%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU178+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 : n003.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 10:43:16 AM UTC 2026
% Result : Theorem 1.73s 0.54s
% Output : CNFRefutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 19
% Syntax : Number of formulae : 281 ( 108 unt; 0 typ; 0 def)
% Number of atoms : 2219 ( 754 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 4422 (1093 ~; 698 |; 12 &;2579 @)
% ( 24 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 5 con; 0-3 aty)
% Number of variables : 859 ( 0 ^; 850 !; 9 ?; 859 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_sK10_SY81,type,
sK10_SY81: $i > $i > $i > $i ).
thf(tp_sK11_SY80,type,
sK11_SY80: $i > $i > $i ).
thf(tp_sK12_SY84,type,
sK12_SY84: $i > $i > $i ).
thf(tp_sK13_SY80,type,
sK13_SY80: $i > $i > $i > $i ).
thf(tp_sK14_SY84,type,
sK14_SY84: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY38,type,
sK3_SY38: $i > $i ).
thf(tp_sK4_SY57,type,
sK4_SY57: $i > $i > $i ).
thf(tp_sK5_SY64,type,
sK5_SY64: $i > $i > $i ).
thf(tp_sK6_SY70,type,
sK6_SY70: $i > $i > $i ).
thf(tp_sK7_SY73,type,
sK7_SY73: $i > $i > $i ).
thf(tp_sK8_SY86,type,
sK8_SY86: $i > $i > $i ).
thf(tp_sK9_SY77,type,
sK9_SY77: $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(6,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(10,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(15,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(23,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(24,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(25,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(26,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(27,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(28,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(29,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(30,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(31,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(33,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(34,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(35,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(36,axiom,
! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
thf(39,conjecture,
! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
thf(40,negated_conjecture,
( ( ! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[39]) ).
thf(41,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[40]) ).
thf(42,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(43,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(44,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(45,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(46,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(47,plain,
$true = $true,
inference(unfold_def,[status(thm)],[23]) ).
thf(48,plain,
$true = $true,
inference(unfold_def,[status(thm)],[24]) ).
thf(49,plain,
$true = $true,
inference(unfold_def,[status(thm)],[25]) ).
thf(50,plain,
$true = $true,
inference(unfold_def,[status(thm)],[26]) ).
thf(51,plain,
$true = $true,
inference(unfold_def,[status(thm)],[27]) ).
thf(52,plain,
$true = $true,
inference(unfold_def,[status(thm)],[28]) ).
thf(53,plain,
$true = $true,
inference(unfold_def,[status(thm)],[29]) ).
thf(54,plain,
$true = $true,
inference(unfold_def,[status(thm)],[30]) ).
thf(55,plain,
$true = $true,
inference(unfold_def,[status(thm)],[31]) ).
thf(56,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)],[33]) ).
thf(57,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)],[34]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(59,plain,
( ( ! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(60,plain,
( ( ( relation @ sK1_A )
=> ( subset @ sK1_A @ ( cartesian_product2 @ ( relation_dom @ sK1_A ) @ ( relation_rng @ sK1_A ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[41]) ).
thf(61,plain,
( ( relation @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[60]) ).
thf(62,plain,
( ( subset @ sK1_A @ ( cartesian_product2 @ ( relation_dom @ sK1_A ) @ ( relation_rng @ sK1_A ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[60]) ).
thf(63,plain,
( ( ~ ( subset @ sK1_A @ ( cartesian_product2 @ ( relation_dom @ sK1_A ) @ ( relation_rng @ sK1_A ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[62]) ).
thf(64,plain,
( ( ! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(65,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(66,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)],[57]) ).
thf(67,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)],[56]) ).
thf(68,plain,
$true = $true,
inference(copy,[status(thm)],[55]) ).
thf(69,plain,
$true = $true,
inference(copy,[status(thm)],[54]) ).
thf(70,plain,
$true = $true,
inference(copy,[status(thm)],[53]) ).
thf(71,plain,
$true = $true,
inference(copy,[status(thm)],[52]) ).
thf(72,plain,
$true = $true,
inference(copy,[status(thm)],[51]) ).
thf(73,plain,
$true = $true,
inference(copy,[status(thm)],[50]) ).
thf(74,plain,
$true = $true,
inference(copy,[status(thm)],[49]) ).
thf(75,plain,
$true = $true,
inference(copy,[status(thm)],[48]) ).
thf(76,plain,
$true = $true,
inference(copy,[status(thm)],[47]) ).
thf(77,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(78,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(80,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(81,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(82,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(83,plain,
( ( ~ ( subset @ sK1_A @ ( cartesian_product2 @ ( relation_dom @ sK1_A ) @ ( relation_rng @ sK1_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(84,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)],[66]) ).
thf(85,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ! [SX2: $i,SX3: $i] :
( SX1
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ! [SX2: $i,SX3: $i] :
( SX1
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(86,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(87,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)],[67]) ).
thf(88,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ~ ( empty @ SX1 ) )
| ~ ( empty @ ( cartesian_product2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(89,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(90,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(91,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(92,plain,
! [SV1: $i] :
( ( ! [SY27: $i] : ( subset @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(93,plain,
( ( subset @ sK1_A @ ( cartesian_product2 @ ( relation_dom @ sK1_A ) @ ( relation_rng @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(94,plain,
! [SV2: $i] :
( ( ~ ( relation @ SV2 )
| ! [SY28: $i] :
~ ( ~ ( ( SY28
!= ( relation_dom @ SV2 ) )
| ! [SY29: $i] :
~ ( ~ ( ~ ( in @ SY29 @ SY28 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY29 @ SY30 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY29 @ SY31 ) @ SV2 )
| ( in @ SY29 @ SY28 ) ) ) )
| ~ ( ~ ! [SY32: $i] :
~ ( ~ ( ~ ( in @ SY32 @ SY28 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY33 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY34 ) @ SV2 )
| ( in @ SY32 @ SY28 ) ) )
| ( SY28
= ( relation_dom @ SV2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(95,plain,
! [SV3: $i] :
( ( ~ ( ~ ( ~ ( relation @ SV3 )
| ! [SY35: $i] :
~ ~ ( ~ ( in @ SY35 @ SV3 )
| ~ ! [SX2: $i,SX3: $i] :
( SY35
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SY38: $i] :
~ ~ ( ~ ( in @ SY38 @ SV3 )
| ~ ! [SX2: $i,SX3: $i] :
( SY38
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(96,plain,
! [SV4: $i] :
( ( ! [SY41: $i] :
~ ( ~ ( ~ ( subset @ SV4 @ SY41 )
| ! [SY42: $i] :
( ~ ( in @ SY42 @ SV4 )
| ( in @ SY42 @ SY41 ) ) )
| ~ ( ~ ! [SY43: $i] :
( ~ ( in @ SY43 @ SV4 )
| ( in @ SY43 @ SY41 ) )
| ( subset @ SV4 @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(97,plain,
! [SV5: $i] :
( ( ~ ( relation @ SV5 )
| ! [SY44: $i] :
~ ( ~ ( ( SY44
!= ( relation_rng @ SV5 ) )
| ! [SY45: $i] :
~ ( ~ ( ~ ( in @ SY45 @ SY44 )
| ~ ! [SY46: $i] :
~ ( in @ ( ordered_pair @ SY46 @ SY45 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY47: $i] :
~ ( in @ ( ordered_pair @ SY47 @ SY45 ) @ SV5 )
| ( in @ SY45 @ SY44 ) ) ) )
| ~ ( ~ ! [SY48: $i] :
~ ( ~ ( ~ ( in @ SY48 @ SY44 )
| ~ ! [SY49: $i] :
~ ( in @ ( ordered_pair @ SY49 @ SY48 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY50: $i] :
~ ( in @ ( ordered_pair @ SY50 @ SY48 ) @ SV5 )
| ( in @ SY48 @ SY44 ) ) )
| ( SY44
= ( relation_rng @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(98,plain,
! [SV6: $i] :
( ( ! [SY51: $i] :
( ~ ~ ( ~ ~ ( empty @ SV6 )
| ~ ~ ( empty @ SY51 ) )
| ~ ( empty @ ( cartesian_product2 @ SV6 @ SY51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(99,plain,
! [SV7: $i] :
( ( ! [SY52: $i] :
~ ( ~ ( ~ ( element @ SV7 @ ( powerset @ SY52 ) )
| ( subset @ SV7 @ SY52 ) )
| ~ ( ~ ( subset @ SV7 @ SY52 )
| ( element @ SV7 @ ( powerset @ SY52 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(100,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(101,plain,
! [SV8: $i] :
( ( ! [SY53: $i,SY54: $i,SY55: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV8 @ SY53 ) @ ( cartesian_product2 @ SY54 @ SY55 ) )
| ~ ( ~ ( in @ SV8 @ SY54 )
| ~ ( in @ SY53 @ SY55 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV8 @ SY54 )
| ~ ( in @ SY53 @ SY55 ) )
| ( in @ ( ordered_pair @ SV8 @ SY53 ) @ ( cartesian_product2 @ SY54 @ SY55 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(102,plain,
! [SV1: $i] :
( ( subset @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(103,plain,
! [SV2: $i] :
( ( ( ~ ( relation @ SV2 ) )
= $true )
| ( ( ! [SY28: $i] :
~ ( ~ ( ( SY28
!= ( relation_dom @ SV2 ) )
| ! [SY29: $i] :
~ ( ~ ( ~ ( in @ SY29 @ SY28 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY29 @ SY30 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY29 @ SY31 ) @ SV2 )
| ( in @ SY29 @ SY28 ) ) ) )
| ~ ( ~ ! [SY32: $i] :
~ ( ~ ( ~ ( in @ SY32 @ SY28 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY33 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY34 ) @ SV2 )
| ( in @ SY32 @ SY28 ) ) )
| ( SY28
= ( relation_dom @ SV2 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(104,plain,
! [SV3: $i] :
( ( ~ ( ~ ( relation @ SV3 )
| ! [SY35: $i] :
~ ~ ( ~ ( in @ SY35 @ SV3 )
| ~ ! [SX2: $i,SX3: $i] :
( SY35
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SY38: $i] :
~ ~ ( ~ ( in @ SY38 @ SV3 )
| ~ ! [SX2: $i,SX3: $i] :
( SY38
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV3 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(105,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV4 @ SV10 )
| ! [SY56: $i] :
( ~ ( in @ SY56 @ SV4 )
| ( in @ SY56 @ SV10 ) ) )
| ~ ( ~ ! [SY57: $i] :
( ~ ( in @ SY57 @ SV4 )
| ( in @ SY57 @ SV10 ) )
| ( subset @ SV4 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(106,plain,
! [SV5: $i] :
( ( ( ~ ( relation @ SV5 ) )
= $true )
| ( ( ! [SY44: $i] :
~ ( ~ ( ( SY44
!= ( relation_rng @ SV5 ) )
| ! [SY45: $i] :
~ ( ~ ( ~ ( in @ SY45 @ SY44 )
| ~ ! [SY46: $i] :
~ ( in @ ( ordered_pair @ SY46 @ SY45 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY47: $i] :
~ ( in @ ( ordered_pair @ SY47 @ SY45 ) @ SV5 )
| ( in @ SY45 @ SY44 ) ) ) )
| ~ ( ~ ! [SY48: $i] :
~ ( ~ ( ~ ( in @ SY48 @ SY44 )
| ~ ! [SY49: $i] :
~ ( in @ ( ordered_pair @ SY49 @ SY48 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY50: $i] :
~ ( in @ ( ordered_pair @ SY50 @ SY48 ) @ SV5 )
| ( in @ SY48 @ SY44 ) ) )
| ( SY44
= ( relation_rng @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(107,plain,
! [SV11: $i,SV6: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV6 )
| ~ ~ ( empty @ SV11 ) )
| ~ ( empty @ ( cartesian_product2 @ SV6 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(108,plain,
! [SV12: $i,SV7: $i] :
( ( ~ ( ~ ( ~ ( element @ SV7 @ ( powerset @ SV12 ) )
| ( subset @ SV7 @ SV12 ) )
| ~ ( ~ ( subset @ SV7 @ SV12 )
| ( element @ SV7 @ ( powerset @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(109,plain,
( ( ~ ~ ( ~ ( empty @ sK2_SX0 )
| ~ ( relation @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[100]) ).
thf(110,plain,
! [SV13: $i,SV8: $i] :
( ( ! [SY58: $i,SY59: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SY58 @ SY59 ) )
| ~ ( ~ ( in @ SV8 @ SY58 )
| ~ ( in @ SV13 @ SY59 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV8 @ SY58 )
| ~ ( in @ SV13 @ SY59 ) )
| ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SY58 @ SY59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(111,plain,
! [SV2: $i] :
( ( ( relation @ SV2 )
= $false )
| ( ( ! [SY28: $i] :
~ ( ~ ( ( SY28
!= ( relation_dom @ SV2 ) )
| ! [SY29: $i] :
~ ( ~ ( ~ ( in @ SY29 @ SY28 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY29 @ SY30 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY29 @ SY31 ) @ SV2 )
| ( in @ SY29 @ SY28 ) ) ) )
| ~ ( ~ ! [SY32: $i] :
~ ( ~ ( ~ ( in @ SY32 @ SY28 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY33 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY34 ) @ SV2 )
| ( in @ SY32 @ SY28 ) ) )
| ( SY28
= ( relation_dom @ SV2 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(112,plain,
! [SV3: $i] :
( ( ~ ( ~ ( relation @ SV3 )
| ! [SY35: $i] :
~ ~ ( ~ ( in @ SY35 @ SV3 )
| ~ ! [SX2: $i,SX3: $i] :
( SY35
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[104]) ).
thf(113,plain,
! [SV3: $i] :
( ( ~ ( ~ ! [SY38: $i] :
~ ~ ( ~ ( in @ SY38 @ SV3 )
| ~ ! [SX2: $i,SX3: $i] :
( SY38
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[104]) ).
thf(114,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ( subset @ SV4 @ SV10 )
| ! [SY56: $i] :
( ~ ( in @ SY56 @ SV4 )
| ( in @ SY56 @ SV10 ) ) )
| ~ ( ~ ! [SY57: $i] :
( ~ ( in @ SY57 @ SV4 )
| ( in @ SY57 @ SV10 ) )
| ( subset @ SV4 @ SV10 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(115,plain,
! [SV5: $i] :
( ( ( relation @ SV5 )
= $false )
| ( ( ! [SY44: $i] :
~ ( ~ ( ( SY44
!= ( relation_rng @ SV5 ) )
| ! [SY45: $i] :
~ ( ~ ( ~ ( in @ SY45 @ SY44 )
| ~ ! [SY46: $i] :
~ ( in @ ( ordered_pair @ SY46 @ SY45 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY47: $i] :
~ ( in @ ( ordered_pair @ SY47 @ SY45 ) @ SV5 )
| ( in @ SY45 @ SY44 ) ) ) )
| ~ ( ~ ! [SY48: $i] :
~ ( ~ ( ~ ( in @ SY48 @ SY44 )
| ~ ! [SY49: $i] :
~ ( in @ ( ordered_pair @ SY49 @ SY48 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY50: $i] :
~ ( in @ ( ordered_pair @ SY50 @ SY48 ) @ SV5 )
| ( in @ SY48 @ SY44 ) ) )
| ( SY44
= ( relation_rng @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(116,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV6 )
| ~ ~ ( empty @ SV11 ) ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV6 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(117,plain,
! [SV12: $i,SV7: $i] :
( ( ~ ( ~ ( element @ SV7 @ ( powerset @ SV12 ) )
| ( subset @ SV7 @ SV12 ) )
| ~ ( ~ ( subset @ SV7 @ SV12 )
| ( element @ SV7 @ ( powerset @ SV12 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(118,plain,
( ( ~ ( ~ ( empty @ sK2_SX0 )
| ~ ( relation @ sK2_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(119,plain,
! [SV14: $i,SV13: $i,SV8: $i] :
( ( ! [SY60: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SY60 ) )
| ~ ( ~ ( in @ SV8 @ SV14 )
| ~ ( in @ SV13 @ SY60 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV8 @ SV14 )
| ~ ( in @ SV13 @ SY60 ) )
| ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SY60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(120,plain,
! [SV2: $i,SV15: $i] :
( ( ( ~ ( ~ ( ( SV15
!= ( relation_dom @ SV2 ) )
| ! [SY61: $i] :
~ ( ~ ( ~ ( in @ SY61 @ SV15 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY61 @ SY30 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY61 @ SY31 ) @ SV2 )
| ( in @ SY61 @ SV15 ) ) ) )
| ~ ( ~ ! [SY64: $i] :
~ ( ~ ( ~ ( in @ SY64 @ SV15 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY64 @ SY33 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY64 @ SY34 ) @ SV2 )
| ( in @ SY64 @ SV15 ) ) )
| ( SV15
= ( relation_dom @ SV2 ) ) ) ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(121,plain,
! [SV3: $i] :
( ( ~ ( relation @ SV3 )
| ! [SY35: $i] :
~ ~ ( ~ ( in @ SY35 @ SV3 )
| ~ ! [SX2: $i,SX3: $i] :
( SY35
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(122,plain,
! [SV3: $i] :
( ( ~ ! [SY38: $i] :
~ ~ ( ~ ( in @ SY38 @ SV3 )
| ~ ! [SX2: $i,SX3: $i] :
( SY38
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(123,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ( subset @ SV4 @ SV10 )
| ! [SY56: $i] :
( ~ ( in @ SY56 @ SV4 )
| ( in @ SY56 @ SV10 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(124,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ! [SY57: $i] :
( ~ ( in @ SY57 @ SV4 )
| ( in @ SY57 @ SV10 ) )
| ( subset @ SV4 @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(125,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ( ~ ( ( SV16
!= ( relation_rng @ SV5 ) )
| ! [SY67: $i] :
~ ( ~ ( ~ ( in @ SY67 @ SV16 )
| ~ ! [SY46: $i] :
~ ( in @ ( ordered_pair @ SY46 @ SY67 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY47: $i] :
~ ( in @ ( ordered_pair @ SY47 @ SY67 ) @ SV5 )
| ( in @ SY67 @ SV16 ) ) ) )
| ~ ( ~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SV16 )
| ~ ! [SY49: $i] :
~ ( in @ ( ordered_pair @ SY49 @ SY70 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY50: $i] :
~ ( in @ ( ordered_pair @ SY50 @ SY70 ) @ SV5 )
| ( in @ SY70 @ SV16 ) ) )
| ( SV16
= ( relation_rng @ SV5 ) ) ) ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(126,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV6 )
| ~ ~ ( empty @ SV11 ) ) )
= $false )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV6 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(127,plain,
! [SV12: $i,SV7: $i] :
( ( ~ ( ~ ( element @ SV7 @ ( powerset @ SV12 ) )
| ( subset @ SV7 @ SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(128,plain,
! [SV12: $i,SV7: $i] :
( ( ~ ( ~ ( subset @ SV7 @ SV12 )
| ( element @ SV7 @ ( powerset @ SV12 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(129,plain,
( ( ~ ( empty @ sK2_SX0 )
| ~ ( relation @ sK2_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(130,plain,
! [SV17: $i,SV14: $i,SV13: $i,SV8: $i] :
( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SV17 ) )
| ~ ( ~ ( in @ SV8 @ SV14 )
| ~ ( in @ SV13 @ SV17 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV8 @ SV14 )
| ~ ( in @ SV13 @ SV17 ) )
| ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(131,plain,
! [SV2: $i,SV15: $i] :
( ( ( ~ ( ( SV15
!= ( relation_dom @ SV2 ) )
| ! [SY61: $i] :
~ ( ~ ( ~ ( in @ SY61 @ SV15 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY61 @ SY30 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY61 @ SY31 ) @ SV2 )
| ( in @ SY61 @ SV15 ) ) ) )
| ~ ( ~ ! [SY64: $i] :
~ ( ~ ( ~ ( in @ SY64 @ SV15 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY64 @ SY33 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY64 @ SY34 ) @ SV2 )
| ( in @ SY64 @ SV15 ) ) )
| ( SV15
= ( relation_dom @ SV2 ) ) ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(132,plain,
! [SV3: $i] :
( ( ( ~ ( relation @ SV3 ) )
= $true )
| ( ( ! [SY35: $i] :
~ ~ ( ~ ( in @ SY35 @ SV3 )
| ~ ! [SX2: $i,SX3: $i] :
( SY35
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(133,plain,
! [SV3: $i] :
( ( ( ~ ! [SY38: $i] :
~ ~ ( ~ ( in @ SY38 @ SV3 )
| ~ ! [SX2: $i,SX3: $i] :
( SY38
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( relation @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(134,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( subset @ SV4 @ SV10 )
| ! [SY56: $i] :
( ~ ( in @ SY56 @ SV4 )
| ( in @ SY56 @ SV10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(135,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ! [SY57: $i] :
( ~ ( in @ SY57 @ SV4 )
| ( in @ SY57 @ SV10 ) )
| ( subset @ SV4 @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(136,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ( ( SV16
!= ( relation_rng @ SV5 ) )
| ! [SY67: $i] :
~ ( ~ ( ~ ( in @ SY67 @ SV16 )
| ~ ! [SY46: $i] :
~ ( in @ ( ordered_pair @ SY46 @ SY67 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY47: $i] :
~ ( in @ ( ordered_pair @ SY47 @ SY67 ) @ SV5 )
| ( in @ SY67 @ SV16 ) ) ) )
| ~ ( ~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SV16 )
| ~ ! [SY49: $i] :
~ ( in @ ( ordered_pair @ SY49 @ SY70 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY50: $i] :
~ ( in @ ( ordered_pair @ SY50 @ SY70 ) @ SV5 )
| ( in @ SY70 @ SV16 ) ) )
| ( SV16
= ( relation_rng @ SV5 ) ) ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(137,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ~ ( empty @ SV6 )
| ~ ~ ( empty @ SV11 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV6 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(138,plain,
! [SV12: $i,SV7: $i] :
( ( ~ ( element @ SV7 @ ( powerset @ SV12 ) )
| ( subset @ SV7 @ SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(139,plain,
! [SV12: $i,SV7: $i] :
( ( ~ ( subset @ SV7 @ SV12 )
| ( element @ SV7 @ ( powerset @ SV12 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(140,plain,
( ( ~ ( empty @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(141,plain,
( ( ~ ( relation @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(142,plain,
! [SV17: $i,SV14: $i,SV13: $i,SV8: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SV17 ) )
| ~ ( ~ ( in @ SV8 @ SV14 )
| ~ ( in @ SV13 @ SV17 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV8 @ SV14 )
| ~ ( in @ SV13 @ SV17 ) )
| ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SV17 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(143,plain,
! [SV2: $i,SV15: $i] :
( ( ( ~ ( ( SV15
!= ( relation_dom @ SV2 ) )
| ! [SY61: $i] :
~ ( ~ ( ~ ( in @ SY61 @ SV15 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY61 @ SY30 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY61 @ SY31 ) @ SV2 )
| ( in @ SY61 @ SV15 ) ) ) ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(144,plain,
! [SV2: $i,SV15: $i] :
( ( ( ~ ( ~ ! [SY64: $i] :
~ ( ~ ( ~ ( in @ SY64 @ SV15 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY64 @ SY33 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY64 @ SY34 ) @ SV2 )
| ( in @ SY64 @ SV15 ) ) )
| ( SV15
= ( relation_dom @ SV2 ) ) ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(145,plain,
! [SV3: $i] :
( ( ( relation @ SV3 )
= $false )
| ( ( ! [SY35: $i] :
~ ~ ( ~ ( in @ SY35 @ SV3 )
| ~ ! [SX2: $i,SX3: $i] :
( SY35
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(146,plain,
! [SV3: $i] :
( ( ( ! [SY38: $i] :
~ ~ ( ~ ( in @ SY38 @ SV3 )
| ~ ! [SX2: $i,SX3: $i] :
( SY38
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $false )
| ( ( relation @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(147,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( subset @ SV4 @ SV10 ) )
= $true )
| ( ( ! [SY56: $i] :
( ~ ( in @ SY56 @ SV4 )
| ( in @ SY56 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(148,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ! [SY57: $i] :
( ~ ( in @ SY57 @ SV4 )
| ( in @ SY57 @ SV10 ) ) )
= $true )
| ( ( subset @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(149,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ( ( SV16
!= ( relation_rng @ SV5 ) )
| ! [SY67: $i] :
~ ( ~ ( ~ ( in @ SY67 @ SV16 )
| ~ ! [SY46: $i] :
~ ( in @ ( ordered_pair @ SY46 @ SY67 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY47: $i] :
~ ( in @ ( ordered_pair @ SY47 @ SY67 ) @ SV5 )
| ( in @ SY67 @ SV16 ) ) ) ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(150,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ( ~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SV16 )
| ~ ! [SY49: $i] :
~ ( in @ ( ordered_pair @ SY49 @ SY70 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY50: $i] :
~ ( in @ ( ordered_pair @ SY50 @ SY70 ) @ SV5 )
| ( in @ SY70 @ SV16 ) ) )
| ( SV16
= ( relation_rng @ SV5 ) ) ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(151,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ~ ( empty @ SV6 ) )
= $true )
| ( ( ~ ~ ( empty @ SV11 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV6 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(152,plain,
! [SV12: $i,SV7: $i] :
( ( ( ~ ( element @ SV7 @ ( powerset @ SV12 ) ) )
= $true )
| ( ( subset @ SV7 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(153,plain,
! [SV12: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV12 ) )
= $true )
| ( ( element @ SV7 @ ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(154,plain,
( ( empty @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(155,plain,
( ( relation @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(156,plain,
! [SV17: $i,SV14: $i,SV13: $i,SV8: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SV17 ) )
| ~ ( ~ ( in @ SV8 @ SV14 )
| ~ ( in @ SV13 @ SV17 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(157,plain,
! [SV17: $i,SV13: $i,SV14: $i,SV8: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV8 @ SV14 )
| ~ ( in @ SV13 @ SV17 ) )
| ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SV17 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(158,plain,
! [SV2: $i,SV15: $i] :
( ( ( ( SV15
!= ( relation_dom @ SV2 ) )
| ! [SY61: $i] :
~ ( ~ ( ~ ( in @ SY61 @ SV15 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY61 @ SY30 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY61 @ SY31 ) @ SV2 )
| ( in @ SY61 @ SV15 ) ) ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(159,plain,
! [SV2: $i,SV15: $i] :
( ( ( ~ ! [SY64: $i] :
~ ( ~ ( ~ ( in @ SY64 @ SV15 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY64 @ SY33 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY64 @ SY34 ) @ SV2 )
| ( in @ SY64 @ SV15 ) ) )
| ( SV15
= ( relation_dom @ SV2 ) ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(160,plain,
! [SV3: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( in @ SV18 @ SV3 )
| ~ ! [SY73: $i,SY74: $i] :
( SV18
!= ( ordered_pair @ SY73 @ SY74 ) ) ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(161,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK3_SY38 @ SV3 ) @ SV3 )
| ~ ! [SY75: $i,SY76: $i] :
( ( sK3_SY38 @ SV3 )
!= ( ordered_pair @ SY75 @ SY76 ) ) ) )
= $false )
| ( ( relation @ SV3 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[146]) ).
thf(162,plain,
! [SV10: $i,SV4: $i] :
( ( ( subset @ SV4 @ SV10 )
= $false )
| ( ( ! [SY56: $i] :
( ~ ( in @ SY56 @ SV4 )
| ( in @ SY56 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(163,plain,
! [SV10: $i,SV4: $i] :
( ( ( ! [SY57: $i] :
( ~ ( in @ SY57 @ SV4 )
| ( in @ SY57 @ SV10 ) ) )
= $false )
| ( ( subset @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(164,plain,
! [SV5: $i,SV16: $i] :
( ( ( ( SV16
!= ( relation_rng @ SV5 ) )
| ! [SY67: $i] :
~ ( ~ ( ~ ( in @ SY67 @ SV16 )
| ~ ! [SY46: $i] :
~ ( in @ ( ordered_pair @ SY46 @ SY67 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY47: $i] :
~ ( in @ ( ordered_pair @ SY47 @ SY67 ) @ SV5 )
| ( in @ SY67 @ SV16 ) ) ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(165,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SV16 )
| ~ ! [SY49: $i] :
~ ( in @ ( ordered_pair @ SY49 @ SY70 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY50: $i] :
~ ( in @ ( ordered_pair @ SY50 @ SY70 ) @ SV5 )
| ( in @ SY70 @ SV16 ) ) )
| ( SV16
= ( relation_rng @ SV5 ) ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(166,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( empty @ SV6 ) )
= $false )
| ( ( ~ ~ ( empty @ SV11 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV6 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(167,plain,
! [SV12: $i,SV7: $i] :
( ( ( element @ SV7 @ ( powerset @ SV12 ) )
= $false )
| ( ( subset @ SV7 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(168,plain,
! [SV12: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV12 )
= $false )
| ( ( element @ SV7 @ ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(169,plain,
! [SV17: $i,SV14: $i,SV13: $i,SV8: $i] :
( ( ~ ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SV17 ) )
| ~ ( ~ ( in @ SV8 @ SV14 )
| ~ ( in @ SV13 @ SV17 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(170,plain,
! [SV17: $i,SV13: $i,SV14: $i,SV8: $i] :
( ( ~ ~ ( ~ ( in @ SV8 @ SV14 )
| ~ ( in @ SV13 @ SV17 ) )
| ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SV17 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(171,plain,
! [SV2: $i,SV15: $i] :
( ( ( SV15
!= ( relation_dom @ SV2 ) )
= $true )
| ( ( ! [SY61: $i] :
~ ( ~ ( ~ ( in @ SY61 @ SV15 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY61 @ SY30 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY61 @ SY31 ) @ SV2 )
| ( in @ SY61 @ SV15 ) ) ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(172,plain,
! [SV2: $i,SV15: $i] :
( ( ( ~ ! [SY64: $i] :
~ ( ~ ( ~ ( in @ SY64 @ SV15 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY64 @ SY33 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY64 @ SY34 ) @ SV2 )
| ( in @ SY64 @ SV15 ) ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(173,plain,
! [SV3: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ SV18 @ SV3 )
| ~ ! [SY73: $i,SY74: $i] :
( SV18
!= ( ordered_pair @ SY73 @ SY74 ) ) ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(174,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY38 @ SV3 ) @ SV3 )
| ~ ! [SY75: $i,SY76: $i] :
( ( sK3_SY38 @ SV3 )
!= ( ordered_pair @ SY75 @ SY76 ) ) ) )
= $true )
| ( ( relation @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(175,plain,
! [SV10: $i,SV4: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ SV4 )
| ( in @ SV19 @ SV10 ) )
= $true )
| ( ( subset @ SV4 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(176,plain,
! [SV4: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK4_SY57 @ SV10 @ SV4 ) @ SV4 )
| ( in @ ( sK4_SY57 @ SV10 @ SV4 ) @ SV10 ) )
= $false )
| ( ( subset @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[163]) ).
thf(177,plain,
! [SV5: $i,SV16: $i] :
( ( ( SV16
!= ( relation_rng @ SV5 ) )
= $true )
| ( ( ! [SY67: $i] :
~ ( ~ ( ~ ( in @ SY67 @ SV16 )
| ~ ! [SY46: $i] :
~ ( in @ ( ordered_pair @ SY46 @ SY67 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY47: $i] :
~ ( in @ ( ordered_pair @ SY47 @ SY67 ) @ SV5 )
| ( in @ SY67 @ SV16 ) ) ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(178,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SV16 )
| ~ ! [SY49: $i] :
~ ( in @ ( ordered_pair @ SY49 @ SY70 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY50: $i] :
~ ( in @ ( ordered_pair @ SY50 @ SY70 ) @ SV5 )
| ( in @ SY70 @ SV16 ) ) ) )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(179,plain,
! [SV11: $i,SV6: $i] :
( ( ( empty @ SV6 )
= $true )
| ( ( ~ ~ ( empty @ SV11 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV6 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(180,plain,
! [SV17: $i,SV14: $i,SV13: $i,SV8: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SV17 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV8 @ SV14 )
| ~ ( in @ SV13 @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(181,plain,
! [SV17: $i,SV13: $i,SV14: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( in @ SV8 @ SV14 )
| ~ ( in @ SV13 @ SV17 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(182,plain,
! [SV2: $i,SV15: $i] :
( ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( ! [SY61: $i] :
~ ( ~ ( ~ ( in @ SY61 @ SV15 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY61 @ SY30 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY61 @ SY31 ) @ SV2 )
| ( in @ SY61 @ SV15 ) ) ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(183,plain,
! [SV2: $i,SV15: $i] :
( ( ( ! [SY64: $i] :
~ ( ~ ( ~ ( in @ SY64 @ SV15 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY64 @ SY33 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY64 @ SY34 ) @ SV2 )
| ( in @ SY64 @ SV15 ) ) ) )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(184,plain,
! [SV3: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ SV3 )
| ~ ! [SY73: $i,SY74: $i] :
( SV18
!= ( ordered_pair @ SY73 @ SY74 ) ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(185,plain,
! [SV3: $i] :
( ( ( ~ ( in @ ( sK3_SY38 @ SV3 ) @ SV3 )
| ~ ! [SY75: $i,SY76: $i] :
( ( sK3_SY38 @ SV3 )
!= ( ordered_pair @ SY75 @ SY76 ) ) )
= $false )
| ( ( relation @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(186,plain,
! [SV10: $i,SV4: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ SV4 ) )
= $true )
| ( ( in @ SV19 @ SV10 )
= $true )
| ( ( subset @ SV4 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(187,plain,
! [SV4: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK4_SY57 @ SV10 @ SV4 ) @ SV4 ) )
= $false )
| ( ( subset @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(188,plain,
! [SV4: $i,SV10: $i] :
( ( ( in @ ( sK4_SY57 @ SV10 @ SV4 ) @ SV10 )
= $false )
| ( ( subset @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(189,plain,
! [SV5: $i,SV16: $i] :
( ( ( SV16
= ( relation_rng @ SV5 ) )
= $false )
| ( ( ! [SY67: $i] :
~ ( ~ ( ~ ( in @ SY67 @ SV16 )
| ~ ! [SY46: $i] :
~ ( in @ ( ordered_pair @ SY46 @ SY67 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY47: $i] :
~ ( in @ ( ordered_pair @ SY47 @ SY67 ) @ SV5 )
| ( in @ SY67 @ SV16 ) ) ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(190,plain,
! [SV5: $i,SV16: $i] :
( ( ( ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SV16 )
| ~ ! [SY49: $i] :
~ ( in @ ( ordered_pair @ SY49 @ SY70 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY50: $i] :
~ ( in @ ( ordered_pair @ SY50 @ SY70 ) @ SV5 )
| ( in @ SY70 @ SV16 ) ) ) )
= $false )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(191,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ( empty @ SV11 ) )
= $false )
| ( ( empty @ SV6 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV6 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(192,plain,
! [SV17: $i,SV14: $i,SV13: $i,SV8: $i] :
( ( ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SV17 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV8 @ SV14 )
| ~ ( in @ SV13 @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(193,plain,
! [SV17: $i,SV13: $i,SV14: $i,SV8: $i] :
( ( ( ~ ( ~ ( in @ SV8 @ SV14 )
| ~ ( in @ SV13 @ SV17 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(194,plain,
! [SV2: $i,SV15: $i,SV20: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV20 @ SV15 )
| ~ ! [SY77: $i] :
~ ( in @ ( ordered_pair @ SV20 @ SY77 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SV20 @ SY78 ) @ SV2 )
| ( in @ SV20 @ SV15 ) ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(195,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 )
| ~ ! [SY79: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY79 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY80: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY80 ) @ SV2 )
| ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 ) ) ) )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[183]) ).
thf(196,plain,
! [SV3: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ SV3 ) )
= $true )
| ( ( ~ ! [SY73: $i,SY74: $i] :
( SV18
!= ( ordered_pair @ SY73 @ SY74 ) ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(197,plain,
! [SV3: $i] :
( ( ( ~ ( in @ ( sK3_SY38 @ SV3 ) @ SV3 ) )
= $false )
| ( ( relation @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(198,plain,
! [SV3: $i] :
( ( ( ~ ! [SY75: $i,SY76: $i] :
( ( sK3_SY38 @ SV3 )
!= ( ordered_pair @ SY75 @ SY76 ) ) )
= $false )
| ( ( relation @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(199,plain,
! [SV10: $i,SV4: $i,SV19: $i] :
( ( ( in @ SV19 @ SV4 )
= $false )
| ( ( in @ SV19 @ SV10 )
= $true )
| ( ( subset @ SV4 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(200,plain,
! [SV4: $i,SV10: $i] :
( ( ( in @ ( sK4_SY57 @ SV10 @ SV4 ) @ SV4 )
= $true )
| ( ( subset @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(201,plain,
! [SV5: $i,SV16: $i,SV21: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV21 @ SV16 )
| ~ ! [SY81: $i] :
~ ( in @ ( ordered_pair @ SY81 @ SV21 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY82: $i] :
~ ( in @ ( ordered_pair @ SY82 @ SV21 ) @ SV5 )
| ( in @ SV21 @ SV16 ) ) ) )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(202,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 )
| ~ ! [SY83: $i] :
~ ( in @ ( ordered_pair @ SY83 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 ) )
| ~ ( ~ ~ ! [SY84: $i] :
~ ( in @ ( ordered_pair @ SY84 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 )
| ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 ) ) ) )
= $false )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[190]) ).
thf(203,plain,
! [SV6: $i,SV11: $i] :
( ( ( empty @ SV11 )
= $true )
| ( ( empty @ SV6 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV6 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(204,plain,
! [SV17: $i,SV13: $i,SV14: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV14 )
| ~ ( in @ SV13 @ SV17 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(205,plain,
! [SV17: $i,SV13: $i,SV14: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV14 )
| ~ ( in @ SV13 @ SV17 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(206,plain,
! [SV2: $i,SV15: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ SV20 @ SV15 )
| ~ ! [SY77: $i] :
~ ( in @ ( ordered_pair @ SV20 @ SY77 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SV20 @ SY78 ) @ SV2 )
| ( in @ SV20 @ SV15 ) ) )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(207,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 )
| ~ ! [SY79: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY79 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY80: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY80 ) @ SV2 )
| ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(208,plain,
! [SV3: $i,SV18: $i] :
( ( ( in @ SV18 @ SV3 )
= $false )
| ( ( ~ ! [SY73: $i,SY74: $i] :
( SV18
!= ( ordered_pair @ SY73 @ SY74 ) ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(209,plain,
! [SV3: $i] :
( ( ( in @ ( sK3_SY38 @ SV3 ) @ SV3 )
= $true )
| ( ( relation @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(210,plain,
! [SV3: $i] :
( ( ( ! [SY75: $i,SY76: $i] :
( ( sK3_SY38 @ SV3 )
!= ( ordered_pair @ SY75 @ SY76 ) ) )
= $true )
| ( ( relation @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(211,plain,
! [SV5: $i,SV16: $i,SV21: $i] :
( ( ( ~ ( ~ ( in @ SV21 @ SV16 )
| ~ ! [SY81: $i] :
~ ( in @ ( ordered_pair @ SY81 @ SV21 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY82: $i] :
~ ( in @ ( ordered_pair @ SY82 @ SV21 ) @ SV5 )
| ( in @ SV21 @ SV16 ) ) )
= $false )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(212,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 )
| ~ ! [SY83: $i] :
~ ( in @ ( ordered_pair @ SY83 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 ) )
| ~ ( ~ ~ ! [SY84: $i] :
~ ( in @ ( ordered_pair @ SY84 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 )
| ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 ) ) )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(213,plain,
! [SV11: $i,SV6: $i] :
( ( ( empty @ ( cartesian_product2 @ SV6 @ SV11 ) )
= $false )
| ( ( empty @ SV6 )
= $true )
| ( ( empty @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(214,plain,
! [SV17: $i,SV13: $i,SV14: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV14 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SV17 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(215,plain,
! [SV14: $i,SV8: $i,SV17: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV17 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SV17 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(216,plain,
! [SV17: $i,SV13: $i,SV14: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV14 ) )
= $true )
| ( ( ~ ( in @ SV13 @ SV17 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(217,plain,
! [SV2: $i,SV15: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ SV20 @ SV15 )
| ~ ! [SY77: $i] :
~ ( in @ ( ordered_pair @ SV20 @ SY77 ) @ SV2 ) ) )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[206]) ).
thf(218,plain,
! [SV15: $i,SV2: $i,SV20: $i] :
( ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SV20 @ SY78 ) @ SV2 )
| ( in @ SV20 @ SV15 ) ) )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[206]) ).
thf(219,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 )
| ~ ! [SY79: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY79 ) @ SV2 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY80: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY80 ) @ SV2 )
| ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(220,plain,
! [SV3: $i,SV18: $i] :
( ( ( ! [SY73: $i,SY74: $i] :
( SV18
!= ( ordered_pair @ SY73 @ SY74 ) ) )
= $false )
| ( ( in @ SV18 @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(221,plain,
! [SV22: $i,SV3: $i] :
( ( ( ! [SY85: $i] :
( ( sK3_SY38 @ SV3 )
!= ( ordered_pair @ SV22 @ SY85 ) ) )
= $true )
| ( ( relation @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(222,plain,
! [SV5: $i,SV16: $i,SV21: $i] :
( ( ( ~ ( ~ ( in @ SV21 @ SV16 )
| ~ ! [SY81: $i] :
~ ( in @ ( ordered_pair @ SY81 @ SV21 ) @ SV5 ) ) )
= $false )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(223,plain,
! [SV16: $i,SV5: $i,SV21: $i] :
( ( ( ~ ( ~ ~ ! [SY82: $i] :
~ ( in @ ( ordered_pair @ SY82 @ SV21 ) @ SV5 )
| ( in @ SV21 @ SV16 ) ) )
= $false )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(224,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 )
| ~ ! [SY83: $i] :
~ ( in @ ( ordered_pair @ SY83 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY84: $i] :
~ ( in @ ( ordered_pair @ SY84 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 )
| ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 ) ) )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(225,plain,
! [SV17: $i,SV13: $i,SV14: $i,SV8: $i] :
( ( ( in @ SV8 @ SV14 )
= $true )
| ( ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(226,plain,
! [SV14: $i,SV8: $i,SV17: $i,SV13: $i] :
( ( ( in @ SV13 @ SV17 )
= $true )
| ( ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(227,plain,
! [SV17: $i,SV13: $i,SV14: $i,SV8: $i] :
( ( ( in @ SV8 @ SV14 )
= $false )
| ( ( ~ ( in @ SV13 @ SV17 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(228,plain,
! [SV2: $i,SV15: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV15 )
| ~ ! [SY77: $i] :
~ ( in @ ( ordered_pair @ SV20 @ SY77 ) @ SV2 ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(229,plain,
! [SV15: $i,SV2: $i,SV20: $i] :
( ( ( ~ ~ ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SV20 @ SY78 ) @ SV2 )
| ( in @ SV20 @ SV15 ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(230,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 )
| ~ ! [SY79: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY79 ) @ SV2 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY80: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY80 ) @ SV2 )
| ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(231,plain,
! [SV3: $i,SV18: $i] :
( ( ( ! [SY86: $i] :
( SV18
!= ( ordered_pair @ ( sK7_SY73 @ SV3 @ SV18 ) @ SY86 ) ) )
= $false )
| ( ( in @ SV18 @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[220]) ).
thf(232,plain,
! [SV23: $i,SV22: $i,SV3: $i] :
( ( ( ( sK3_SY38 @ SV3 )
!= ( ordered_pair @ SV22 @ SV23 ) )
= $true )
| ( ( relation @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(233,plain,
! [SV5: $i,SV16: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ SV16 )
| ~ ! [SY81: $i] :
~ ( in @ ( ordered_pair @ SY81 @ SV21 ) @ SV5 ) )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(234,plain,
! [SV16: $i,SV5: $i,SV21: $i] :
( ( ( ~ ~ ! [SY82: $i] :
~ ( in @ ( ordered_pair @ SY82 @ SV21 ) @ SV5 )
| ( in @ SV21 @ SV16 ) )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(235,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 )
| ~ ! [SY83: $i] :
~ ( in @ ( ordered_pair @ SY83 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY84: $i] :
~ ( in @ ( ordered_pair @ SY84 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 )
| ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 ) ) )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(236,plain,
! [SV14: $i,SV8: $i,SV17: $i,SV13: $i] :
( ( ( in @ SV13 @ SV17 )
= $false )
| ( ( in @ SV8 @ SV14 )
= $false )
| ( ( in @ ( ordered_pair @ SV8 @ SV13 ) @ ( cartesian_product2 @ SV14 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(237,plain,
! [SV2: $i,SV15: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV15 ) )
= $true )
| ( ( ~ ! [SY77: $i] :
~ ( in @ ( ordered_pair @ SV20 @ SY77 ) @ SV2 ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(238,plain,
! [SV15: $i,SV2: $i,SV20: $i] :
( ( ( ~ ~ ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SV20 @ SY78 ) @ SV2 ) )
= $true )
| ( ( in @ SV20 @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(239,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY80: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY80 ) @ SV2 )
| ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(240,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ! [SY79: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY79 ) @ SV2 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY80: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY80 ) @ SV2 )
| ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(241,plain,
! [SV3: $i,SV18: $i] :
( ( ( SV18
!= ( ordered_pair @ ( sK7_SY73 @ SV3 @ SV18 ) @ ( sK8_SY86 @ SV3 @ SV18 ) ) )
= $false )
| ( ( in @ SV18 @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[231]) ).
thf(242,plain,
! [SV23: $i,SV22: $i,SV3: $i] :
( ( ( ( sK3_SY38 @ SV3 )
= ( ordered_pair @ SV22 @ SV23 ) )
= $false )
| ( ( relation @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(243,plain,
! [SV5: $i,SV16: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ SV16 ) )
= $true )
| ( ( ~ ! [SY81: $i] :
~ ( in @ ( ordered_pair @ SY81 @ SV21 ) @ SV5 ) )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(244,plain,
! [SV16: $i,SV5: $i,SV21: $i] :
( ( ( ~ ~ ! [SY82: $i] :
~ ( in @ ( ordered_pair @ SY82 @ SV21 ) @ SV5 ) )
= $true )
| ( ( in @ SV21 @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(245,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY84: $i] :
~ ( in @ ( ordered_pair @ SY84 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 )
| ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 ) ) )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(246,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ! [SY83: $i] :
~ ( in @ ( ordered_pair @ SY83 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY84: $i] :
~ ( in @ ( ordered_pair @ SY84 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 )
| ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 ) ) )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(247,plain,
! [SV2: $i,SV15: $i,SV20: $i] :
( ( ( in @ SV20 @ SV15 )
= $false )
| ( ( ~ ! [SY77: $i] :
~ ( in @ ( ordered_pair @ SV20 @ SY77 ) @ SV2 ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(248,plain,
! [SV15: $i,SV2: $i,SV20: $i] :
( ( ( ~ ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SV20 @ SY78 ) @ SV2 ) )
= $false )
| ( ( in @ SV20 @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(249,plain,
! [SV15: $i,SV2: $i] :
( ( ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 )
= $true )
| ( ( ~ ( ~ ~ ! [SY80: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY80 ) @ SV2 )
| ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(250,plain,
! [SV15: $i,SV2: $i] :
( ( ( ! [SY79: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY79 ) @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY80: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY80 ) @ SV2 )
| ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(251,plain,
! [SV3: $i,SV18: $i] :
( ( ( SV18
= ( ordered_pair @ ( sK7_SY73 @ SV3 @ SV18 ) @ ( sK8_SY86 @ SV3 @ SV18 ) ) )
= $true )
| ( ( in @ SV18 @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(252,plain,
! [SV5: $i,SV16: $i,SV21: $i] :
( ( ( in @ SV21 @ SV16 )
= $false )
| ( ( ~ ! [SY81: $i] :
~ ( in @ ( ordered_pair @ SY81 @ SV21 ) @ SV5 ) )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(253,plain,
! [SV16: $i,SV5: $i,SV21: $i] :
( ( ( ~ ! [SY82: $i] :
~ ( in @ ( ordered_pair @ SY82 @ SV21 ) @ SV5 ) )
= $false )
| ( ( in @ SV21 @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(254,plain,
! [SV16: $i,SV5: $i] :
( ( ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 )
= $true )
| ( ( ~ ( ~ ~ ! [SY84: $i] :
~ ( in @ ( ordered_pair @ SY84 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 )
| ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 ) ) )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(255,plain,
! [SV16: $i,SV5: $i] :
( ( ( ! [SY83: $i] :
~ ( in @ ( ordered_pair @ SY83 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY84: $i] :
~ ( in @ ( ordered_pair @ SY84 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 )
| ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 ) ) )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(256,plain,
! [SV15: $i,SV2: $i,SV20: $i] :
( ( ( ! [SY77: $i] :
~ ( in @ ( ordered_pair @ SV20 @ SY77 ) @ SV2 ) )
= $false )
| ( ( in @ SV20 @ SV15 )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(257,plain,
! [SV15: $i,SV2: $i,SV20: $i] :
( ( ( ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SV20 @ SY78 ) @ SV2 ) )
= $true )
| ( ( in @ SV20 @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(258,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ~ ! [SY80: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY80 ) @ SV2 )
| ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(259,plain,
! [SV24: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV24 ) @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY80: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY80 ) @ SV2 )
| ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(260,plain,
! [SV16: $i,SV5: $i,SV21: $i] :
( ( ( ! [SY81: $i] :
~ ( in @ ( ordered_pair @ SY81 @ SV21 ) @ SV5 ) )
= $false )
| ( ( in @ SV21 @ SV16 )
= $false )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(261,plain,
! [SV16: $i,SV5: $i,SV21: $i] :
( ( ( ! [SY82: $i] :
~ ( in @ ( ordered_pair @ SY82 @ SV21 ) @ SV5 ) )
= $true )
| ( ( in @ SV21 @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(262,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ~ ! [SY84: $i] :
~ ( in @ ( ordered_pair @ SY84 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 )
| ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 ) )
= $false )
| ( ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(263,plain,
! [SV16: $i,SV5: $i,SV25: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV25 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY84: $i] :
~ ( in @ ( ordered_pair @ SY84 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 )
| ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 ) ) )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(264,plain,
! [SV2: $i,SV15: $i,SV20: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV20 @ ( sK9_SY77 @ SV15 @ SV2 @ SV20 ) ) @ SV2 ) )
= $false )
| ( ( in @ SV20 @ SV15 )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[256]) ).
thf(265,plain,
! [SV15: $i,SV2: $i,SV26: $i,SV20: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV20 @ SV26 ) @ SV2 ) )
= $true )
| ( ( in @ SV20 @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(266,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ~ ! [SY80: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY80 ) @ SV2 ) )
= $false )
| ( ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(267,plain,
! [SV15: $i,SV2: $i] :
( ( ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(268,plain,
! [SV24: $i,SV15: $i,SV2: $i] :
( ( ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV24 ) @ SV2 )
= $false )
| ( ( ~ ( ~ ~ ! [SY80: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY80 ) @ SV2 )
| ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(269,plain,
! [SV21: $i,SV5: $i,SV16: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_SY81 @ SV16 @ SV5 @ SV21 ) @ SV21 ) @ SV5 ) )
= $false )
| ( ( in @ SV21 @ SV16 )
= $false )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[260]) ).
thf(270,plain,
! [SV16: $i,SV5: $i,SV21: $i,SV27: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV27 @ SV21 ) @ SV5 ) )
= $true )
| ( ( in @ SV21 @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(271,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ~ ! [SY84: $i] :
~ ( in @ ( ordered_pair @ SY84 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 ) )
= $false )
| ( ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(272,plain,
! [SV16: $i,SV5: $i] :
( ( ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 )
= $false )
| ( ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(273,plain,
! [SV16: $i,SV5: $i,SV25: $i] :
( ( ( in @ ( ordered_pair @ SV25 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 )
= $false )
| ( ( ~ ( ~ ~ ! [SY84: $i] :
~ ( in @ ( ordered_pair @ SY84 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 )
| ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 ) ) )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(274,plain,
! [SV2: $i,SV15: $i,SV20: $i] :
( ( ( in @ ( ordered_pair @ SV20 @ ( sK9_SY77 @ SV15 @ SV2 @ SV20 ) ) @ SV2 )
= $true )
| ( ( in @ SV20 @ SV15 )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(275,plain,
! [SV15: $i,SV2: $i,SV26: $i,SV20: $i] :
( ( ( in @ ( ordered_pair @ SV20 @ SV26 ) @ SV2 )
= $false )
| ( ( in @ SV20 @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(276,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ! [SY80: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY80 ) @ SV2 ) )
= $true )
| ( ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(277,plain,
! [SV24: $i,SV15: $i,SV2: $i] :
( ( ( ~ ~ ! [SY80: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY80 ) @ SV2 )
| ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV24 ) @ SV2 )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(278,plain,
! [SV21: $i,SV5: $i,SV16: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_SY81 @ SV16 @ SV5 @ SV21 ) @ SV21 ) @ SV5 )
= $true )
| ( ( in @ SV21 @ SV16 )
= $false )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(279,plain,
! [SV16: $i,SV5: $i,SV21: $i,SV27: $i] :
( ( ( in @ ( ordered_pair @ SV27 @ SV21 ) @ SV5 )
= $false )
| ( ( in @ SV21 @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(280,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ! [SY84: $i] :
~ ( in @ ( ordered_pair @ SY84 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 ) )
= $true )
| ( ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(281,plain,
! [SV25: $i,SV16: $i,SV5: $i] :
( ( ( ~ ~ ! [SY84: $i] :
~ ( in @ ( ordered_pair @ SY84 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 )
| ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV25 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 )
= $false )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(282,plain,
! [SV15: $i,SV2: $i] :
( ( ( ! [SY80: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY80 ) @ SV2 ) )
= $false )
| ( ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(283,plain,
! [SV24: $i,SV15: $i,SV2: $i] :
( ( ( ~ ~ ! [SY80: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY80 ) @ SV2 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV24 ) @ SV2 )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(284,plain,
! [SV24: $i,SV15: $i,SV2: $i] :
( ( ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV24 ) @ SV2 )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(285,plain,
! [SV16: $i,SV5: $i] :
( ( ( ! [SY84: $i] :
~ ( in @ ( ordered_pair @ SY84 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 ) )
= $false )
| ( ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(286,plain,
! [SV25: $i,SV16: $i,SV5: $i] :
( ( ( ~ ~ ! [SY84: $i] :
~ ( in @ ( ordered_pair @ SY84 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV25 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 )
= $false )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(287,plain,
! [SV25: $i,SV16: $i,SV5: $i] :
( ( ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 )
= $false )
| ( ( in @ ( ordered_pair @ SV25 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 )
= $false )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(288,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ ( sK11_SY80 @ SV15 @ SV2 ) ) @ SV2 ) )
= $false )
| ( ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[282]) ).
thf(289,plain,
! [SV24: $i,SV15: $i,SV2: $i] :
( ( ( ~ ! [SY80: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY80 ) @ SV2 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV24 ) @ SV2 )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(290,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK12_SY84 @ SV16 @ SV5 ) @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 ) )
= $false )
| ( ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[285]) ).
thf(291,plain,
! [SV25: $i,SV16: $i,SV5: $i] :
( ( ( ~ ! [SY84: $i] :
~ ( in @ ( ordered_pair @ SY84 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV25 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 )
= $false )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(292,plain,
! [SV15: $i,SV2: $i] :
( ( ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ ( sK11_SY80 @ SV15 @ SV2 ) ) @ SV2 )
= $true )
| ( ( in @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(293,plain,
! [SV24: $i,SV15: $i,SV2: $i] :
( ( ( ! [SY80: $i] :
~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SY80 ) @ SV2 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV24 ) @ SV2 )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(294,plain,
! [SV5: $i,SV16: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_SY84 @ SV16 @ SV5 ) @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 )
= $true )
| ( ( in @ ( sK6_SY70 @ SV5 @ SV16 ) @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(295,plain,
! [SV25: $i,SV16: $i,SV5: $i] :
( ( ( ! [SY84: $i] :
~ ( in @ ( ordered_pair @ SY84 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV25 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 )
= $false )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(296,plain,
! [SV24: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ ( sK13_SY80 @ SV24 @ SV15 @ SV2 ) ) @ SV2 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV24 ) @ SV2 )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[293]) ).
thf(297,plain,
! [SV5: $i,SV16: $i,SV25: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_SY84 @ SV25 @ SV16 @ SV5 ) @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV25 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 )
= $false )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[295]) ).
thf(298,plain,
! [SV24: $i,SV15: $i,SV2: $i] :
( ( ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ ( sK13_SY80 @ SV24 @ SV15 @ SV2 ) ) @ SV2 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK5_SY64 @ SV2 @ SV15 ) @ SV24 ) @ SV2 )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(299,plain,
! [SV5: $i,SV16: $i,SV25: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_SY84 @ SV25 @ SV16 @ SV5 ) @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 )
= $true )
| ( ( in @ ( ordered_pair @ SV25 @ ( sK6_SY70 @ SV5 @ SV16 ) ) @ SV5 )
= $false )
| ( ( SV16
= ( relation_rng @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(300,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[68,299,298,294,292,287,284,279,278,275,274,272,267,251,242,236,226,225,213,209,200,199,188,168,167,155,154,102,93,82,76,75,74,73,72,71,70,69]) ).
thf(301,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[300]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU178+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n003.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 15:04:54 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.73/0.54
% 1.73/0.54 No.of.Axioms: 18
% 1.73/0.54
% 1.73/0.54 Length.of.Defs: 0
% 1.73/0.54
% 1.73/0.54 Contains.Choice.Funs: false
% 1.73/0.54 ........
% 1.73/0.54
% 1.73/0.54 ********************************
% 1.73/0.54 * All subproblems solved! *
% 1.73/0.54 ********************************
% 1.73/0.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:19,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:300,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.73/0.54
% 1.73/0.54 %**** Beginning of derivation protocol ****
% 1.73/0.54 % SZS output start CNFRefutation
% See solution above
% 1.73/0.54
% 1.73/0.54 %**** End of derivation protocol ****
% 1.73/0.54 %**** no. of clauses in derivation: 281 ****
% 1.73/0.54 %**** clause counter: 300 ****
% 1.73/0.54
% 1.73/0.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:19,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:300,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------