%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU206+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 : n001.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 10:43:24 AM UTC 2026
% Result : Theorem 1.12s 0.47s
% Output : CNFRefutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 22
% Syntax : Number of formulae : 333 ( 106 unt; 0 typ; 0 def)
% Number of atoms : 3069 (1048 equ; 0 cnn)
% Maximal formula atoms : 5 ( 9 avg)
% Number of connectives : 6319 (1577 ~;1011 |; 24 &;3658 @)
% ( 18 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 6 con; 0-4 aty)
% Number of variables : 982 ( 0 ^; 967 !; 15 ?; 982 :)
% Comments :
%------------------------------------------------------------------------------
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_image,type,
relation_image: $i > $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_sK10_SY74,type,
sK10_SY74: $i > $i > $i ).
thf(tp_sK11_SY78,type,
sK11_SY78: $i > $i > $i ).
thf(tp_sK12_SY82,type,
sK12_SY82: $i > $i > $i > $i ).
thf(tp_sK13_SY74,type,
sK13_SY74: $i > $i > $i > $i ).
thf(tp_sK14_SY78,type,
sK14_SY78: $i > $i > $i > $i ).
thf(tp_sK15_SY82,type,
sK15_SY82: $i > $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY56,type,
sK4_SY56: $i > $i > $i ).
thf(tp_sK5_SY62,type,
sK5_SY62: $i > $i > $i ).
thf(tp_sK6_SY68,type,
sK6_SY68: $i > $i > $i > $i ).
thf(tp_sK7_SY71,type,
sK7_SY71: $i > $i > $i > $i ).
thf(tp_sK8_SY75,type,
sK8_SY75: $i > $i > $i > $i ).
thf(tp_sK9_SY79,type,
sK9_SY79: $i > $i > $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(9,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
thf(13,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(16,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(17,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(18,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(19,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(20,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(21,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(28,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(29,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(30,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(31,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(32,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(33,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(34,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(35,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(36,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(38,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(39,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
thf(41,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ E @ D ) @ A )
& ( in @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
thf(44,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(46,conjecture,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
thf(47,negated_conjecture,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[46]) ).
thf(48,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[47]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(50,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(51,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(52,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(53,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(54,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(55,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(56,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(57,plain,
$true = $true,
inference(unfold_def,[status(thm)],[28]) ).
thf(58,plain,
$true = $true,
inference(unfold_def,[status(thm)],[29]) ).
thf(59,plain,
$true = $true,
inference(unfold_def,[status(thm)],[30]) ).
thf(60,plain,
$true = $true,
inference(unfold_def,[status(thm)],[31]) ).
thf(61,plain,
$true = $true,
inference(unfold_def,[status(thm)],[32]) ).
thf(62,plain,
$true = $true,
inference(unfold_def,[status(thm)],[33]) ).
thf(63,plain,
$true = $true,
inference(unfold_def,[status(thm)],[34]) ).
thf(64,plain,
$true = $true,
inference(unfold_def,[status(thm)],[35]) ).
thf(65,plain,
$true = $true,
inference(unfold_def,[status(thm)],[36]) ).
thf(66,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)],[38]) ).
thf(67,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(68,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ E @ D ) @ A )
& ( in @ E @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(69,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(70,plain,
( ( ( relation @ sK1_A )
=> ( ( relation_image @ sK1_A @ ( relation_dom @ sK1_A ) )
= ( relation_rng @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[48]) ).
thf(71,plain,
( ( relation @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[70]) ).
thf(72,plain,
( ( ( relation_image @ sK1_A @ ( relation_dom @ sK1_A ) )
= ( relation_rng @ sK1_A ) )
= $false ),
inference(standard_cnf,[status(thm)],[70]) ).
thf(73,plain,
( ( ( relation_image @ sK1_A @ ( relation_dom @ sK1_A ) )
!= ( relation_rng @ sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[72]) ).
thf(74,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(75,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ E @ D ) @ A )
& ( in @ E @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(76,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(77,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(78,plain,
$true = $true,
inference(copy,[status(thm)],[65]) ).
thf(79,plain,
$true = $true,
inference(copy,[status(thm)],[64]) ).
thf(80,plain,
$true = $true,
inference(copy,[status(thm)],[63]) ).
thf(81,plain,
$true = $true,
inference(copy,[status(thm)],[62]) ).
thf(82,plain,
$true = $true,
inference(copy,[status(thm)],[61]) ).
thf(83,plain,
$true = $true,
inference(copy,[status(thm)],[60]) ).
thf(84,plain,
$true = $true,
inference(copy,[status(thm)],[59]) ).
thf(85,plain,
$true = $true,
inference(copy,[status(thm)],[58]) ).
thf(86,plain,
$true = $true,
inference(copy,[status(thm)],[57]) ).
thf(87,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(88,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(89,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(90,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(91,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(92,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(93,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(94,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(95,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(96,plain,
( ( ( relation_image @ sK1_A @ ( relation_dom @ sK1_A ) )
!= ( relation_rng @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(97,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(98,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(99,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(100,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_rng @ SX0 ) )
| ~ ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(101,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( relation_image @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX4 @ SX3 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX4 @ SX3 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX4 @ SX3 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX4 @ SX3 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( relation_image @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(102,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(103,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(104,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_dom @ SX0 ) )
| ~ ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(105,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(106,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_image @ SX1 @ SX0 ) @ ( relation_rng @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(107,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( relation_rng @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(108,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(109,plain,
( ( ( relation_image @ sK1_A @ ( relation_dom @ sK1_A ) )
= ( relation_rng @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(110,plain,
! [SV1: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV1 )
| ~ ( relation @ SV1 ) )
| ~ ( empty @ ( relation_dom @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(111,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(112,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(113,plain,
! [SV2: $i] :
( ( ~ ( empty @ SV2 )
| ~ ( ~ ( empty @ ( relation_rng @ SV2 ) )
| ~ ( relation @ ( relation_rng @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(114,plain,
! [SV3: $i] :
( ( ~ ( relation @ SV3 )
| ! [SY23: $i,SY24: $i] :
~ ( ~ ( ( SY24
!= ( relation_image @ SV3 @ SY23 ) )
| ! [SY25: $i] :
~ ( ~ ( ~ ( in @ SY25 @ SY24 )
| ~ ! [SY26: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY26 @ SY25 ) @ SV3 )
| ~ ( in @ SY26 @ SY23 ) ) )
| ~ ( ~ ~ ! [SY27: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY27 @ SY25 ) @ SV3 )
| ~ ( in @ SY27 @ SY23 ) )
| ( in @ SY25 @ SY24 ) ) ) )
| ~ ( ~ ! [SY28: $i] :
~ ( ~ ( ~ ( in @ SY28 @ SY24 )
| ~ ! [SY29: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY29 @ SY28 ) @ SV3 )
| ~ ( in @ SY29 @ SY23 ) ) )
| ~ ( ~ ~ ! [SY30: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY30 @ SY28 ) @ SV3 )
| ~ ( in @ SY30 @ SY23 ) )
| ( in @ SY28 @ SY24 ) ) )
| ( SY24
= ( relation_image @ SV3 @ SY23 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(115,plain,
! [SV4: $i] :
( ( ~ ( empty @ SV4 )
| ( relation @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(116,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(117,plain,
! [SV5: $i] :
( ( ~ ( empty @ SV5 )
| ~ ( ~ ( empty @ ( relation_dom @ SV5 ) )
| ~ ( relation @ ( relation_dom @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(118,plain,
! [SV6: $i] :
( ( ~ ( relation @ SV6 )
| ! [SY31: $i] :
~ ( ~ ( ( SY31
!= ( relation_dom @ SV6 ) )
| ! [SY32: $i] :
~ ( ~ ( ~ ( in @ SY32 @ SY31 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY33 ) @ SV6 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY34 ) @ SV6 )
| ( in @ SY32 @ SY31 ) ) ) )
| ~ ( ~ ! [SY35: $i] :
~ ( ~ ( ~ ( in @ SY35 @ SY31 )
| ~ ! [SY36: $i] :
~ ( in @ ( ordered_pair @ SY35 @ SY36 ) @ SV6 ) )
| ~ ( ~ ~ ! [SY37: $i] :
~ ( in @ ( ordered_pair @ SY35 @ SY37 ) @ SV6 )
| ( in @ SY35 @ SY31 ) ) )
| ( SY31
= ( relation_dom @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(119,plain,
! [SV7: $i] :
( ( ! [SY38: $i] :
( ~ ( relation @ SY38 )
| ( subset @ ( relation_image @ SY38 @ SV7 ) @ ( relation_rng @ SY38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(120,plain,
! [SV8: $i] :
( ( ~ ( relation @ SV8 )
| ! [SY39: $i] :
~ ( ~ ( ( SY39
!= ( relation_rng @ SV8 ) )
| ! [SY40: $i] :
~ ( ~ ( ~ ( in @ SY40 @ SY39 )
| ~ ! [SY41: $i] :
~ ( in @ ( ordered_pair @ SY41 @ SY40 ) @ SV8 ) )
| ~ ( ~ ~ ! [SY42: $i] :
~ ( in @ ( ordered_pair @ SY42 @ SY40 ) @ SV8 )
| ( in @ SY40 @ SY39 ) ) ) )
| ~ ( ~ ! [SY43: $i] :
~ ( ~ ( ~ ( in @ SY43 @ SY39 )
| ~ ! [SY44: $i] :
~ ( in @ ( ordered_pair @ SY44 @ SY43 ) @ SV8 ) )
| ~ ( ~ ~ ! [SY45: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY43 ) @ SV8 )
| ( in @ SY43 @ SY39 ) ) )
| ( SY39
= ( relation_rng @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(121,plain,
! [SV9: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV9 )
| ~ ( relation @ SV9 ) )
| ~ ( empty @ ( relation_rng @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(122,plain,
! [SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV1 )
| ~ ( relation @ SV1 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(123,plain,
( ( ~ ~ ( ~ ( empty @ sK2_SX0 )
| ~ ( relation @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[111]) ).
thf(124,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[112]) ).
thf(125,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV2 ) )
| ~ ( relation @ ( relation_rng @ SV2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(126,plain,
! [SV3: $i] :
( ( ( ~ ( relation @ SV3 ) )
= $true )
| ( ( ! [SY23: $i,SY24: $i] :
~ ( ~ ( ( SY24
!= ( relation_image @ SV3 @ SY23 ) )
| ! [SY25: $i] :
~ ( ~ ( ~ ( in @ SY25 @ SY24 )
| ~ ! [SY26: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY26 @ SY25 ) @ SV3 )
| ~ ( in @ SY26 @ SY23 ) ) )
| ~ ( ~ ~ ! [SY27: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY27 @ SY25 ) @ SV3 )
| ~ ( in @ SY27 @ SY23 ) )
| ( in @ SY25 @ SY24 ) ) ) )
| ~ ( ~ ! [SY28: $i] :
~ ( ~ ( ~ ( in @ SY28 @ SY24 )
| ~ ! [SY29: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY29 @ SY28 ) @ SV3 )
| ~ ( in @ SY29 @ SY23 ) ) )
| ~ ( ~ ~ ! [SY30: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY30 @ SY28 ) @ SV3 )
| ~ ( in @ SY30 @ SY23 ) )
| ( in @ SY28 @ SY24 ) ) )
| ( SY24
= ( relation_image @ SV3 @ SY23 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(127,plain,
! [SV4: $i] :
( ( ( ~ ( empty @ SV4 ) )
= $true )
| ( ( relation @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(128,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(129,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(130,plain,
! [SV5: $i] :
( ( ( ~ ( empty @ SV5 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV5 ) )
| ~ ( relation @ ( relation_dom @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(131,plain,
! [SV6: $i] :
( ( ( ~ ( relation @ SV6 ) )
= $true )
| ( ( ! [SY31: $i] :
~ ( ~ ( ( SY31
!= ( relation_dom @ SV6 ) )
| ! [SY32: $i] :
~ ( ~ ( ~ ( in @ SY32 @ SY31 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY33 ) @ SV6 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY34 ) @ SV6 )
| ( in @ SY32 @ SY31 ) ) ) )
| ~ ( ~ ! [SY35: $i] :
~ ( ~ ( ~ ( in @ SY35 @ SY31 )
| ~ ! [SY36: $i] :
~ ( in @ ( ordered_pair @ SY35 @ SY36 ) @ SV6 ) )
| ~ ( ~ ~ ! [SY37: $i] :
~ ( in @ ( ordered_pair @ SY35 @ SY37 ) @ SV6 )
| ( in @ SY35 @ SY31 ) ) )
| ( SY31
= ( relation_dom @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(132,plain,
! [SV7: $i,SV10: $i] :
( ( ~ ( relation @ SV10 )
| ( subset @ ( relation_image @ SV10 @ SV7 ) @ ( relation_rng @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(133,plain,
! [SV8: $i] :
( ( ( ~ ( relation @ SV8 ) )
= $true )
| ( ( ! [SY39: $i] :
~ ( ~ ( ( SY39
!= ( relation_rng @ SV8 ) )
| ! [SY40: $i] :
~ ( ~ ( ~ ( in @ SY40 @ SY39 )
| ~ ! [SY41: $i] :
~ ( in @ ( ordered_pair @ SY41 @ SY40 ) @ SV8 ) )
| ~ ( ~ ~ ! [SY42: $i] :
~ ( in @ ( ordered_pair @ SY42 @ SY40 ) @ SV8 )
| ( in @ SY40 @ SY39 ) ) ) )
| ~ ( ~ ! [SY43: $i] :
~ ( ~ ( ~ ( in @ SY43 @ SY39 )
| ~ ! [SY44: $i] :
~ ( in @ ( ordered_pair @ SY44 @ SY43 ) @ SV8 ) )
| ~ ( ~ ~ ! [SY45: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY43 ) @ SV8 )
| ( in @ SY43 @ SY39 ) ) )
| ( SY39
= ( relation_rng @ SV8 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(134,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV9 )
| ~ ( relation @ SV9 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(135,plain,
! [SV1: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV1 )
| ~ ( relation @ SV1 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_dom @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(136,plain,
( ( ~ ( ~ ( empty @ sK2_SX0 )
| ~ ( relation @ sK2_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(137,plain,
( ( ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(138,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV2 ) )
| ~ ( relation @ ( relation_rng @ SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(139,plain,
! [SV3: $i] :
( ( ( relation @ SV3 )
= $false )
| ( ( ! [SY23: $i,SY24: $i] :
~ ( ~ ( ( SY24
!= ( relation_image @ SV3 @ SY23 ) )
| ! [SY25: $i] :
~ ( ~ ( ~ ( in @ SY25 @ SY24 )
| ~ ! [SY26: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY26 @ SY25 ) @ SV3 )
| ~ ( in @ SY26 @ SY23 ) ) )
| ~ ( ~ ~ ! [SY27: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY27 @ SY25 ) @ SV3 )
| ~ ( in @ SY27 @ SY23 ) )
| ( in @ SY25 @ SY24 ) ) ) )
| ~ ( ~ ! [SY28: $i] :
~ ( ~ ( ~ ( in @ SY28 @ SY24 )
| ~ ! [SY29: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY29 @ SY28 ) @ SV3 )
| ~ ( in @ SY29 @ SY23 ) ) )
| ~ ( ~ ~ ! [SY30: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY30 @ SY28 ) @ SV3 )
| ~ ( in @ SY30 @ SY23 ) )
| ( in @ SY28 @ SY24 ) ) )
| ( SY24
= ( relation_image @ SV3 @ SY23 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(140,plain,
! [SV4: $i] :
( ( ( empty @ SV4 )
= $false )
| ( ( relation @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(141,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(142,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(143,plain,
! [SV5: $i] :
( ( ( empty @ SV5 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV5 ) )
| ~ ( relation @ ( relation_dom @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(144,plain,
! [SV6: $i] :
( ( ( relation @ SV6 )
= $false )
| ( ( ! [SY31: $i] :
~ ( ~ ( ( SY31
!= ( relation_dom @ SV6 ) )
| ! [SY32: $i] :
~ ( ~ ( ~ ( in @ SY32 @ SY31 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY33 ) @ SV6 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY34 ) @ SV6 )
| ( in @ SY32 @ SY31 ) ) ) )
| ~ ( ~ ! [SY35: $i] :
~ ( ~ ( ~ ( in @ SY35 @ SY31 )
| ~ ! [SY36: $i] :
~ ( in @ ( ordered_pair @ SY35 @ SY36 ) @ SV6 ) )
| ~ ( ~ ~ ! [SY37: $i] :
~ ( in @ ( ordered_pair @ SY35 @ SY37 ) @ SV6 )
| ( in @ SY35 @ SY31 ) ) )
| ( SY31
= ( relation_dom @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(145,plain,
! [SV7: $i,SV10: $i] :
( ( ( ~ ( relation @ SV10 ) )
= $true )
| ( ( subset @ ( relation_image @ SV10 @ SV7 ) @ ( relation_rng @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(146,plain,
! [SV8: $i] :
( ( ( relation @ SV8 )
= $false )
| ( ( ! [SY39: $i] :
~ ( ~ ( ( SY39
!= ( relation_rng @ SV8 ) )
| ! [SY40: $i] :
~ ( ~ ( ~ ( in @ SY40 @ SY39 )
| ~ ! [SY41: $i] :
~ ( in @ ( ordered_pair @ SY41 @ SY40 ) @ SV8 ) )
| ~ ( ~ ~ ! [SY42: $i] :
~ ( in @ ( ordered_pair @ SY42 @ SY40 ) @ SV8 )
| ( in @ SY40 @ SY39 ) ) ) )
| ~ ( ~ ! [SY43: $i] :
~ ( ~ ( ~ ( in @ SY43 @ SY39 )
| ~ ! [SY44: $i] :
~ ( in @ ( ordered_pair @ SY44 @ SY43 ) @ SV8 ) )
| ~ ( ~ ~ ! [SY45: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY43 ) @ SV8 )
| ( in @ SY43 @ SY39 ) ) )
| ( SY39
= ( relation_rng @ SV8 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(147,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV9 )
| ~ ( relation @ SV9 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_rng @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(148,plain,
! [SV1: $i] :
( ( ( ~ ~ ( empty @ SV1 )
| ~ ( relation @ SV1 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(149,plain,
( ( ~ ( empty @ sK2_SX0 )
| ~ ( relation @ sK2_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(150,plain,
( ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(151,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV2 ) )
| ~ ( relation @ ( relation_rng @ SV2 ) ) )
= $false )
| ( ( empty @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(152,plain,
! [SV11: $i,SV3: $i] :
( ( ( ! [SY46: $i] :
~ ( ~ ( ( SY46
!= ( relation_image @ SV3 @ SV11 ) )
| ! [SY47: $i] :
~ ( ~ ( ~ ( in @ SY47 @ SY46 )
| ~ ! [SY48: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY48 @ SY47 ) @ SV3 )
| ~ ( in @ SY48 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY49: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY49 @ SY47 ) @ SV3 )
| ~ ( in @ SY49 @ SV11 ) )
| ( in @ SY47 @ SY46 ) ) ) )
| ~ ( ~ ! [SY50: $i] :
~ ( ~ ( ~ ( in @ SY50 @ SY46 )
| ~ ! [SY51: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY51 @ SY50 ) @ SV3 )
| ~ ( in @ SY51 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY52 @ SY50 ) @ SV3 )
| ~ ( in @ SY52 @ SV11 ) )
| ( in @ SY50 @ SY46 ) ) )
| ( SY46
= ( relation_image @ SV3 @ SV11 ) ) ) ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(153,plain,
! [SV5: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV5 ) )
| ~ ( relation @ ( relation_dom @ SV5 ) ) )
= $false )
| ( ( empty @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(154,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ( ~ ( ( SV12
!= ( relation_dom @ SV6 ) )
| ! [SY53: $i] :
~ ( ~ ( ~ ( in @ SY53 @ SV12 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY53 @ SY33 ) @ SV6 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY53 @ SY34 ) @ SV6 )
| ( in @ SY53 @ SV12 ) ) ) )
| ~ ( ~ ! [SY56: $i] :
~ ( ~ ( ~ ( in @ SY56 @ SV12 )
| ~ ! [SY36: $i] :
~ ( in @ ( ordered_pair @ SY56 @ SY36 ) @ SV6 ) )
| ~ ( ~ ~ ! [SY37: $i] :
~ ( in @ ( ordered_pair @ SY56 @ SY37 ) @ SV6 )
| ( in @ SY56 @ SV12 ) ) )
| ( SV12
= ( relation_dom @ SV6 ) ) ) ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(155,plain,
! [SV7: $i,SV10: $i] :
( ( ( relation @ SV10 )
= $false )
| ( ( subset @ ( relation_image @ SV10 @ SV7 ) @ ( relation_rng @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(156,plain,
! [SV8: $i,SV13: $i] :
( ( ( ~ ( ~ ( ( SV13
!= ( relation_rng @ SV8 ) )
| ! [SY59: $i] :
~ ( ~ ( ~ ( in @ SY59 @ SV13 )
| ~ ! [SY41: $i] :
~ ( in @ ( ordered_pair @ SY41 @ SY59 ) @ SV8 ) )
| ~ ( ~ ~ ! [SY42: $i] :
~ ( in @ ( ordered_pair @ SY42 @ SY59 ) @ SV8 )
| ( in @ SY59 @ SV13 ) ) ) )
| ~ ( ~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SV13 )
| ~ ! [SY44: $i] :
~ ( in @ ( ordered_pair @ SY44 @ SY62 ) @ SV8 ) )
| ~ ( ~ ~ ! [SY45: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY62 ) @ SV8 )
| ( in @ SY62 @ SV13 ) ) )
| ( SV13
= ( relation_rng @ SV8 ) ) ) ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(157,plain,
! [SV9: $i] :
( ( ( ~ ~ ( empty @ SV9 )
| ~ ( relation @ SV9 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(158,plain,
! [SV1: $i] :
( ( ( ~ ~ ( empty @ SV1 ) )
= $true )
| ( ( ~ ( relation @ SV1 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(159,plain,
( ( ~ ( empty @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(160,plain,
( ( ~ ( relation @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(161,plain,
( ( ~ ~ ( empty @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(162,plain,
( ( ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(163,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV2 ) ) )
= $false )
| ( ( empty @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(164,plain,
! [SV2: $i] :
( ( ( ~ ( relation @ ( relation_rng @ SV2 ) ) )
= $false )
| ( ( empty @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(165,plain,
! [SV11: $i,SV3: $i,SV14: $i] :
( ( ( ~ ( ~ ( ( SV14
!= ( relation_image @ SV3 @ SV11 ) )
| ! [SY65: $i] :
~ ( ~ ( ~ ( in @ SY65 @ SV14 )
| ~ ! [SY48: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY48 @ SY65 ) @ SV3 )
| ~ ( in @ SY48 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY49: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY49 @ SY65 ) @ SV3 )
| ~ ( in @ SY49 @ SV11 ) )
| ( in @ SY65 @ SV14 ) ) ) )
| ~ ( ~ ! [SY68: $i] :
~ ( ~ ( ~ ( in @ SY68 @ SV14 )
| ~ ! [SY51: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY51 @ SY68 ) @ SV3 )
| ~ ( in @ SY51 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY52 @ SY68 ) @ SV3 )
| ~ ( in @ SY52 @ SV11 ) )
| ( in @ SY68 @ SV14 ) ) )
| ( SV14
= ( relation_image @ SV3 @ SV11 ) ) ) ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(166,plain,
! [SV5: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV5 ) ) )
= $false )
| ( ( empty @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(167,plain,
! [SV5: $i] :
( ( ( ~ ( relation @ ( relation_dom @ SV5 ) ) )
= $false )
| ( ( empty @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(168,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ( ( SV12
!= ( relation_dom @ SV6 ) )
| ! [SY53: $i] :
~ ( ~ ( ~ ( in @ SY53 @ SV12 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY53 @ SY33 ) @ SV6 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY53 @ SY34 ) @ SV6 )
| ( in @ SY53 @ SV12 ) ) ) )
| ~ ( ~ ! [SY56: $i] :
~ ( ~ ( ~ ( in @ SY56 @ SV12 )
| ~ ! [SY36: $i] :
~ ( in @ ( ordered_pair @ SY56 @ SY36 ) @ SV6 ) )
| ~ ( ~ ~ ! [SY37: $i] :
~ ( in @ ( ordered_pair @ SY56 @ SY37 ) @ SV6 )
| ( in @ SY56 @ SV12 ) ) )
| ( SV12
= ( relation_dom @ SV6 ) ) ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(169,plain,
! [SV8: $i,SV13: $i] :
( ( ( ~ ( ( SV13
!= ( relation_rng @ SV8 ) )
| ! [SY59: $i] :
~ ( ~ ( ~ ( in @ SY59 @ SV13 )
| ~ ! [SY41: $i] :
~ ( in @ ( ordered_pair @ SY41 @ SY59 ) @ SV8 ) )
| ~ ( ~ ~ ! [SY42: $i] :
~ ( in @ ( ordered_pair @ SY42 @ SY59 ) @ SV8 )
| ( in @ SY59 @ SV13 ) ) ) )
| ~ ( ~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SV13 )
| ~ ! [SY44: $i] :
~ ( in @ ( ordered_pair @ SY44 @ SY62 ) @ SV8 ) )
| ~ ( ~ ~ ! [SY45: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY62 ) @ SV8 )
| ( in @ SY62 @ SV13 ) ) )
| ( SV13
= ( relation_rng @ SV8 ) ) ) )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(170,plain,
! [SV9: $i] :
( ( ( ~ ~ ( empty @ SV9 ) )
= $true )
| ( ( ~ ( relation @ SV9 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(171,plain,
! [SV1: $i] :
( ( ( ~ ( empty @ SV1 ) )
= $false )
| ( ( ~ ( relation @ SV1 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(172,plain,
( ( empty @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(173,plain,
( ( relation @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(174,plain,
( ( ~ ( empty @ sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(175,plain,
( ( relation @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(176,plain,
! [SV2: $i] :
( ( ( empty @ ( relation_rng @ SV2 ) )
= $true )
| ( ( empty @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(177,plain,
! [SV2: $i] :
( ( ( relation @ ( relation_rng @ SV2 ) )
= $true )
| ( ( empty @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(178,plain,
! [SV11: $i,SV3: $i,SV14: $i] :
( ( ( ~ ( ( SV14
!= ( relation_image @ SV3 @ SV11 ) )
| ! [SY65: $i] :
~ ( ~ ( ~ ( in @ SY65 @ SV14 )
| ~ ! [SY48: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY48 @ SY65 ) @ SV3 )
| ~ ( in @ SY48 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY49: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY49 @ SY65 ) @ SV3 )
| ~ ( in @ SY49 @ SV11 ) )
| ( in @ SY65 @ SV14 ) ) ) )
| ~ ( ~ ! [SY68: $i] :
~ ( ~ ( ~ ( in @ SY68 @ SV14 )
| ~ ! [SY51: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY51 @ SY68 ) @ SV3 )
| ~ ( in @ SY51 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY52 @ SY68 ) @ SV3 )
| ~ ( in @ SY52 @ SV11 ) )
| ( in @ SY68 @ SV14 ) ) )
| ( SV14
= ( relation_image @ SV3 @ SV11 ) ) ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(179,plain,
! [SV5: $i] :
( ( ( empty @ ( relation_dom @ SV5 ) )
= $true )
| ( ( empty @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(180,plain,
! [SV5: $i] :
( ( ( relation @ ( relation_dom @ SV5 ) )
= $true )
| ( ( empty @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(181,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ( ( SV12
!= ( relation_dom @ SV6 ) )
| ! [SY53: $i] :
~ ( ~ ( ~ ( in @ SY53 @ SV12 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY53 @ SY33 ) @ SV6 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY53 @ SY34 ) @ SV6 )
| ( in @ SY53 @ SV12 ) ) ) ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(182,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ( ~ ! [SY56: $i] :
~ ( ~ ( ~ ( in @ SY56 @ SV12 )
| ~ ! [SY36: $i] :
~ ( in @ ( ordered_pair @ SY56 @ SY36 ) @ SV6 ) )
| ~ ( ~ ~ ! [SY37: $i] :
~ ( in @ ( ordered_pair @ SY56 @ SY37 ) @ SV6 )
| ( in @ SY56 @ SV12 ) ) )
| ( SV12
= ( relation_dom @ SV6 ) ) ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(183,plain,
! [SV8: $i,SV13: $i] :
( ( ( ~ ( ( SV13
!= ( relation_rng @ SV8 ) )
| ! [SY59: $i] :
~ ( ~ ( ~ ( in @ SY59 @ SV13 )
| ~ ! [SY41: $i] :
~ ( in @ ( ordered_pair @ SY41 @ SY59 ) @ SV8 ) )
| ~ ( ~ ~ ! [SY42: $i] :
~ ( in @ ( ordered_pair @ SY42 @ SY59 ) @ SV8 )
| ( in @ SY59 @ SV13 ) ) ) ) )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(184,plain,
! [SV8: $i,SV13: $i] :
( ( ( ~ ( ~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SV13 )
| ~ ! [SY44: $i] :
~ ( in @ ( ordered_pair @ SY44 @ SY62 ) @ SV8 ) )
| ~ ( ~ ~ ! [SY45: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY62 ) @ SV8 )
| ( in @ SY62 @ SV13 ) ) )
| ( SV13
= ( relation_rng @ SV8 ) ) ) )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(185,plain,
! [SV9: $i] :
( ( ( ~ ( empty @ SV9 ) )
= $false )
| ( ( ~ ( relation @ SV9 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(186,plain,
! [SV1: $i] :
( ( ( empty @ SV1 )
= $true )
| ( ( ~ ( relation @ SV1 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(187,plain,
( ( empty @ sK3_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(188,plain,
! [SV11: $i,SV3: $i,SV14: $i] :
( ( ( ~ ( ( SV14
!= ( relation_image @ SV3 @ SV11 ) )
| ! [SY65: $i] :
~ ( ~ ( ~ ( in @ SY65 @ SV14 )
| ~ ! [SY48: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY48 @ SY65 ) @ SV3 )
| ~ ( in @ SY48 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY49: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY49 @ SY65 ) @ SV3 )
| ~ ( in @ SY49 @ SV11 ) )
| ( in @ SY65 @ SV14 ) ) ) ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(189,plain,
! [SV11: $i,SV3: $i,SV14: $i] :
( ( ( ~ ( ~ ! [SY68: $i] :
~ ( ~ ( ~ ( in @ SY68 @ SV14 )
| ~ ! [SY51: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY51 @ SY68 ) @ SV3 )
| ~ ( in @ SY51 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY52 @ SY68 ) @ SV3 )
| ~ ( in @ SY52 @ SV11 ) )
| ( in @ SY68 @ SV14 ) ) )
| ( SV14
= ( relation_image @ SV3 @ SV11 ) ) ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(190,plain,
! [SV6: $i,SV12: $i] :
( ( ( ( SV12
!= ( relation_dom @ SV6 ) )
| ! [SY53: $i] :
~ ( ~ ( ~ ( in @ SY53 @ SV12 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY53 @ SY33 ) @ SV6 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY53 @ SY34 ) @ SV6 )
| ( in @ SY53 @ SV12 ) ) ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(191,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ! [SY56: $i] :
~ ( ~ ( ~ ( in @ SY56 @ SV12 )
| ~ ! [SY36: $i] :
~ ( in @ ( ordered_pair @ SY56 @ SY36 ) @ SV6 ) )
| ~ ( ~ ~ ! [SY37: $i] :
~ ( in @ ( ordered_pair @ SY56 @ SY37 ) @ SV6 )
| ( in @ SY56 @ SV12 ) ) )
| ( SV12
= ( relation_dom @ SV6 ) ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(192,plain,
! [SV8: $i,SV13: $i] :
( ( ( ( SV13
!= ( relation_rng @ SV8 ) )
| ! [SY59: $i] :
~ ( ~ ( ~ ( in @ SY59 @ SV13 )
| ~ ! [SY41: $i] :
~ ( in @ ( ordered_pair @ SY41 @ SY59 ) @ SV8 ) )
| ~ ( ~ ~ ! [SY42: $i] :
~ ( in @ ( ordered_pair @ SY42 @ SY59 ) @ SV8 )
| ( in @ SY59 @ SV13 ) ) ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(193,plain,
! [SV8: $i,SV13: $i] :
( ( ( ~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SV13 )
| ~ ! [SY44: $i] :
~ ( in @ ( ordered_pair @ SY44 @ SY62 ) @ SV8 ) )
| ~ ( ~ ~ ! [SY45: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY62 ) @ SV8 )
| ( in @ SY62 @ SV13 ) ) )
| ( SV13
= ( relation_rng @ SV8 ) ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(194,plain,
! [SV9: $i] :
( ( ( empty @ SV9 )
= $true )
| ( ( ~ ( relation @ SV9 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(195,plain,
! [SV1: $i] :
( ( ( relation @ SV1 )
= $false )
| ( ( empty @ SV1 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(196,plain,
! [SV11: $i,SV3: $i,SV14: $i] :
( ( ( ( SV14
!= ( relation_image @ SV3 @ SV11 ) )
| ! [SY65: $i] :
~ ( ~ ( ~ ( in @ SY65 @ SV14 )
| ~ ! [SY48: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY48 @ SY65 ) @ SV3 )
| ~ ( in @ SY48 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY49: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY49 @ SY65 ) @ SV3 )
| ~ ( in @ SY49 @ SV11 ) )
| ( in @ SY65 @ SV14 ) ) ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(197,plain,
! [SV11: $i,SV3: $i,SV14: $i] :
( ( ( ~ ! [SY68: $i] :
~ ( ~ ( ~ ( in @ SY68 @ SV14 )
| ~ ! [SY51: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY51 @ SY68 ) @ SV3 )
| ~ ( in @ SY51 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY52 @ SY68 ) @ SV3 )
| ~ ( in @ SY52 @ SV11 ) )
| ( in @ SY68 @ SV14 ) ) )
| ( SV14
= ( relation_image @ SV3 @ SV11 ) ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(198,plain,
! [SV6: $i,SV12: $i] :
( ( ( SV12
!= ( relation_dom @ SV6 ) )
= $true )
| ( ( ! [SY53: $i] :
~ ( ~ ( ~ ( in @ SY53 @ SV12 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY53 @ SY33 ) @ SV6 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY53 @ SY34 ) @ SV6 )
| ( in @ SY53 @ SV12 ) ) ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(199,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ! [SY56: $i] :
~ ( ~ ( ~ ( in @ SY56 @ SV12 )
| ~ ! [SY36: $i] :
~ ( in @ ( ordered_pair @ SY56 @ SY36 ) @ SV6 ) )
| ~ ( ~ ~ ! [SY37: $i] :
~ ( in @ ( ordered_pair @ SY56 @ SY37 ) @ SV6 )
| ( in @ SY56 @ SV12 ) ) ) )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(200,plain,
! [SV8: $i,SV13: $i] :
( ( ( SV13
!= ( relation_rng @ SV8 ) )
= $true )
| ( ( ! [SY59: $i] :
~ ( ~ ( ~ ( in @ SY59 @ SV13 )
| ~ ! [SY41: $i] :
~ ( in @ ( ordered_pair @ SY41 @ SY59 ) @ SV8 ) )
| ~ ( ~ ~ ! [SY42: $i] :
~ ( in @ ( ordered_pair @ SY42 @ SY59 ) @ SV8 )
| ( in @ SY59 @ SV13 ) ) ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(201,plain,
! [SV8: $i,SV13: $i] :
( ( ( ~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SV13 )
| ~ ! [SY44: $i] :
~ ( in @ ( ordered_pair @ SY44 @ SY62 ) @ SV8 ) )
| ~ ( ~ ~ ! [SY45: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY62 ) @ SV8 )
| ( in @ SY62 @ SV13 ) ) ) )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(202,plain,
! [SV9: $i] :
( ( ( relation @ SV9 )
= $false )
| ( ( empty @ SV9 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(203,plain,
! [SV1: $i] :
( ( ( empty @ ( relation_dom @ SV1 ) )
= $false )
| ( ( empty @ SV1 )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(204,plain,
! [SV11: $i,SV3: $i,SV14: $i] :
( ( ( SV14
!= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( ! [SY65: $i] :
~ ( ~ ( ~ ( in @ SY65 @ SV14 )
| ~ ! [SY48: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY48 @ SY65 ) @ SV3 )
| ~ ( in @ SY48 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY49: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY49 @ SY65 ) @ SV3 )
| ~ ( in @ SY49 @ SV11 ) )
| ( in @ SY65 @ SV14 ) ) ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(205,plain,
! [SV11: $i,SV3: $i,SV14: $i] :
( ( ( ~ ! [SY68: $i] :
~ ( ~ ( ~ ( in @ SY68 @ SV14 )
| ~ ! [SY51: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY51 @ SY68 ) @ SV3 )
| ~ ( in @ SY51 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY52 @ SY68 ) @ SV3 )
| ~ ( in @ SY52 @ SV11 ) )
| ( in @ SY68 @ SV14 ) ) ) )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(206,plain,
! [SV6: $i,SV12: $i] :
( ( ( SV12
= ( relation_dom @ SV6 ) )
= $false )
| ( ( ! [SY53: $i] :
~ ( ~ ( ~ ( in @ SY53 @ SV12 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY53 @ SY33 ) @ SV6 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY53 @ SY34 ) @ SV6 )
| ( in @ SY53 @ SV12 ) ) ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(207,plain,
! [SV6: $i,SV12: $i] :
( ( ( ! [SY56: $i] :
~ ( ~ ( ~ ( in @ SY56 @ SV12 )
| ~ ! [SY36: $i] :
~ ( in @ ( ordered_pair @ SY56 @ SY36 ) @ SV6 ) )
| ~ ( ~ ~ ! [SY37: $i] :
~ ( in @ ( ordered_pair @ SY56 @ SY37 ) @ SV6 )
| ( in @ SY56 @ SV12 ) ) ) )
= $false )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(208,plain,
! [SV8: $i,SV13: $i] :
( ( ( SV13
= ( relation_rng @ SV8 ) )
= $false )
| ( ( ! [SY59: $i] :
~ ( ~ ( ~ ( in @ SY59 @ SV13 )
| ~ ! [SY41: $i] :
~ ( in @ ( ordered_pair @ SY41 @ SY59 ) @ SV8 ) )
| ~ ( ~ ~ ! [SY42: $i] :
~ ( in @ ( ordered_pair @ SY42 @ SY59 ) @ SV8 )
| ( in @ SY59 @ SV13 ) ) ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(209,plain,
! [SV8: $i,SV13: $i] :
( ( ( ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SV13 )
| ~ ! [SY44: $i] :
~ ( in @ ( ordered_pair @ SY44 @ SY62 ) @ SV8 ) )
| ~ ( ~ ~ ! [SY45: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY62 ) @ SV8 )
| ( in @ SY62 @ SV13 ) ) ) )
= $false )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(210,plain,
! [SV9: $i] :
( ( ( empty @ ( relation_rng @ SV9 ) )
= $false )
| ( ( empty @ SV9 )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(211,plain,
! [SV11: $i,SV3: $i,SV14: $i] :
( ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( ! [SY65: $i] :
~ ( ~ ( ~ ( in @ SY65 @ SV14 )
| ~ ! [SY48: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY48 @ SY65 ) @ SV3 )
| ~ ( in @ SY48 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY49: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY49 @ SY65 ) @ SV3 )
| ~ ( in @ SY49 @ SV11 ) )
| ( in @ SY65 @ SV14 ) ) ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(212,plain,
! [SV11: $i,SV3: $i,SV14: $i] :
( ( ( ! [SY68: $i] :
~ ( ~ ( ~ ( in @ SY68 @ SV14 )
| ~ ! [SY51: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY51 @ SY68 ) @ SV3 )
| ~ ( in @ SY51 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY52 @ SY68 ) @ SV3 )
| ~ ( in @ SY52 @ SV11 ) )
| ( in @ SY68 @ SV14 ) ) ) )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(213,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV15 @ SV12 )
| ~ ! [SY71: $i] :
~ ( in @ ( ordered_pair @ SV15 @ SY71 ) @ SV6 ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ( in @ ( ordered_pair @ SV15 @ SY72 ) @ SV6 )
| ( in @ SV15 @ SV12 ) ) ) )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(214,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 )
| ~ ! [SY73: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY73 ) @ SV6 ) )
| ~ ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY74 ) @ SV6 )
| ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 ) ) ) )
= $false )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[207]) ).
thf(215,plain,
! [SV8: $i,SV13: $i,SV16: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV16 @ SV13 )
| ~ ! [SY75: $i] :
~ ( in @ ( ordered_pair @ SY75 @ SV16 ) @ SV8 ) )
| ~ ( ~ ~ ! [SY76: $i] :
~ ( in @ ( ordered_pair @ SY76 @ SV16 ) @ SV8 )
| ( in @ SV16 @ SV13 ) ) ) )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(216,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 )
| ~ ! [SY77: $i] :
~ ( in @ ( ordered_pair @ SY77 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 ) )
| ~ ( ~ ~ ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SY78 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 )
| ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 ) ) ) )
= $false )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[209]) ).
thf(217,plain,
! [SV11: $i,SV3: $i,SV14: $i,SV17: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV17 @ SV14 )
| ~ ! [SY79: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY79 @ SV17 ) @ SV3 )
| ~ ( in @ SY79 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY80: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY80 @ SV17 ) @ SV3 )
| ~ ( in @ SY80 @ SV11 ) )
| ( in @ SV17 @ SV14 ) ) ) )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(218,plain,
! [SV14: $i,SV3: $i,SV11: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 )
| ~ ! [SY81: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY81 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY81 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY82 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY82 @ SV11 ) )
| ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 ) ) ) )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[212]) ).
thf(219,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( ~ ( ~ ( in @ SV15 @ SV12 )
| ~ ! [SY71: $i] :
~ ( in @ ( ordered_pair @ SV15 @ SY71 ) @ SV6 ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ( in @ ( ordered_pair @ SV15 @ SY72 ) @ SV6 )
| ( in @ SV15 @ SV12 ) ) )
= $false )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(220,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 )
| ~ ! [SY73: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY73 ) @ SV6 ) )
| ~ ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY74 ) @ SV6 )
| ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 ) ) )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(221,plain,
! [SV8: $i,SV13: $i,SV16: $i] :
( ( ( ~ ( ~ ( in @ SV16 @ SV13 )
| ~ ! [SY75: $i] :
~ ( in @ ( ordered_pair @ SY75 @ SV16 ) @ SV8 ) )
| ~ ( ~ ~ ! [SY76: $i] :
~ ( in @ ( ordered_pair @ SY76 @ SV16 ) @ SV8 )
| ( in @ SV16 @ SV13 ) ) )
= $false )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(222,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 )
| ~ ! [SY77: $i] :
~ ( in @ ( ordered_pair @ SY77 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 ) )
| ~ ( ~ ~ ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SY78 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 )
| ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(223,plain,
! [SV11: $i,SV3: $i,SV14: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ SV17 @ SV14 )
| ~ ! [SY79: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY79 @ SV17 ) @ SV3 )
| ~ ( in @ SY79 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY80: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY80 @ SV17 ) @ SV3 )
| ~ ( in @ SY80 @ SV11 ) )
| ( in @ SV17 @ SV14 ) ) )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(224,plain,
! [SV14: $i,SV3: $i,SV11: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 )
| ~ ! [SY81: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY81 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY81 @ SV11 ) ) )
| ~ ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY82 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY82 @ SV11 ) )
| ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(225,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( ~ ( ~ ( in @ SV15 @ SV12 )
| ~ ! [SY71: $i] :
~ ( in @ ( ordered_pair @ SV15 @ SY71 ) @ SV6 ) ) )
= $false )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(226,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ( ~ ( ~ ~ ! [SY72: $i] :
~ ( in @ ( ordered_pair @ SV15 @ SY72 ) @ SV6 )
| ( in @ SV15 @ SV12 ) ) )
= $false )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(227,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 )
| ~ ! [SY73: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY73 ) @ SV6 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY74 ) @ SV6 )
| ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 ) ) )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(228,plain,
! [SV8: $i,SV13: $i,SV16: $i] :
( ( ( ~ ( ~ ( in @ SV16 @ SV13 )
| ~ ! [SY75: $i] :
~ ( in @ ( ordered_pair @ SY75 @ SV16 ) @ SV8 ) ) )
= $false )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(229,plain,
! [SV13: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( ~ ~ ! [SY76: $i] :
~ ( in @ ( ordered_pair @ SY76 @ SV16 ) @ SV8 )
| ( in @ SV16 @ SV13 ) ) )
= $false )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(230,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 )
| ~ ! [SY77: $i] :
~ ( in @ ( ordered_pair @ SY77 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SY78 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 )
| ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(231,plain,
! [SV11: $i,SV3: $i,SV14: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ SV17 @ SV14 )
| ~ ! [SY79: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY79 @ SV17 ) @ SV3 )
| ~ ( in @ SY79 @ SV11 ) ) ) )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(232,plain,
! [SV14: $i,SV11: $i,SV3: $i,SV17: $i] :
( ( ( ~ ( ~ ~ ! [SY80: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY80 @ SV17 ) @ SV3 )
| ~ ( in @ SY80 @ SV11 ) )
| ( in @ SV17 @ SV14 ) ) )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(233,plain,
! [SV14: $i,SV3: $i,SV11: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 )
| ~ ! [SY81: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY81 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY81 @ SV11 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY82 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY82 @ SV11 ) )
| ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(234,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( ~ ( in @ SV15 @ SV12 )
| ~ ! [SY71: $i] :
~ ( in @ ( ordered_pair @ SV15 @ SY71 ) @ SV6 ) )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(235,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ( ~ ~ ! [SY72: $i] :
~ ( in @ ( ordered_pair @ SV15 @ SY72 ) @ SV6 )
| ( in @ SV15 @ SV12 ) )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(236,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 )
| ~ ! [SY73: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY73 ) @ SV6 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY74 ) @ SV6 )
| ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 ) ) )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(237,plain,
! [SV8: $i,SV13: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ SV13 )
| ~ ! [SY75: $i] :
~ ( in @ ( ordered_pair @ SY75 @ SV16 ) @ SV8 ) )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(238,plain,
! [SV13: $i,SV8: $i,SV16: $i] :
( ( ( ~ ~ ! [SY76: $i] :
~ ( in @ ( ordered_pair @ SY76 @ SV16 ) @ SV8 )
| ( in @ SV16 @ SV13 ) )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(239,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 )
| ~ ! [SY77: $i] :
~ ( in @ ( ordered_pair @ SY77 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SY78 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 )
| ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(240,plain,
! [SV11: $i,SV3: $i,SV14: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ SV14 )
| ~ ! [SY79: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY79 @ SV17 ) @ SV3 )
| ~ ( in @ SY79 @ SV11 ) ) )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(241,plain,
! [SV14: $i,SV11: $i,SV3: $i,SV17: $i] :
( ( ( ~ ~ ! [SY80: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY80 @ SV17 ) @ SV3 )
| ~ ( in @ SY80 @ SV11 ) )
| ( in @ SV17 @ SV14 ) )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(242,plain,
! [SV14: $i,SV3: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 )
| ~ ! [SY81: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY81 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY81 @ SV11 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY82 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY82 @ SV11 ) )
| ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(243,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( ~ ( in @ SV15 @ SV12 ) )
= $true )
| ( ( ~ ! [SY71: $i] :
~ ( in @ ( ordered_pair @ SV15 @ SY71 ) @ SV6 ) )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(244,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ( ~ ~ ! [SY72: $i] :
~ ( in @ ( ordered_pair @ SV15 @ SY72 ) @ SV6 ) )
= $true )
| ( ( in @ SV15 @ SV12 )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(245,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY74 ) @ SV6 )
| ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 ) ) )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(246,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ! [SY73: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY73 ) @ SV6 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY74 ) @ SV6 )
| ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 ) ) )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(247,plain,
! [SV8: $i,SV13: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ SV13 ) )
= $true )
| ( ( ~ ! [SY75: $i] :
~ ( in @ ( ordered_pair @ SY75 @ SV16 ) @ SV8 ) )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(248,plain,
! [SV13: $i,SV8: $i,SV16: $i] :
( ( ( ~ ~ ! [SY76: $i] :
~ ( in @ ( ordered_pair @ SY76 @ SV16 ) @ SV8 ) )
= $true )
| ( ( in @ SV16 @ SV13 )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(249,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SY78 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 )
| ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(250,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ! [SY77: $i] :
~ ( in @ ( ordered_pair @ SY77 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SY78 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 )
| ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(251,plain,
! [SV11: $i,SV3: $i,SV14: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ SV14 ) )
= $true )
| ( ( ~ ! [SY79: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY79 @ SV17 ) @ SV3 )
| ~ ( in @ SY79 @ SV11 ) ) )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(252,plain,
! [SV14: $i,SV11: $i,SV3: $i,SV17: $i] :
( ( ( ~ ~ ! [SY80: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY80 @ SV17 ) @ SV3 )
| ~ ( in @ SY80 @ SV11 ) ) )
= $true )
| ( ( in @ SV17 @ SV14 )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(253,plain,
! [SV14: $i,SV3: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY82 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY82 @ SV11 ) )
| ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(254,plain,
! [SV14: $i,SV3: $i,SV11: $i] :
( ( ( ~ ! [SY81: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY81 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY81 @ SV11 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY82 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY82 @ SV11 ) )
| ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(255,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( in @ SV15 @ SV12 )
= $false )
| ( ( ~ ! [SY71: $i] :
~ ( in @ ( ordered_pair @ SV15 @ SY71 ) @ SV6 ) )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(256,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ( ~ ! [SY72: $i] :
~ ( in @ ( ordered_pair @ SV15 @ SY72 ) @ SV6 ) )
= $false )
| ( ( in @ SV15 @ SV12 )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(257,plain,
! [SV12: $i,SV6: $i] :
( ( ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 )
= $true )
| ( ( ~ ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY74 ) @ SV6 )
| ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 ) ) )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(258,plain,
! [SV12: $i,SV6: $i] :
( ( ( ! [SY73: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY73 ) @ SV6 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY74 ) @ SV6 )
| ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 ) ) )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(259,plain,
! [SV8: $i,SV13: $i,SV16: $i] :
( ( ( in @ SV16 @ SV13 )
= $false )
| ( ( ~ ! [SY75: $i] :
~ ( in @ ( ordered_pair @ SY75 @ SV16 ) @ SV8 ) )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(260,plain,
! [SV13: $i,SV8: $i,SV16: $i] :
( ( ( ~ ! [SY76: $i] :
~ ( in @ ( ordered_pair @ SY76 @ SV16 ) @ SV8 ) )
= $false )
| ( ( in @ SV16 @ SV13 )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(261,plain,
! [SV13: $i,SV8: $i] :
( ( ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 )
= $true )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SY78 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 )
| ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(262,plain,
! [SV13: $i,SV8: $i] :
( ( ( ! [SY77: $i] :
~ ( in @ ( ordered_pair @ SY77 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SY78 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 )
| ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(263,plain,
! [SV11: $i,SV3: $i,SV14: $i,SV17: $i] :
( ( ( in @ SV17 @ SV14 )
= $false )
| ( ( ~ ! [SY79: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY79 @ SV17 ) @ SV3 )
| ~ ( in @ SY79 @ SV11 ) ) )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(264,plain,
! [SV14: $i,SV11: $i,SV3: $i,SV17: $i] :
( ( ( ~ ! [SY80: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY80 @ SV17 ) @ SV3 )
| ~ ( in @ SY80 @ SV11 ) ) )
= $false )
| ( ( in @ SV17 @ SV14 )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(265,plain,
! [SV14: $i,SV3: $i,SV11: $i] :
( ( ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 )
= $true )
| ( ( ~ ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY82 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY82 @ SV11 ) )
| ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(266,plain,
! [SV14: $i,SV3: $i,SV11: $i] :
( ( ( ! [SY81: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY81 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY81 @ SV11 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY82 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY82 @ SV11 ) )
| ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(267,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ( ! [SY71: $i] :
~ ( in @ ( ordered_pair @ SV15 @ SY71 ) @ SV6 ) )
= $false )
| ( ( in @ SV15 @ SV12 )
= $false )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(268,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ( ! [SY72: $i] :
~ ( in @ ( ordered_pair @ SV15 @ SY72 ) @ SV6 ) )
= $true )
| ( ( in @ SV15 @ SV12 )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(269,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY74 ) @ SV6 )
| ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 ) )
= $false )
| ( ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(270,plain,
! [SV18: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV18 ) @ SV6 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY74 ) @ SV6 )
| ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 ) ) )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(271,plain,
! [SV13: $i,SV8: $i,SV16: $i] :
( ( ( ! [SY75: $i] :
~ ( in @ ( ordered_pair @ SY75 @ SV16 ) @ SV8 ) )
= $false )
| ( ( in @ SV16 @ SV13 )
= $false )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(272,plain,
! [SV13: $i,SV8: $i,SV16: $i] :
( ( ( ! [SY76: $i] :
~ ( in @ ( ordered_pair @ SY76 @ SV16 ) @ SV8 ) )
= $true )
| ( ( in @ SV16 @ SV13 )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(273,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ~ ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SY78 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 )
| ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 ) )
= $false )
| ( ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(274,plain,
! [SV13: $i,SV8: $i,SV19: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV19 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SY78 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 )
| ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(275,plain,
! [SV14: $i,SV11: $i,SV3: $i,SV17: $i] :
( ( ( ! [SY79: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY79 @ SV17 ) @ SV3 )
| ~ ( in @ SY79 @ SV11 ) ) )
= $false )
| ( ( in @ SV17 @ SV14 )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(276,plain,
! [SV14: $i,SV11: $i,SV3: $i,SV17: $i] :
( ( ( ! [SY80: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY80 @ SV17 ) @ SV3 )
| ~ ( in @ SY80 @ SV11 ) ) )
= $true )
| ( ( in @ SV17 @ SV14 )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(277,plain,
! [SV14: $i,SV3: $i,SV11: $i] :
( ( ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY82 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY82 @ SV11 ) )
| ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 ) )
= $false )
| ( ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(278,plain,
! [SV14: $i,SV3: $i,SV11: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV20 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SV20 @ SV11 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY82 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY82 @ SV11 ) )
| ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(279,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV15 @ ( sK7_SY71 @ SV12 @ SV6 @ SV15 ) ) @ SV6 ) )
= $false )
| ( ( in @ SV15 @ SV12 )
= $false )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[267]) ).
thf(280,plain,
! [SV12: $i,SV6: $i,SV21: $i,SV15: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV15 @ SV21 ) @ SV6 ) )
= $true )
| ( ( in @ SV15 @ SV12 )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(281,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY74 ) @ SV6 ) )
= $false )
| ( ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(282,plain,
! [SV12: $i,SV6: $i] :
( ( ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 )
= $false )
| ( ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(283,plain,
! [SV18: $i,SV12: $i,SV6: $i] :
( ( ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV18 ) @ SV6 )
= $false )
| ( ( ~ ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY74 ) @ SV6 )
| ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 ) ) )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(284,plain,
! [SV16: $i,SV8: $i,SV13: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK8_SY75 @ SV13 @ SV8 @ SV16 ) @ SV16 ) @ SV8 ) )
= $false )
| ( ( in @ SV16 @ SV13 )
= $false )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[271]) ).
thf(285,plain,
! [SV13: $i,SV8: $i,SV16: $i,SV22: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV22 @ SV16 ) @ SV8 ) )
= $true )
| ( ( in @ SV16 @ SV13 )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(286,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ~ ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SY78 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 ) )
= $false )
| ( ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(287,plain,
! [SV13: $i,SV8: $i] :
( ( ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 )
= $false )
| ( ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(288,plain,
! [SV13: $i,SV8: $i,SV19: $i] :
( ( ( in @ ( ordered_pair @ SV19 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 )
= $false )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SY78 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 )
| ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(289,plain,
! [SV17: $i,SV3: $i,SV11: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK9_SY79 @ SV14 @ SV11 @ SV3 @ SV17 ) @ SV17 ) @ SV3 )
| ~ ( in @ ( sK9_SY79 @ SV14 @ SV11 @ SV3 @ SV17 ) @ SV11 ) ) )
= $false )
| ( ( in @ SV17 @ SV14 )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[275]) ).
thf(290,plain,
! [SV14: $i,SV11: $i,SV3: $i,SV17: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV23 @ SV17 ) @ SV3 )
| ~ ( in @ SV23 @ SV11 ) ) )
= $true )
| ( ( in @ SV17 @ SV14 )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(291,plain,
! [SV14: $i,SV3: $i,SV11: $i] :
( ( ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY82 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY82 @ SV11 ) ) )
= $false )
| ( ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(292,plain,
! [SV14: $i,SV3: $i,SV11: $i] :
( ( ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 )
= $false )
| ( ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(293,plain,
! [SV14: $i,SV3: $i,SV11: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV20 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SV20 @ SV11 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY82 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY82 @ SV11 ) )
| ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(294,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( in @ ( ordered_pair @ SV15 @ ( sK7_SY71 @ SV12 @ SV6 @ SV15 ) ) @ SV6 )
= $true )
| ( ( in @ SV15 @ SV12 )
= $false )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(295,plain,
! [SV12: $i,SV6: $i,SV21: $i,SV15: $i] :
( ( ( in @ ( ordered_pair @ SV15 @ SV21 ) @ SV6 )
= $false )
| ( ( in @ SV15 @ SV12 )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(296,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY74 ) @ SV6 ) )
= $true )
| ( ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(297,plain,
! [SV18: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY74 ) @ SV6 )
| ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV18 ) @ SV6 )
= $false )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(298,plain,
! [SV16: $i,SV8: $i,SV13: $i] :
( ( ( in @ ( ordered_pair @ ( sK8_SY75 @ SV13 @ SV8 @ SV16 ) @ SV16 ) @ SV8 )
= $true )
| ( ( in @ SV16 @ SV13 )
= $false )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(299,plain,
! [SV13: $i,SV8: $i,SV16: $i,SV22: $i] :
( ( ( in @ ( ordered_pair @ SV22 @ SV16 ) @ SV8 )
= $false )
| ( ( in @ SV16 @ SV13 )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(300,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SY78 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 ) )
= $true )
| ( ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(301,plain,
! [SV19: $i,SV13: $i,SV8: $i] :
( ( ( ~ ~ ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SY78 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 )
| ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV19 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 )
= $false )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(302,plain,
! [SV17: $i,SV3: $i,SV11: $i,SV14: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK9_SY79 @ SV14 @ SV11 @ SV3 @ SV17 ) @ SV17 ) @ SV3 )
| ~ ( in @ ( sK9_SY79 @ SV14 @ SV11 @ SV3 @ SV17 ) @ SV11 ) ) )
= $true )
| ( ( in @ SV17 @ SV14 )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(303,plain,
! [SV14: $i,SV11: $i,SV3: $i,SV17: $i,SV23: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV23 @ SV17 ) @ SV3 )
| ~ ( in @ SV23 @ SV11 ) ) )
= $false )
| ( ( in @ SV17 @ SV14 )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(304,plain,
! [SV14: $i,SV3: $i,SV11: $i] :
( ( ( ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY82 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY82 @ SV11 ) ) )
= $true )
| ( ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[291]) ).
thf(305,plain,
! [SV14: $i,SV3: $i,SV11: $i,SV20: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV20 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SV20 @ SV11 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY82 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY82 @ SV11 ) )
| ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(306,plain,
! [SV12: $i,SV6: $i] :
( ( ( ! [SY74: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY74 ) @ SV6 ) )
= $false )
| ( ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(307,plain,
! [SV18: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY74 ) @ SV6 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV18 ) @ SV6 )
= $false )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(308,plain,
! [SV18: $i,SV12: $i,SV6: $i] :
( ( ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV18 ) @ SV6 )
= $false )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(309,plain,
! [SV13: $i,SV8: $i] :
( ( ( ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SY78 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 ) )
= $false )
| ( ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(310,plain,
! [SV19: $i,SV13: $i,SV8: $i] :
( ( ( ~ ~ ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SY78 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV19 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 )
= $false )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(311,plain,
! [SV19: $i,SV13: $i,SV8: $i] :
( ( ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 )
= $false )
| ( ( in @ ( ordered_pair @ SV19 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 )
= $false )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(312,plain,
! [SV17: $i,SV3: $i,SV11: $i,SV14: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK9_SY79 @ SV14 @ SV11 @ SV3 @ SV17 ) @ SV17 ) @ SV3 )
| ~ ( in @ ( sK9_SY79 @ SV14 @ SV11 @ SV3 @ SV17 ) @ SV11 ) )
= $false )
| ( ( in @ SV17 @ SV14 )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(313,plain,
! [SV14: $i,SV11: $i,SV3: $i,SV17: $i,SV23: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV23 @ SV17 ) @ SV3 )
| ~ ( in @ SV23 @ SV11 ) )
= $true )
| ( ( in @ SV17 @ SV14 )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[303]) ).
thf(314,plain,
! [SV14: $i,SV3: $i,SV11: $i] :
( ( ( ! [SY82: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY82 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY82 @ SV11 ) ) )
= $false )
| ( ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(315,plain,
! [SV14: $i,SV3: $i,SV11: $i,SV20: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV20 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 ) )
= $true )
| ( ( ~ ( in @ SV20 @ SV11 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY82 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY82 @ SV11 ) )
| ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(316,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ ( sK10_SY74 @ SV12 @ SV6 ) ) @ SV6 ) )
= $false )
| ( ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[306]) ).
thf(317,plain,
! [SV18: $i,SV12: $i,SV6: $i] :
( ( ( ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY74 ) @ SV6 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV18 ) @ SV6 )
= $false )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(318,plain,
! [SV8: $i,SV13: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK11_SY78 @ SV13 @ SV8 ) @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 ) )
= $false )
| ( ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[309]) ).
thf(319,plain,
! [SV19: $i,SV13: $i,SV8: $i] :
( ( ( ~ ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SY78 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV19 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 )
= $false )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(320,plain,
! [SV17: $i,SV3: $i,SV11: $i,SV14: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK9_SY79 @ SV14 @ SV11 @ SV3 @ SV17 ) @ SV17 ) @ SV3 ) )
= $false )
| ( ( in @ SV17 @ SV14 )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[312]) ).
thf(321,plain,
! [SV17: $i,SV3: $i,SV11: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK9_SY79 @ SV14 @ SV11 @ SV3 @ SV17 ) @ SV11 ) )
= $false )
| ( ( in @ SV17 @ SV14 )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[312]) ).
thf(322,plain,
! [SV14: $i,SV11: $i,SV3: $i,SV17: $i,SV23: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV23 @ SV17 ) @ SV3 ) )
= $true )
| ( ( ~ ( in @ SV23 @ SV11 ) )
= $true )
| ( ( in @ SV17 @ SV14 )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(323,plain,
! [SV11: $i,SV3: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK12_SY82 @ SV14 @ SV3 @ SV11 ) @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ ( sK12_SY82 @ SV14 @ SV3 @ SV11 ) @ SV11 ) ) )
= $false )
| ( ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[314]) ).
thf(324,plain,
! [SV14: $i,SV3: $i,SV11: $i,SV20: $i] :
( ( ( in @ ( ordered_pair @ SV20 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
= $false )
| ( ( ~ ( in @ SV20 @ SV11 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY82 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY82 @ SV11 ) )
| ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(325,plain,
! [SV12: $i,SV6: $i] :
( ( ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ ( sK10_SY74 @ SV12 @ SV6 ) ) @ SV6 )
= $true )
| ( ( in @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV12 )
= $true )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(326,plain,
! [SV18: $i,SV12: $i,SV6: $i] :
( ( ( ! [SY74: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SY74 ) @ SV6 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV18 ) @ SV6 )
= $false )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(327,plain,
! [SV8: $i,SV13: $i] :
( ( ( in @ ( ordered_pair @ ( sK11_SY78 @ SV13 @ SV8 ) @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 )
= $true )
| ( ( in @ ( sK5_SY62 @ SV8 @ SV13 ) @ SV13 )
= $true )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[318]) ).
thf(328,plain,
! [SV19: $i,SV13: $i,SV8: $i] :
( ( ( ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SY78 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV19 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 )
= $false )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(329,plain,
! [SV17: $i,SV3: $i,SV11: $i,SV14: $i] :
( ( ( in @ ( ordered_pair @ ( sK9_SY79 @ SV14 @ SV11 @ SV3 @ SV17 ) @ SV17 ) @ SV3 )
= $true )
| ( ( in @ SV17 @ SV14 )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(330,plain,
! [SV17: $i,SV3: $i,SV11: $i,SV14: $i] :
( ( ( in @ ( sK9_SY79 @ SV14 @ SV11 @ SV3 @ SV17 ) @ SV11 )
= $true )
| ( ( in @ SV17 @ SV14 )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(331,plain,
! [SV14: $i,SV11: $i,SV3: $i,SV17: $i,SV23: $i] :
( ( ( in @ ( ordered_pair @ SV23 @ SV17 ) @ SV3 )
= $false )
| ( ( ~ ( in @ SV23 @ SV11 ) )
= $true )
| ( ( in @ SV17 @ SV14 )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(332,plain,
! [SV11: $i,SV3: $i,SV14: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_SY82 @ SV14 @ SV3 @ SV11 ) @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ ( sK12_SY82 @ SV14 @ SV3 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(333,plain,
! [SV14: $i,SV3: $i,SV11: $i,SV20: $i] :
( ( ( in @ SV20 @ SV11 )
= $false )
| ( ( in @ ( ordered_pair @ SV20 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
= $false )
| ( ( ~ ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY82 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY82 @ SV11 ) )
| ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(334,plain,
! [SV18: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ ( sK13_SY74 @ SV18 @ SV12 @ SV6 ) ) @ SV6 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV18 ) @ SV6 )
= $false )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[326]) ).
thf(335,plain,
! [SV8: $i,SV13: $i,SV19: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_SY78 @ SV19 @ SV13 @ SV8 ) @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV19 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 )
= $false )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[328]) ).
thf(336,plain,
! [SV14: $i,SV3: $i,SV17: $i,SV11: $i,SV23: $i] :
( ( ( in @ SV23 @ SV11 )
= $false )
| ( ( in @ ( ordered_pair @ SV23 @ SV17 ) @ SV3 )
= $false )
| ( ( in @ SV17 @ SV14 )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(337,plain,
! [SV11: $i,SV3: $i,SV14: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK12_SY82 @ SV14 @ SV3 @ SV11 ) @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ ( sK12_SY82 @ SV14 @ SV3 @ SV11 ) @ SV11 ) )
= $false )
| ( ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(338,plain,
! [SV20: $i,SV14: $i,SV3: $i,SV11: $i] :
( ( ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY82 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY82 @ SV11 ) )
| ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV20 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
= $false )
| ( ( in @ SV20 @ SV11 )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(339,plain,
! [SV18: $i,SV12: $i,SV6: $i] :
( ( ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ ( sK13_SY74 @ SV18 @ SV12 @ SV6 ) ) @ SV6 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK4_SY56 @ SV6 @ SV12 ) @ SV18 ) @ SV6 )
= $false )
| ( ( SV12
= ( relation_dom @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(340,plain,
! [SV8: $i,SV13: $i,SV19: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_SY78 @ SV19 @ SV13 @ SV8 ) @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 )
= $true )
| ( ( in @ ( ordered_pair @ SV19 @ ( sK5_SY62 @ SV8 @ SV13 ) ) @ SV8 )
= $false )
| ( ( SV13
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(341,plain,
! [SV11: $i,SV3: $i,SV14: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK12_SY82 @ SV14 @ SV3 @ SV11 ) @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 ) )
= $false )
| ( ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[337]) ).
thf(342,plain,
! [SV11: $i,SV3: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK12_SY82 @ SV14 @ SV3 @ SV11 ) @ SV11 ) )
= $false )
| ( ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[337]) ).
thf(343,plain,
! [SV20: $i,SV14: $i,SV3: $i,SV11: $i] :
( ( ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY82 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY82 @ SV11 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV20 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
= $false )
| ( ( in @ SV20 @ SV11 )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[338]) ).
thf(344,plain,
! [SV20: $i,SV14: $i,SV3: $i,SV11: $i] :
( ( ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 )
= $false )
| ( ( in @ ( ordered_pair @ SV20 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
= $false )
| ( ( in @ SV20 @ SV11 )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[338]) ).
thf(345,plain,
! [SV11: $i,SV3: $i,SV14: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_SY82 @ SV14 @ SV3 @ SV11 ) @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
= $true )
| ( ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(346,plain,
! [SV11: $i,SV3: $i,SV14: $i] :
( ( ( in @ ( sK12_SY82 @ SV14 @ SV3 @ SV11 ) @ SV11 )
= $true )
| ( ( in @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(347,plain,
! [SV20: $i,SV14: $i,SV3: $i,SV11: $i] :
( ( ( ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY82 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY82 @ SV11 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV20 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
= $false )
| ( ( in @ SV20 @ SV11 )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(348,plain,
! [SV20: $i,SV14: $i,SV3: $i,SV11: $i] :
( ( ( ! [SY82: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY82 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ SY82 @ SV11 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV20 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
= $false )
| ( ( in @ SV20 @ SV11 )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(349,plain,
! [SV11: $i,SV3: $i,SV14: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK15_SY82 @ SV20 @ SV14 @ SV3 @ SV11 ) @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ ( sK15_SY82 @ SV20 @ SV14 @ SV3 @ SV11 ) @ SV11 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV20 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
= $false )
| ( ( in @ SV20 @ SV11 )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[348]) ).
thf(350,plain,
! [SV11: $i,SV3: $i,SV14: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK15_SY82 @ SV20 @ SV14 @ SV3 @ SV11 ) @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ ( sK15_SY82 @ SV20 @ SV14 @ SV3 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV20 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
= $false )
| ( ( in @ SV20 @ SV11 )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(351,plain,
! [SV11: $i,SV3: $i,SV14: $i,SV20: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK15_SY82 @ SV20 @ SV14 @ SV3 @ SV11 ) @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
| ~ ( in @ ( sK15_SY82 @ SV20 @ SV14 @ SV3 @ SV11 ) @ SV11 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV20 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
= $false )
| ( ( in @ SV20 @ SV11 )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(352,plain,
! [SV11: $i,SV3: $i,SV14: $i,SV20: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK15_SY82 @ SV20 @ SV14 @ SV3 @ SV11 ) @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV20 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
= $false )
| ( ( in @ SV20 @ SV11 )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[351]) ).
thf(353,plain,
! [SV11: $i,SV3: $i,SV14: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK15_SY82 @ SV20 @ SV14 @ SV3 @ SV11 ) @ SV11 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV20 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
= $false )
| ( ( in @ SV20 @ SV11 )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[351]) ).
thf(354,plain,
! [SV11: $i,SV3: $i,SV14: $i,SV20: $i] :
( ( ( in @ ( ordered_pair @ ( sK15_SY82 @ SV20 @ SV14 @ SV3 @ SV11 ) @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
= $true )
| ( ( in @ ( ordered_pair @ SV20 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
= $false )
| ( ( in @ SV20 @ SV11 )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(355,plain,
! [SV11: $i,SV3: $i,SV14: $i,SV20: $i] :
( ( ( in @ ( sK15_SY82 @ SV20 @ SV14 @ SV3 @ SV11 ) @ SV11 )
= $true )
| ( ( in @ ( ordered_pair @ SV20 @ ( sK6_SY68 @ SV11 @ SV3 @ SV14 ) ) @ SV3 )
= $false )
| ( ( in @ SV20 @ SV11 )
= $false )
| ( ( SV14
= ( relation_image @ SV3 @ SV11 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(356,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[78,355,354,346,345,344,340,339,336,330,329,327,325,311,308,299,298,295,294,292,287,282,210,203,187,180,179,177,176,175,173,172,155,142,141,140,109,95,86,85,84,83,82,81,80,79]) ).
thf(357,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[356]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU206+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
% 0.07/0.17 % Computer : n001.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 15:11:09 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.12/0.47
% 1.12/0.47 No.of.Axioms: 21
% 1.12/0.47
% 1.12/0.47 Length.of.Defs: 0
% 1.12/0.47
% 1.12/0.47 Contains.Choice.Funs: false
% 1.12/0.47 ..........
% 1.12/0.47
% 1.12/0.47 ********************************
% 1.12/0.47 * All subproblems solved! *
% 1.12/0.47 ********************************
% 1.12/0.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:22,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:356,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.12/0.47
% 1.12/0.47 %**** Beginning of derivation protocol ****
% 1.12/0.47 % SZS output start CNFRefutation
% See solution above
% 1.12/0.47
% 1.12/0.47 %**** End of derivation protocol ****
% 1.12/0.47 %**** no. of clauses in derivation: 333 ****
% 1.12/0.47 %**** clause counter: 356 ****
% 1.12/0.47
% 1.12/0.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:22,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:356,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------