SV113 @ SV115 )
= $false )
| ( ( element @ SV113 @ ( powerset @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(516,plain,
! [SV116: $i,SV85: $i,SV120: $i] :
( ( ( ~ ( relation_of2 @ SV120 @ SV85 @ SV116 ) )
= $true )
| ( ( relation_of2_as_subset @ SV120 @ SV85 @ SV116 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(517,plain,
! [SV117: $i,SV85: $i,SV121: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV121 @ SV85 @ SV117 ) )
= $true )
| ( ( relation_of2 @ SV121 @ SV85 @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(518,plain,
! [SV124: $i] :
( ( ~ ( in @ ( ordered_pair @ SV124 @ sK5_SY74 ) @ sK3_SY71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(519,plain,
! [SV86: $i,SV125: $i] :
( ( ( ~ ( ~ ( ! [SY182: $i] :
~ ( in @ ( ordered_pair @ SY182 @ ( sK13_C @ SV125 @ SV86 ) ) @ SV86 )
| ~ ( in @ ( sK13_C @ SV125 @ SV86 ) @ SV125 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SV125 @ SV86 ) @ ( sK13_C @ SV125 @ SV86 ) ) @ SV86 )
| ( in @ ( sK13_C @ SV125 @ SV86 ) @ SV125 ) ) )
| ( SV125
= ( relation_rng @ SV86 ) ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(520,plain,
! [SV86: $i,SV126: $i] :
( ( ( ( SV126
!= ( relation_rng @ SV86 ) )
| ~ ( ~ ! [SY183: $i] :
( ! [SY163: $i] :
~ ( in @ ( ordered_pair @ SY163 @ SY183 ) @ SV86 )
| ( in @ SY183 @ SV126 ) )
| ~ ! [SY185: $i] :
( ~ ( in @ SY185 @ SV126 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY185 @ SV126 @ SV86 ) @ SY185 ) @ SV86 ) ) ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(521,plain,
! [SV87: $i,SV105: $i] :
( ( ( ~ ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV87 ) )
= $true )
| ( ( ~ ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV105 ) )
= $true )
| ( ( SV87 = SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[508]) ).
thf(522,plain,
! [SV87: $i,SV105: $i] :
( ( ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV87 )
= $true )
| ( ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV105 )
= $true )
| ( ( SV87 = SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(523,plain,
! [SV118: $i,SV88: $i,SV122: $i] :
( ( ( ~ ( relation @ SV122 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV88 @ SV118 ) @ SV122 )
| ( in @ SV88 @ ( relation_dom @ SV122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[510]) ).
thf(524,plain,
! [SV119: $i,SV88: $i,SV123: $i] :
( ( ( ~ ( relation @ SV123 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV88 @ SV119 ) @ SV123 )
| ( in @ SV119 @ ( relation_rng @ SV123 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[511]) ).
thf(525,plain,
! [SV81: $i,SV102: $i,SV111: $i] :
( ( ( empty @ SV111 )
= $false )
| ( ( element @ SV102 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV81 @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(526,plain,
! [SV116: $i,SV85: $i,SV120: $i] :
( ( ( relation_of2 @ SV120 @ SV85 @ SV116 )
= $false )
| ( ( relation_of2_as_subset @ SV120 @ SV85 @ SV116 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(527,plain,
! [SV117: $i,SV85: $i,SV121: $i] :
( ( ( relation_of2_as_subset @ SV121 @ SV85 @ SV117 )
= $false )
| ( ( relation_of2 @ SV121 @ SV85 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(528,plain,
! [SV124: $i] :
( ( in @ ( ordered_pair @ SV124 @ sK5_SY74 ) @ sK3_SY71 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(529,plain,
! [SV86: $i,SV125: $i] :
( ( ( ~ ( ~ ( ! [SY182: $i] :
~ ( in @ ( ordered_pair @ SY182 @ ( sK13_C @ SV125 @ SV86 ) ) @ SV86 )
| ~ ( in @ ( sK13_C @ SV125 @ SV86 ) @ SV125 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SV125 @ SV86 ) @ ( sK13_C @ SV125 @ SV86 ) ) @ SV86 )
| ( in @ ( sK13_C @ SV125 @ SV86 ) @ SV125 ) ) ) )
= $true )
| ( ( SV125
= ( relation_rng @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(530,plain,
! [SV86: $i,SV126: $i] :
( ( ( SV126
!= ( relation_rng @ SV86 ) )
= $true )
| ( ( ~ ( ~ ! [SY183: $i] :
( ! [SY163: $i] :
~ ( in @ ( ordered_pair @ SY163 @ SY183 ) @ SV86 )
| ( in @ SY183 @ SV126 ) )
| ~ ! [SY185: $i] :
( ~ ( in @ SY185 @ SV126 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY185 @ SV126 @ SV86 ) @ SY185 ) @ SV86 ) ) ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[520]) ).
thf(531,plain,
! [SV87: $i,SV105: $i] :
( ( ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV87 )
= $false )
| ( ( ~ ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV105 ) )
= $true )
| ( ( SV87 = SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(532,plain,
! [SV118: $i,SV88: $i,SV122: $i] :
( ( ( relation @ SV122 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV88 @ SV118 ) @ SV122 )
| ( in @ SV88 @ ( relation_dom @ SV122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(533,plain,
! [SV119: $i,SV88: $i,SV123: $i] :
( ( ( relation @ SV123 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV88 @ SV119 ) @ SV123 )
| ( in @ SV119 @ ( relation_rng @ SV123 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(534,plain,
! [SV86: $i,SV125: $i] :
( ( ( ~ ( ! [SY182: $i] :
~ ( in @ ( ordered_pair @ SY182 @ ( sK13_C @ SV125 @ SV86 ) ) @ SV86 )
| ~ ( in @ ( sK13_C @ SV125 @ SV86 ) @ SV125 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SV125 @ SV86 ) @ ( sK13_C @ SV125 @ SV86 ) ) @ SV86 )
| ( in @ ( sK13_C @ SV125 @ SV86 ) @ SV125 ) ) )
= $false )
| ( ( SV125
= ( relation_rng @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(535,plain,
! [SV86: $i,SV126: $i] :
( ( ( SV126
= ( relation_rng @ SV86 ) )
= $false )
| ( ( ~ ( ~ ! [SY183: $i] :
( ! [SY163: $i] :
~ ( in @ ( ordered_pair @ SY163 @ SY183 ) @ SV86 )
| ( in @ SY183 @ SV126 ) )
| ~ ! [SY185: $i] :
( ~ ( in @ SY185 @ SV126 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY185 @ SV126 @ SV86 ) @ SY185 ) @ SV86 ) ) ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(536,plain,
! [SV87: $i,SV105: $i] :
( ( ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV105 )
= $false )
| ( ( in @ ( sK6_C @ SV105 @ SV87 ) @ SV87 )
= $false )
| ( ( SV87 = SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(537,plain,
! [SV122: $i,SV118: $i,SV88: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV88 @ SV118 ) @ SV122 ) )
= $true )
| ( ( in @ SV88 @ ( relation_dom @ SV122 ) )
= $true )
| ( ( relation @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[532]) ).
thf(538,plain,
! [SV123: $i,SV119: $i,SV88: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV88 @ SV119 ) @ SV123 ) )
= $true )
| ( ( in @ SV119 @ ( relation_rng @ SV123 ) )
= $true )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[533]) ).
thf(539,plain,
! [SV86: $i,SV125: $i] :
( ( ( ~ ( ! [SY182: $i] :
~ ( in @ ( ordered_pair @ SY182 @ ( sK13_C @ SV125 @ SV86 ) ) @ SV86 )
| ~ ( in @ ( sK13_C @ SV125 @ SV86 ) @ SV125 ) ) )
= $false )
| ( ( SV125
= ( relation_rng @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[534]) ).
thf(540,plain,
! [SV86: $i,SV125: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SV125 @ SV86 ) @ ( sK13_C @ SV125 @ SV86 ) ) @ SV86 )
| ( in @ ( sK13_C @ SV125 @ SV86 ) @ SV125 ) ) )
= $false )
| ( ( SV125
= ( relation_rng @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[534]) ).
thf(541,plain,
! [SV126: $i,SV86: $i] :
( ( ( ~ ! [SY183: $i] :
( ! [SY163: $i] :
~ ( in @ ( ordered_pair @ SY163 @ SY183 ) @ SV86 )
| ( in @ SY183 @ SV126 ) )
| ~ ! [SY185: $i] :
( ~ ( in @ SY185 @ SV126 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY185 @ SV126 @ SV86 ) @ SY185 ) @ SV86 ) ) )
= $false )
| ( ( SV126
= ( relation_rng @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(542,plain,
! [SV122: $i,SV118: $i,SV88: $i] :
( ( ( in @ ( ordered_pair @ SV88 @ SV118 ) @ SV122 )
= $false )
| ( ( in @ SV88 @ ( relation_dom @ SV122 ) )
= $true )
| ( ( relation @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(543,plain,
! [SV123: $i,SV119: $i,SV88: $i] :
( ( ( in @ ( ordered_pair @ SV88 @ SV119 ) @ SV123 )
= $false )
| ( ( in @ SV119 @ ( relation_rng @ SV123 ) )
= $true )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(544,plain,
! [SV86: $i,SV125: $i] :
( ( ( ! [SY182: $i] :
~ ( in @ ( ordered_pair @ SY182 @ ( sK13_C @ SV125 @ SV86 ) ) @ SV86 )
| ~ ( in @ ( sK13_C @ SV125 @ SV86 ) @ SV125 ) )
= $true )
| ( ( SV125
= ( relation_rng @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[539]) ).
thf(545,plain,
! [SV86: $i,SV125: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SV125 @ SV86 ) @ ( sK13_C @ SV125 @ SV86 ) ) @ SV86 )
| ( in @ ( sK13_C @ SV125 @ SV86 ) @ SV125 ) )
= $true )
| ( ( SV125
= ( relation_rng @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[540]) ).
thf(546,plain,
! [SV126: $i,SV86: $i] :
( ( ( ~ ! [SY183: $i] :
( ! [SY163: $i] :
~ ( in @ ( ordered_pair @ SY163 @ SY183 ) @ SV86 )
| ( in @ SY183 @ SV126 ) ) )
= $false )
| ( ( SV126
= ( relation_rng @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[541]) ).
thf(547,plain,
! [SV86: $i,SV126: $i] :
( ( ( ~ ! [SY185: $i] :
( ~ ( in @ SY185 @ SV126 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY185 @ SV126 @ SV86 ) @ SY185 ) @ SV86 ) ) )
= $false )
| ( ( SV126
= ( relation_rng @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[541]) ).
thf(548,plain,
! [SV86: $i,SV125: $i] :
( ( ( ! [SY182: $i] :
~ ( in @ ( ordered_pair @ SY182 @ ( sK13_C @ SV125 @ SV86 ) ) @ SV86 ) )
= $true )
| ( ( ~ ( in @ ( sK13_C @ SV125 @ SV86 ) @ SV125 ) )
= $true )
| ( ( SV125
= ( relation_rng @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[544]) ).
thf(549,plain,
! [SV86: $i,SV125: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SV125 @ SV86 ) @ ( sK13_C @ SV125 @ SV86 ) ) @ SV86 )
= $true )
| ( ( in @ ( sK13_C @ SV125 @ SV86 ) @ SV125 )
= $true )
| ( ( SV125
= ( relation_rng @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(550,plain,
! [SV126: $i,SV86: $i] :
( ( ( ! [SY183: $i] :
( ! [SY163: $i] :
~ ( in @ ( ordered_pair @ SY163 @ SY183 ) @ SV86 )
| ( in @ SY183 @ SV126 ) ) )
= $true )
| ( ( SV126
= ( relation_rng @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[546]) ).
thf(551,plain,
! [SV86: $i,SV126: $i] :
( ( ( ! [SY185: $i] :
( ~ ( in @ SY185 @ SV126 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY185 @ SV126 @ SV86 ) @ SY185 ) @ SV86 ) ) )
= $true )
| ( ( SV126
= ( relation_rng @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[547]) ).
thf(552,plain,
! [SV86: $i,SV125: $i,SV127: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV127 @ ( sK13_C @ SV125 @ SV86 ) ) @ SV86 ) )
= $true )
| ( ( ~ ( in @ ( sK13_C @ SV125 @ SV86 ) @ SV125 ) )
= $true )
| ( ( SV125
= ( relation_rng @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(553,plain,
! [SV126: $i,SV86: $i,SV128: $i] :
( ( ( ! [SY186: $i] :
~ ( in @ ( ordered_pair @ SY186 @ SV128 ) @ SV86 )
| ( in @ SV128 @ SV126 ) )
= $true )
| ( ( SV126
= ( relation_rng @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(554,plain,
! [SV86: $i,SV126: $i,SV129: $i] :
( ( ( ~ ( in @ SV129 @ SV126 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV129 @ SV126 @ SV86 ) @ SV129 ) @ SV86 ) )
= $true )
| ( ( SV126
= ( relation_rng @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(555,plain,
! [SV86: $i,SV125: $i,SV127: $i] :
( ( ( in @ ( ordered_pair @ SV127 @ ( sK13_C @ SV125 @ SV86 ) ) @ SV86 )
= $false )
| ( ( ~ ( in @ ( sK13_C @ SV125 @ SV86 ) @ SV125 ) )
= $true )
| ( ( SV125
= ( relation_rng @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(556,plain,
! [SV126: $i,SV86: $i,SV128: $i] :
( ( ( ! [SY186: $i] :
~ ( in @ ( ordered_pair @ SY186 @ SV128 ) @ SV86 ) )
= $true )
| ( ( in @ SV128 @ SV126 )
= $true )
| ( ( SV126
= ( relation_rng @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(557,plain,
! [SV86: $i,SV126: $i,SV129: $i] :
( ( ( ~ ( in @ SV129 @ SV126 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK12_D @ SV129 @ SV126 @ SV86 ) @ SV129 ) @ SV86 )
= $true )
| ( ( SV126
= ( relation_rng @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(558,plain,
! [SV127: $i,SV86: $i,SV125: $i] :
( ( ( in @ ( sK13_C @ SV125 @ SV86 ) @ SV125 )
= $false )
| ( ( in @ ( ordered_pair @ SV127 @ ( sK13_C @ SV125 @ SV86 ) ) @ SV86 )
= $false )
| ( ( SV125
= ( relation_rng @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(559,plain,
! [SV126: $i,SV86: $i,SV128: $i,SV130: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV130 @ SV128 ) @ SV86 ) )
= $true )
| ( ( in @ SV128 @ SV126 )
= $true )
| ( ( SV126
= ( relation_rng @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(560,plain,
! [SV86: $i,SV126: $i,SV129: $i] :
( ( ( in @ SV129 @ SV126 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK12_D @ SV129 @ SV126 @ SV86 ) @ SV129 ) @ SV86 )
= $true )
| ( ( SV126
= ( relation_rng @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(561,plain,
! [SV126: $i,SV86: $i,SV128: $i,SV130: $i] :
( ( ( in @ ( ordered_pair @ SV130 @ SV128 ) @ SV86 )
= $false )
| ( ( in @ SV128 @ SV126 )
= $true )
| ( ( SV126
= ( relation_rng @ SV86 ) )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(562,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[341,561,560,558,549,543,542,536,528,527,526,525,522,515,514,512,505,499,483,480,479,478,477,476,475,460,449,442,436,414,413,410,409,393,391,388,373,358,356,351,350,348,347,346,345,344,343,342]) ).
thf(563,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[562,335]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU266+1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n017.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 15:06:01 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 218.46/36.66
% 218.46/36.66 No.of.Axioms: 37
% 218.46/36.66
% 218.46/36.66 Length.of.Defs: 0
% 218.46/36.66
% 218.46/36.66 Contains.Choice.Funs: false
% 218.46/36.66 .................
% 218.46/36.66
% 218.46/36.66 ********************************
% 218.46/36.66 * All subproblems solved! *
% 218.46/36.66 ********************************
% 218.46/36.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:38,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:263,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:562,loop_count:0,foatp_calls:1,translation:fof_full)
% 218.46/36.66
% 218.46/36.66 %**** Beginning of derivation protocol ****
% 218.46/36.66 % SZS output start CNFRefutation
% See solution above
% 218.46/36.66
% 218.46/36.66 %**** End of derivation protocol ****
% 218.46/36.66 %**** no. of clauses in derivation: 563 ****
% 218.46/36.66 %**** clause counter: 562 ****
% 218.46/36.66
% 218.46/36.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:38,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:263,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:562,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------