%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU267+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:43:44 AM UTC 2026
% Result : Theorem 1.12s 0.56s
% Output : CNFRefutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 29
% Syntax : Number of formulae : 274 ( 148 unt; 0 typ; 0 def)
% Number of atoms : 1683 (1148 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 2271 ( 610 ~; 520 |; 9 &;1104 @)
% ( 8 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 81 ( 78 usr; 5 con; 0-4 aty)
% Number of variables : 943 ( 0 ^; 927 !; 16 ?; 943 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_antisymmetric,type,
antisymmetric: $i > $o ).
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_are_equipotent,type,
are_equipotent: $i > $i > $o ).
thf(tp_being_limit_ordinal,type,
being_limit_ordinal: $i > $o ).
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_cast_to_subset,type,
cast_to_subset: $i > $i ).
thf(tp_complements_of_subsets,type,
complements_of_subsets: $i > $i > $i ).
thf(tp_connected,type,
connected: $i > $o ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
thf(tp_fiber,type,
fiber: $i > $i > $i ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_function_inverse,type,
function_inverse: $i > $i ).
thf(tp_identity_relation,type,
identity_relation: $i > $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_is_antisymmetric_in,type,
is_antisymmetric_in: $i > $i > $o ).
thf(tp_is_connected_in,type,
is_connected_in: $i > $i > $o ).
thf(tp_is_reflexive_in,type,
is_reflexive_in: $i > $i > $o ).
thf(tp_is_transitive_in,type,
is_transitive_in: $i > $i > $o ).
thf(tp_is_well_founded_in,type,
is_well_founded_in: $i > $i > $o ).
thf(tp_meet_of_subsets,type,
meet_of_subsets: $i > $i > $i ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_ordinal_subset,type,
ordinal_subset: $i > $i > $o ).
thf(tp_pair_first,type,
pair_first: $i > $i ).
thf(tp_pair_second,type,
pair_second: $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_reflexive,type,
reflexive: $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_composition,type,
relation_composition: $i > $i > $i ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_dom_as_subset,type,
relation_dom_as_subset: $i > $i > $i > $i ).
thf(tp_relation_dom_restriction,type,
relation_dom_restriction: $i > $i > $i ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_relation_field,type,
relation_field: $i > $i ).
thf(tp_relation_image,type,
relation_image: $i > $i > $i ).
thf(tp_relation_inverse,type,
relation_inverse: $i > $i ).
thf(tp_relation_inverse_image,type,
relation_inverse_image: $i > $i > $i ).
thf(tp_relation_isomorphism,type,
relation_isomorphism: $i > $i > $i > $o ).
thf(tp_relation_of2,type,
relation_of2: $i > $i > $i > $o ).
thf(tp_relation_of2_as_subset,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(tp_relation_restriction,type,
relation_restriction: $i > $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_relation_rng_as_subset,type,
relation_rng_as_subset: $i > $i > $i > $i ).
thf(tp_relation_rng_restriction,type,
relation_rng_restriction: $i > $i > $i ).
thf(tp_sK10_SY90,type,
sK10_SY90: $i > $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY20,type,
sK2_SY20: $i ).
thf(tp_sK3_SY46,type,
sK3_SY46: $i > $i > $i > $i > $i ).
thf(tp_sK4_SY50,type,
sK4_SY50: $i > $i > $i > $i > $i ).
thf(tp_sK5_SY53,type,
sK5_SY53: $i > $i > $i > $i > $i ).
thf(tp_sK6_SY55,type,
sK6_SY55: $i > $i > $i > $i > $i ).
thf(tp_sK7_SY81,type,
sK7_SY81: $i > $i > $i > $i > $i ).
thf(tp_sK8_SY85,type,
sK8_SY85: $i > $i > $i > $i > $i ).
thf(tp_sK9_SY88,type,
sK9_SY88: $i > $i > $i > $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_meet,type,
set_meet: $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_complement,type,
subset_complement: $i > $i > $i ).
thf(tp_subset_difference,type,
subset_difference: $i > $i > $i > $i ).
thf(tp_succ,type,
succ: $i > $i ).
thf(tp_transitive,type,
transitive: $i > $o ).
thf(tp_union,type,
union: $i > $i ).
thf(tp_union_of_subsets,type,
union_of_subsets: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(tp_unordered_triple,type,
unordered_triple: $i > $i > $i > $i ).
thf(tp_well_founded_relation,type,
well_founded_relation: $i > $o ).
thf(tp_well_ordering,type,
well_ordering: $i > $o ).
thf(tp_well_orders,type,
well_orders: $i > $i > $o ).
thf(66,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(80,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(81,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(82,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(92,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(93,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(96,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(97,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(99,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(100,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(101,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(103,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(105,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(106,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_mcart_1) ).
thf(108,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(109,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(110,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord1) ).
thf(111,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(112,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(113,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(114,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_ordinal1) ).
thf(115,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_mcart_1) ).
thf(116,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(117,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_enumset1) ).
thf(118,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_relat_1) ).
thf(158,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( ordered_pair @ B @ C ) )
=> ! [B: $i] :
( ( B
= ( pair_second @ A ) )
<=> ! [C: $i,D: $i] :
( ( A
= ( ordered_pair @ C @ D ) )
=> ( B = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_mcart_1) ).
thf(168,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( ordered_pair @ B @ C ) )
=> ! [B: $i] :
( ( B
= ( pair_first @ A ) )
<=> ! [C: $i,D: $i] :
( ( A
= ( ordered_pair @ C @ D ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_mcart_1) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(342,conjecture,
! [A: $i,B: $i] :
( ( ( pair_first @ ( ordered_pair @ A @ B ) )
= A )
& ( ( pair_second @ ( ordered_pair @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_mcart_1) ).
thf(343,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( ( pair_first @ ( ordered_pair @ A @ B ) )
= A )
& ( ( pair_second @ ( ordered_pair @ A @ B ) )
= B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[342]) ).
thf(344,plain,
( ( ! [A: $i,B: $i] :
( ( ( pair_first @ ( ordered_pair @ A @ B ) )
= A )
& ( ( pair_second @ ( ordered_pair @ A @ B ) )
= B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[343]) ).
thf(345,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(346,plain,
$true = $true,
inference(unfold_def,[status(thm)],[80]) ).
thf(347,plain,
$true = $true,
inference(unfold_def,[status(thm)],[81]) ).
thf(348,plain,
$true = $true,
inference(unfold_def,[status(thm)],[82]) ).
thf(349,plain,
$true = $true,
inference(unfold_def,[status(thm)],[92]) ).
thf(350,plain,
$true = $true,
inference(unfold_def,[status(thm)],[93]) ).
thf(351,plain,
$true = $true,
inference(unfold_def,[status(thm)],[96]) ).
thf(352,plain,
$true = $true,
inference(unfold_def,[status(thm)],[97]) ).
thf(353,plain,
$true = $true,
inference(unfold_def,[status(thm)],[99]) ).
thf(354,plain,
$true = $true,
inference(unfold_def,[status(thm)],[100]) ).
thf(355,plain,
$true = $true,
inference(unfold_def,[status(thm)],[101]) ).
thf(356,plain,
$true = $true,
inference(unfold_def,[status(thm)],[103]) ).
thf(357,plain,
$true = $true,
inference(unfold_def,[status(thm)],[105]) ).
thf(358,plain,
$true = $true,
inference(unfold_def,[status(thm)],[106]) ).
thf(359,plain,
$true = $true,
inference(unfold_def,[status(thm)],[108]) ).
thf(360,plain,
$true = $true,
inference(unfold_def,[status(thm)],[109]) ).
thf(361,plain,
$true = $true,
inference(unfold_def,[status(thm)],[110]) ).
thf(362,plain,
$true = $true,
inference(unfold_def,[status(thm)],[111]) ).
thf(363,plain,
$true = $true,
inference(unfold_def,[status(thm)],[112]) ).
thf(364,plain,
$true = $true,
inference(unfold_def,[status(thm)],[113]) ).
thf(365,plain,
$true = $true,
inference(unfold_def,[status(thm)],[114]) ).
thf(366,plain,
$true = $true,
inference(unfold_def,[status(thm)],[115]) ).
thf(367,plain,
$true = $true,
inference(unfold_def,[status(thm)],[116]) ).
thf(368,plain,
$true = $true,
inference(unfold_def,[status(thm)],[117]) ).
thf(369,plain,
$true = $true,
inference(unfold_def,[status(thm)],[118]) ).
thf(370,plain,
( ( ! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( ordered_pair @ B @ C ) )
=> ! [B: $i] :
( ( B
= ( pair_second @ A ) )
<=> ! [C: $i,D: $i] :
( ( A
= ( ordered_pair @ C @ D ) )
=> ( B = D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(371,plain,
( ( ! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( ordered_pair @ B @ C ) )
=> ! [B: $i] :
( ( B
= ( pair_first @ A ) )
<=> ! [C: $i,D: $i] :
( ( A
= ( ordered_pair @ C @ D ) )
=> ( B = C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(372,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(373,plain,
( ( ! [SY20: $i] :
( ( ( pair_first @ ( ordered_pair @ sK1_A @ SY20 ) )
= sK1_A )
& ( ( pair_second @ ( ordered_pair @ sK1_A @ SY20 ) )
= SY20 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[344]) ).
thf(374,plain,
( ( ( ( pair_first @ ( ordered_pair @ sK1_A @ sK2_SY20 ) )
= sK1_A )
& ( ( pair_second @ ( ordered_pair @ sK1_A @ sK2_SY20 ) )
= sK2_SY20 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[373]) ).
thf(375,plain,
( ( ( pair_first @ ( ordered_pair @ sK1_A @ sK2_SY20 ) )
= sK1_A )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[374]) ).
thf(376,plain,
( ( ( pair_second @ ( ordered_pair @ sK1_A @ sK2_SY20 ) )
= sK2_SY20 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[374]) ).
thf(377,plain,
( ( ( pair_first @ ( ordered_pair @ sK1_A @ sK2_SY20 ) )
!= sK1_A )
= $true ),
inference(polarity_switch,[status(thm)],[375]) ).
thf(378,plain,
( ( ( pair_second @ ( ordered_pair @ sK1_A @ sK2_SY20 ) )
!= sK2_SY20 )
= $true ),
inference(polarity_switch,[status(thm)],[376]) ).
thf(379,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(380,plain,
( ( ! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( ordered_pair @ B @ C ) )
=> ! [B: $i] :
( ( B
= ( pair_first @ A ) )
<=> ! [C: $i,D: $i] :
( ( A
= ( ordered_pair @ C @ D ) )
=> ( B = C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(381,plain,
( ( ! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( ordered_pair @ B @ C ) )
=> ! [B: $i] :
( ( B
= ( pair_second @ A ) )
<=> ! [C: $i,D: $i] :
( ( A
= ( ordered_pair @ C @ D ) )
=> ( B = D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(382,plain,
$true = $true,
inference(copy,[status(thm)],[369]) ).
thf(383,plain,
$true = $true,
inference(copy,[status(thm)],[368]) ).
thf(384,plain,
$true = $true,
inference(copy,[status(thm)],[367]) ).
thf(385,plain,
$true = $true,
inference(copy,[status(thm)],[366]) ).
thf(386,plain,
$true = $true,
inference(copy,[status(thm)],[365]) ).
thf(387,plain,
$true = $true,
inference(copy,[status(thm)],[364]) ).
thf(388,plain,
$true = $true,
inference(copy,[status(thm)],[363]) ).
thf(389,plain,
$true = $true,
inference(copy,[status(thm)],[362]) ).
thf(390,plain,
$true = $true,
inference(copy,[status(thm)],[361]) ).
thf(391,plain,
$true = $true,
inference(copy,[status(thm)],[360]) ).
thf(392,plain,
$true = $true,
inference(copy,[status(thm)],[359]) ).
thf(393,plain,
$true = $true,
inference(copy,[status(thm)],[358]) ).
thf(394,plain,
$true = $true,
inference(copy,[status(thm)],[357]) ).
thf(395,plain,
$true = $true,
inference(copy,[status(thm)],[356]) ).
thf(396,plain,
$true = $true,
inference(copy,[status(thm)],[355]) ).
thf(397,plain,
$true = $true,
inference(copy,[status(thm)],[354]) ).
thf(398,plain,
$true = $true,
inference(copy,[status(thm)],[353]) ).
thf(399,plain,
$true = $true,
inference(copy,[status(thm)],[352]) ).
thf(400,plain,
$true = $true,
inference(copy,[status(thm)],[351]) ).
thf(401,plain,
$true = $true,
inference(copy,[status(thm)],[350]) ).
thf(402,plain,
$true = $true,
inference(copy,[status(thm)],[349]) ).
thf(403,plain,
$true = $true,
inference(copy,[status(thm)],[348]) ).
thf(404,plain,
$true = $true,
inference(copy,[status(thm)],[347]) ).
thf(405,plain,
$true = $true,
inference(copy,[status(thm)],[346]) ).
thf(406,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(407,plain,
( ( ( pair_first @ ( ordered_pair @ sK1_A @ sK2_SY20 ) )
!= sK1_A )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(408,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(409,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
( SX0
!= ( ordered_pair @ SX1 @ SX2 ) )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( pair_first @ SX0 ) )
| ! [SX2: $i,SX3: $i] :
( ( SX0
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX1 = SX2 ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX0
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX1 = SX2 ) )
| ( SX1
= ( pair_first @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(410,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
( SX0
!= ( ordered_pair @ SX1 @ SX2 ) )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( pair_second @ SX0 ) )
| ! [SX2: $i,SX3: $i] :
( ( SX0
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX0
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) )
| ( SX1
= ( pair_second @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(411,plain,
! [SV1: $i] :
( ( ! [SY21: $i] :
~ ( empty @ ( ordered_pair @ SV1 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(412,plain,
( ( ( pair_first @ ( ordered_pair @ sK1_A @ sK2_SY20 ) )
= sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(413,plain,
! [SV2: $i] :
( ( ! [SY22: $i,SY23: $i,SY24: $i] :
( ( ( ordered_pair @ SV2 @ SY22 )
!= ( ordered_pair @ SY23 @ SY24 ) )
| ~ ( ( SV2 != SY23 )
| ( SY22 != SY24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(414,plain,
! [SV3: $i] :
( ( ~ ~ ! [SY25: $i] :
~ ~ ! [SY26: $i] :
( SV3
!= ( ordered_pair @ SY25 @ SY26 ) )
| ! [SY27: $i] :
~ ( ~ ( ( SY27
!= ( pair_first @ SV3 ) )
| ! [SY28: $i,SY29: $i] :
( ( SV3
!= ( ordered_pair @ SY28 @ SY29 ) )
| ( SY27 = SY28 ) ) )
| ~ ( ~ ! [SY30: $i,SY31: $i] :
( ( SV3
!= ( ordered_pair @ SY30 @ SY31 ) )
| ( SY27 = SY30 ) )
| ( SY27
= ( pair_first @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(415,plain,
! [SV4: $i] :
( ( ~ ~ ! [SY32: $i] :
~ ~ ! [SY33: $i] :
( SV4
!= ( ordered_pair @ SY32 @ SY33 ) )
| ! [SY34: $i] :
~ ( ~ ( ( SY34
!= ( pair_second @ SV4 ) )
| ! [SY35: $i,SY36: $i] :
( ( SV4
!= ( ordered_pair @ SY35 @ SY36 ) )
| ( SY34 = SY36 ) ) )
| ~ ( ~ ! [SY37: $i,SY38: $i] :
( ( SV4
!= ( ordered_pair @ SY37 @ SY38 ) )
| ( SY34 = SY38 ) )
| ( SY34
= ( pair_second @ SV4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(416,plain,
! [SV5: $i,SV1: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV1 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(417,plain,
! [SV6: $i,SV2: $i] :
( ( ! [SY39: $i,SY40: $i] :
( ( ( ordered_pair @ SV2 @ SV6 )
!= ( ordered_pair @ SY39 @ SY40 ) )
| ~ ( ( SV2 != SY39 )
| ( SV6 != SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(418,plain,
! [SV3: $i] :
( ( ( ~ ~ ! [SY25: $i] :
~ ~ ! [SY26: $i] :
( SV3
!= ( ordered_pair @ SY25 @ SY26 ) ) )
= $true )
| ( ( ! [SY27: $i] :
~ ( ~ ( ( SY27
!= ( pair_first @ SV3 ) )
| ! [SY28: $i,SY29: $i] :
( ( SV3
!= ( ordered_pair @ SY28 @ SY29 ) )
| ( SY27 = SY28 ) ) )
| ~ ( ~ ! [SY30: $i,SY31: $i] :
( ( SV3
!= ( ordered_pair @ SY30 @ SY31 ) )
| ( SY27 = SY30 ) )
| ( SY27
= ( pair_first @ SV3 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(419,plain,
! [SV4: $i] :
( ( ( ~ ~ ! [SY32: $i] :
~ ~ ! [SY33: $i] :
( SV4
!= ( ordered_pair @ SY32 @ SY33 ) ) )
= $true )
| ( ( ! [SY34: $i] :
~ ( ~ ( ( SY34
!= ( pair_second @ SV4 ) )
| ! [SY35: $i,SY36: $i] :
( ( SV4
!= ( ordered_pair @ SY35 @ SY36 ) )
| ( SY34 = SY36 ) ) )
| ~ ( ~ ! [SY37: $i,SY38: $i] :
( ( SV4
!= ( ordered_pair @ SY37 @ SY38 ) )
| ( SY34 = SY38 ) )
| ( SY34
= ( pair_second @ SV4 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(420,plain,
! [SV5: $i,SV1: $i] :
( ( empty @ ( ordered_pair @ SV1 @ SV5 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(421,plain,
! [SV7: $i,SV6: $i,SV2: $i] :
( ( ! [SY41: $i] :
( ( ( ordered_pair @ SV2 @ SV6 )
!= ( ordered_pair @ SV7 @ SY41 ) )
| ~ ( ( SV2 != SV7 )
| ( SV6 != SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(422,plain,
! [SV3: $i] :
( ( ( ~ ! [SY25: $i] :
~ ~ ! [SY26: $i] :
( SV3
!= ( ordered_pair @ SY25 @ SY26 ) ) )
= $false )
| ( ( ! [SY27: $i] :
~ ( ~ ( ( SY27
!= ( pair_first @ SV3 ) )
| ! [SY28: $i,SY29: $i] :
( ( SV3
!= ( ordered_pair @ SY28 @ SY29 ) )
| ( SY27 = SY28 ) ) )
| ~ ( ~ ! [SY30: $i,SY31: $i] :
( ( SV3
!= ( ordered_pair @ SY30 @ SY31 ) )
| ( SY27 = SY30 ) )
| ( SY27
= ( pair_first @ SV3 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(423,plain,
! [SV4: $i] :
( ( ( ~ ! [SY32: $i] :
~ ~ ! [SY33: $i] :
( SV4
!= ( ordered_pair @ SY32 @ SY33 ) ) )
= $false )
| ( ( ! [SY34: $i] :
~ ( ~ ( ( SY34
!= ( pair_second @ SV4 ) )
| ! [SY35: $i,SY36: $i] :
( ( SV4
!= ( ordered_pair @ SY35 @ SY36 ) )
| ( SY34 = SY36 ) ) )
| ~ ( ~ ! [SY37: $i,SY38: $i] :
( ( SV4
!= ( ordered_pair @ SY37 @ SY38 ) )
| ( SY34 = SY38 ) )
| ( SY34
= ( pair_second @ SV4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(424,plain,
! [SV8: $i,SV7: $i,SV6: $i,SV2: $i] :
( ( ( ( ordered_pair @ SV2 @ SV6 )
!= ( ordered_pair @ SV7 @ SV8 ) )
| ~ ( ( SV2 != SV7 )
| ( SV6 != SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(425,plain,
! [SV3: $i] :
( ( ( ! [SY25: $i] :
~ ~ ! [SY26: $i] :
( SV3
!= ( ordered_pair @ SY25 @ SY26 ) ) )
= $true )
| ( ( ! [SY27: $i] :
~ ( ~ ( ( SY27
!= ( pair_first @ SV3 ) )
| ! [SY28: $i,SY29: $i] :
( ( SV3
!= ( ordered_pair @ SY28 @ SY29 ) )
| ( SY27 = SY28 ) ) )
| ~ ( ~ ! [SY30: $i,SY31: $i] :
( ( SV3
!= ( ordered_pair @ SY30 @ SY31 ) )
| ( SY27 = SY30 ) )
| ( SY27
= ( pair_first @ SV3 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[422]) ).
thf(426,plain,
! [SV4: $i] :
( ( ( ! [SY32: $i] :
~ ~ ! [SY33: $i] :
( SV4
!= ( ordered_pair @ SY32 @ SY33 ) ) )
= $true )
| ( ( ! [SY34: $i] :
~ ( ~ ( ( SY34
!= ( pair_second @ SV4 ) )
| ! [SY35: $i,SY36: $i] :
( ( SV4
!= ( ordered_pair @ SY35 @ SY36 ) )
| ( SY34 = SY36 ) ) )
| ~ ( ~ ! [SY37: $i,SY38: $i] :
( ( SV4
!= ( ordered_pair @ SY37 @ SY38 ) )
| ( SY34 = SY38 ) )
| ( SY34
= ( pair_second @ SV4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[423]) ).
thf(427,plain,
! [SV8: $i,SV7: $i,SV6: $i,SV2: $i] :
( ( ( ( ordered_pair @ SV2 @ SV6 )
!= ( ordered_pair @ SV7 @ SV8 ) )
= $true )
| ( ( ~ ( ( SV2 != SV7 )
| ( SV6 != SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(428,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ~ ! [SY42: $i] :
( SV3
!= ( ordered_pair @ SV9 @ SY42 ) ) )
= $true )
| ( ( ! [SY27: $i] :
~ ( ~ ( ( SY27
!= ( pair_first @ SV3 ) )
| ! [SY28: $i,SY29: $i] :
( ( SV3
!= ( ordered_pair @ SY28 @ SY29 ) )
| ( SY27 = SY28 ) ) )
| ~ ( ~ ! [SY30: $i,SY31: $i] :
( ( SV3
!= ( ordered_pair @ SY30 @ SY31 ) )
| ( SY27 = SY30 ) )
| ( SY27
= ( pair_first @ SV3 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(429,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ~ ! [SY43: $i] :
( SV4
!= ( ordered_pair @ SV10 @ SY43 ) ) )
= $true )
| ( ( ! [SY34: $i] :
~ ( ~ ( ( SY34
!= ( pair_second @ SV4 ) )
| ! [SY35: $i,SY36: $i] :
( ( SV4
!= ( ordered_pair @ SY35 @ SY36 ) )
| ( SY34 = SY36 ) ) )
| ~ ( ~ ! [SY37: $i,SY38: $i] :
( ( SV4
!= ( ordered_pair @ SY37 @ SY38 ) )
| ( SY34 = SY38 ) )
| ( SY34
= ( pair_second @ SV4 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(430,plain,
! [SV8: $i,SV7: $i,SV6: $i,SV2: $i] :
( ( ( ( ordered_pair @ SV2 @ SV6 )
= ( ordered_pair @ SV7 @ SV8 ) )
= $false )
| ( ( ~ ( ( SV2 != SV7 )
| ( SV6 != SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(431,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ! [SY42: $i] :
( SV3
!= ( ordered_pair @ SV9 @ SY42 ) ) )
= $false )
| ( ( ! [SY27: $i] :
~ ( ~ ( ( SY27
!= ( pair_first @ SV3 ) )
| ! [SY28: $i,SY29: $i] :
( ( SV3
!= ( ordered_pair @ SY28 @ SY29 ) )
| ( SY27 = SY28 ) ) )
| ~ ( ~ ! [SY30: $i,SY31: $i] :
( ( SV3
!= ( ordered_pair @ SY30 @ SY31 ) )
| ( SY27 = SY30 ) )
| ( SY27
= ( pair_first @ SV3 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(432,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ! [SY43: $i] :
( SV4
!= ( ordered_pair @ SV10 @ SY43 ) ) )
= $false )
| ( ( ! [SY34: $i] :
~ ( ~ ( ( SY34
!= ( pair_second @ SV4 ) )
| ! [SY35: $i,SY36: $i] :
( ( SV4
!= ( ordered_pair @ SY35 @ SY36 ) )
| ( SY34 = SY36 ) ) )
| ~ ( ~ ! [SY37: $i,SY38: $i] :
( ( SV4
!= ( ordered_pair @ SY37 @ SY38 ) )
| ( SY34 = SY38 ) )
| ( SY34
= ( pair_second @ SV4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(433,plain,
! [SV8: $i,SV6: $i,SV7: $i,SV2: $i] :
( ( ( ( SV2 != SV7 )
| ( SV6 != SV8 ) )
= $false )
| ( ( ( ordered_pair @ SV2 @ SV6 )
= ( ordered_pair @ SV7 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(434,plain,
! [SV9: $i,SV3: $i] :
( ( ( ! [SY42: $i] :
( SV3
!= ( ordered_pair @ SV9 @ SY42 ) ) )
= $true )
| ( ( ! [SY27: $i] :
~ ( ~ ( ( SY27
!= ( pair_first @ SV3 ) )
| ! [SY28: $i,SY29: $i] :
( ( SV3
!= ( ordered_pair @ SY28 @ SY29 ) )
| ( SY27 = SY28 ) ) )
| ~ ( ~ ! [SY30: $i,SY31: $i] :
( ( SV3
!= ( ordered_pair @ SY30 @ SY31 ) )
| ( SY27 = SY30 ) )
| ( SY27
= ( pair_first @ SV3 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(435,plain,
! [SV10: $i,SV4: $i] :
( ( ( ! [SY43: $i] :
( SV4
!= ( ordered_pair @ SV10 @ SY43 ) ) )
= $true )
| ( ( ! [SY34: $i] :
~ ( ~ ( ( SY34
!= ( pair_second @ SV4 ) )
| ! [SY35: $i,SY36: $i] :
( ( SV4
!= ( ordered_pair @ SY35 @ SY36 ) )
| ( SY34 = SY36 ) ) )
| ~ ( ~ ! [SY37: $i,SY38: $i] :
( ( SV4
!= ( ordered_pair @ SY37 @ SY38 ) )
| ( SY34 = SY38 ) )
| ( SY34
= ( pair_second @ SV4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(436,plain,
! [SV8: $i,SV6: $i,SV7: $i,SV2: $i] :
( ( ( SV2 != SV7 )
= $false )
| ( ( ( ordered_pair @ SV2 @ SV6 )
= ( ordered_pair @ SV7 @ SV8 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(437,plain,
! [SV7: $i,SV2: $i,SV8: $i,SV6: $i] :
( ( ( SV6 != SV8 )
= $false )
| ( ( ( ordered_pair @ SV2 @ SV6 )
= ( ordered_pair @ SV7 @ SV8 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(438,plain,
! [SV11: $i,SV9: $i,SV3: $i] :
( ( ( SV3
!= ( ordered_pair @ SV9 @ SV11 ) )
= $true )
| ( ( ! [SY27: $i] :
~ ( ~ ( ( SY27
!= ( pair_first @ SV3 ) )
| ! [SY28: $i,SY29: $i] :
( ( SV3
!= ( ordered_pair @ SY28 @ SY29 ) )
| ( SY27 = SY28 ) ) )
| ~ ( ~ ! [SY30: $i,SY31: $i] :
( ( SV3
!= ( ordered_pair @ SY30 @ SY31 ) )
| ( SY27 = SY30 ) )
| ( SY27
= ( pair_first @ SV3 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(439,plain,
! [SV12: $i,SV10: $i,SV4: $i] :
( ( ( SV4
!= ( ordered_pair @ SV10 @ SV12 ) )
= $true )
| ( ( ! [SY34: $i] :
~ ( ~ ( ( SY34
!= ( pair_second @ SV4 ) )
| ! [SY35: $i,SY36: $i] :
( ( SV4
!= ( ordered_pair @ SY35 @ SY36 ) )
| ( SY34 = SY36 ) ) )
| ~ ( ~ ! [SY37: $i,SY38: $i] :
( ( SV4
!= ( ordered_pair @ SY37 @ SY38 ) )
| ( SY34 = SY38 ) )
| ( SY34
= ( pair_second @ SV4 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(440,plain,
! [SV8: $i,SV6: $i,SV7: $i,SV2: $i] :
( ( ( SV2 = SV7 )
= $true )
| ( ( ( ordered_pair @ SV2 @ SV6 )
= ( ordered_pair @ SV7 @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[436]) ).
thf(441,plain,
! [SV7: $i,SV2: $i,SV8: $i,SV6: $i] :
( ( ( SV6 = SV8 )
= $true )
| ( ( ( ordered_pair @ SV2 @ SV6 )
= ( ordered_pair @ SV7 @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[437]) ).
thf(442,plain,
! [SV11: $i,SV9: $i,SV3: $i] :
( ( ( SV3
= ( ordered_pair @ SV9 @ SV11 ) )
= $false )
| ( ( ! [SY27: $i] :
~ ( ~ ( ( SY27
!= ( pair_first @ SV3 ) )
| ! [SY28: $i,SY29: $i] :
( ( SV3
!= ( ordered_pair @ SY28 @ SY29 ) )
| ( SY27 = SY28 ) ) )
| ~ ( ~ ! [SY30: $i,SY31: $i] :
( ( SV3
!= ( ordered_pair @ SY30 @ SY31 ) )
| ( SY27 = SY30 ) )
| ( SY27
= ( pair_first @ SV3 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(443,plain,
! [SV12: $i,SV10: $i,SV4: $i] :
( ( ( SV4
= ( ordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( ! [SY34: $i] :
~ ( ~ ( ( SY34
!= ( pair_second @ SV4 ) )
| ! [SY35: $i,SY36: $i] :
( ( SV4
!= ( ordered_pair @ SY35 @ SY36 ) )
| ( SY34 = SY36 ) ) )
| ~ ( ~ ! [SY37: $i,SY38: $i] :
( ( SV4
!= ( ordered_pair @ SY37 @ SY38 ) )
| ( SY34 = SY38 ) )
| ( SY34
= ( pair_second @ SV4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(444,plain,
! [SV11: $i,SV9: $i,SV3: $i,SV13: $i] :
( ( ( ~ ( ~ ( ( SV13
!= ( pair_first @ SV3 ) )
| ! [SY44: $i,SY45: $i] :
( ( SV3
!= ( ordered_pair @ SY44 @ SY45 ) )
| ( SV13 = SY44 ) ) )
| ~ ( ~ ! [SY46: $i,SY47: $i] :
( ( SV3
!= ( ordered_pair @ SY46 @ SY47 ) )
| ( SV13 = SY46 ) )
| ( SV13
= ( pair_first @ SV3 ) ) ) ) )
= $true )
| ( ( SV3
= ( ordered_pair @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(445,plain,
! [SV12: $i,SV10: $i,SV4: $i,SV14: $i] :
( ( ( ~ ( ~ ( ( SV14
!= ( pair_second @ SV4 ) )
| ! [SY48: $i,SY49: $i] :
( ( SV4
!= ( ordered_pair @ SY48 @ SY49 ) )
| ( SV14 = SY49 ) ) )
| ~ ( ~ ! [SY50: $i,SY51: $i] :
( ( SV4
!= ( ordered_pair @ SY50 @ SY51 ) )
| ( SV14 = SY51 ) )
| ( SV14
= ( pair_second @ SV4 ) ) ) ) )
= $true )
| ( ( SV4
= ( ordered_pair @ SV10 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(446,plain,
! [SV11: $i,SV9: $i,SV3: $i,SV13: $i] :
( ( ( ~ ( ( SV13
!= ( pair_first @ SV3 ) )
| ! [SY44: $i,SY45: $i] :
( ( SV3
!= ( ordered_pair @ SY44 @ SY45 ) )
| ( SV13 = SY44 ) ) )
| ~ ( ~ ! [SY46: $i,SY47: $i] :
( ( SV3
!= ( ordered_pair @ SY46 @ SY47 ) )
| ( SV13 = SY46 ) )
| ( SV13
= ( pair_first @ SV3 ) ) ) )
= $false )
| ( ( SV3
= ( ordered_pair @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(447,plain,
! [SV12: $i,SV10: $i,SV4: $i,SV14: $i] :
( ( ( ~ ( ( SV14
!= ( pair_second @ SV4 ) )
| ! [SY48: $i,SY49: $i] :
( ( SV4
!= ( ordered_pair @ SY48 @ SY49 ) )
| ( SV14 = SY49 ) ) )
| ~ ( ~ ! [SY50: $i,SY51: $i] :
( ( SV4
!= ( ordered_pair @ SY50 @ SY51 ) )
| ( SV14 = SY51 ) )
| ( SV14
= ( pair_second @ SV4 ) ) ) )
= $false )
| ( ( SV4
= ( ordered_pair @ SV10 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(448,plain,
! [SV11: $i,SV9: $i,SV3: $i,SV13: $i] :
( ( ( ~ ( ( SV13
!= ( pair_first @ SV3 ) )
| ! [SY44: $i,SY45: $i] :
( ( SV3
!= ( ordered_pair @ SY44 @ SY45 ) )
| ( SV13 = SY44 ) ) ) )
= $false )
| ( ( SV3
= ( ordered_pair @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[446]) ).
thf(449,plain,
! [SV11: $i,SV9: $i,SV13: $i,SV3: $i] :
( ( ( ~ ( ~ ! [SY46: $i,SY47: $i] :
( ( SV3
!= ( ordered_pair @ SY46 @ SY47 ) )
| ( SV13 = SY46 ) )
| ( SV13
= ( pair_first @ SV3 ) ) ) )
= $false )
| ( ( SV3
= ( ordered_pair @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[446]) ).
thf(450,plain,
! [SV12: $i,SV10: $i,SV4: $i,SV14: $i] :
( ( ( ~ ( ( SV14
!= ( pair_second @ SV4 ) )
| ! [SY48: $i,SY49: $i] :
( ( SV4
!= ( ordered_pair @ SY48 @ SY49 ) )
| ( SV14 = SY49 ) ) ) )
= $false )
| ( ( SV4
= ( ordered_pair @ SV10 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[447]) ).
thf(451,plain,
! [SV12: $i,SV10: $i,SV14: $i,SV4: $i] :
( ( ( ~ ( ~ ! [SY50: $i,SY51: $i] :
( ( SV4
!= ( ordered_pair @ SY50 @ SY51 ) )
| ( SV14 = SY51 ) )
| ( SV14
= ( pair_second @ SV4 ) ) ) )
= $false )
| ( ( SV4
= ( ordered_pair @ SV10 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[447]) ).
thf(452,plain,
! [SV11: $i,SV9: $i,SV3: $i,SV13: $i] :
( ( ( ( SV13
!= ( pair_first @ SV3 ) )
| ! [SY44: $i,SY45: $i] :
( ( SV3
!= ( ordered_pair @ SY44 @ SY45 ) )
| ( SV13 = SY44 ) ) )
= $true )
| ( ( SV3
= ( ordered_pair @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(453,plain,
! [SV11: $i,SV9: $i,SV13: $i,SV3: $i] :
( ( ( ~ ! [SY46: $i,SY47: $i] :
( ( SV3
!= ( ordered_pair @ SY46 @ SY47 ) )
| ( SV13 = SY46 ) )
| ( SV13
= ( pair_first @ SV3 ) ) )
= $true )
| ( ( SV3
= ( ordered_pair @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(454,plain,
! [SV12: $i,SV10: $i,SV4: $i,SV14: $i] :
( ( ( ( SV14
!= ( pair_second @ SV4 ) )
| ! [SY48: $i,SY49: $i] :
( ( SV4
!= ( ordered_pair @ SY48 @ SY49 ) )
| ( SV14 = SY49 ) ) )
= $true )
| ( ( SV4
= ( ordered_pair @ SV10 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(455,plain,
! [SV12: $i,SV10: $i,SV14: $i,SV4: $i] :
( ( ( ~ ! [SY50: $i,SY51: $i] :
( ( SV4
!= ( ordered_pair @ SY50 @ SY51 ) )
| ( SV14 = SY51 ) )
| ( SV14
= ( pair_second @ SV4 ) ) )
= $true )
| ( ( SV4
= ( ordered_pair @ SV10 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(456,plain,
! [SV11: $i,SV9: $i,SV3: $i,SV13: $i] :
( ( ( SV13
!= ( pair_first @ SV3 ) )
= $true )
| ( ( ! [SY44: $i,SY45: $i] :
( ( SV3
!= ( ordered_pair @ SY44 @ SY45 ) )
| ( SV13 = SY44 ) ) )
= $true )
| ( ( SV3
= ( ordered_pair @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(457,plain,
! [SV11: $i,SV9: $i,SV13: $i,SV3: $i] :
( ( ( ~ ! [SY46: $i,SY47: $i] :
( ( SV3
!= ( ordered_pair @ SY46 @ SY47 ) )
| ( SV13 = SY46 ) ) )
= $true )
| ( ( SV13
= ( pair_first @ SV3 ) )
= $true )
| ( ( SV3
= ( ordered_pair @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[453]) ).
thf(458,plain,
! [SV12: $i,SV10: $i,SV4: $i,SV14: $i] :
( ( ( SV14
!= ( pair_second @ SV4 ) )
= $true )
| ( ( ! [SY48: $i,SY49: $i] :
( ( SV4
!= ( ordered_pair @ SY48 @ SY49 ) )
| ( SV14 = SY49 ) ) )
= $true )
| ( ( SV4
= ( ordered_pair @ SV10 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(459,plain,
! [SV12: $i,SV10: $i,SV14: $i,SV4: $i] :
( ( ( ~ ! [SY50: $i,SY51: $i] :
( ( SV4
!= ( ordered_pair @ SY50 @ SY51 ) )
| ( SV14 = SY51 ) ) )
= $true )
| ( ( SV14
= ( pair_second @ SV4 ) )
= $true )
| ( ( SV4
= ( ordered_pair @ SV10 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(460,plain,
! [SV11: $i,SV9: $i,SV3: $i,SV13: $i] :
( ( ( SV13
= ( pair_first @ SV3 ) )
= $false )
| ( ( ! [SY44: $i,SY45: $i] :
( ( SV3
!= ( ordered_pair @ SY44 @ SY45 ) )
| ( SV13 = SY44 ) ) )
= $true )
| ( ( SV3
= ( ordered_pair @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(461,plain,
! [SV11: $i,SV9: $i,SV13: $i,SV3: $i] :
( ( ( ! [SY46: $i,SY47: $i] :
( ( SV3
!= ( ordered_pair @ SY46 @ SY47 ) )
| ( SV13 = SY46 ) ) )
= $false )
| ( ( SV13
= ( pair_first @ SV3 ) )
= $true )
| ( ( SV3
= ( ordered_pair @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(462,plain,
! [SV12: $i,SV10: $i,SV4: $i,SV14: $i] :
( ( ( SV14
= ( pair_second @ SV4 ) )
= $false )
| ( ( ! [SY48: $i,SY49: $i] :
( ( SV4
!= ( ordered_pair @ SY48 @ SY49 ) )
| ( SV14 = SY49 ) ) )
= $true )
| ( ( SV4
= ( ordered_pair @ SV10 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(463,plain,
! [SV12: $i,SV10: $i,SV14: $i,SV4: $i] :
( ( ( ! [SY50: $i,SY51: $i] :
( ( SV4
!= ( ordered_pair @ SY50 @ SY51 ) )
| ( SV14 = SY51 ) ) )
= $false )
| ( ( SV14
= ( pair_second @ SV4 ) )
= $true )
| ( ( SV4
= ( ordered_pair @ SV10 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(464,plain,
! [SV11: $i,SV9: $i,SV13: $i,SV15: $i,SV3: $i] :
( ( ( ! [SY52: $i] :
( ( SV3
!= ( ordered_pair @ SV15 @ SY52 ) )
| ( SV13 = SV15 ) ) )
= $true )
| ( ( SV13
= ( pair_first @ SV3 ) )
= $false )
| ( ( SV3
= ( ordered_pair @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(465,plain,
! [SV13: $i,SV9: $i,SV11: $i,SV3: $i] :
( ( ( ! [SY53: $i] :
( ( SV3
!= ( ordered_pair @ ( sK3_SY46 @ SV11 @ SV9 @ SV13 @ SV3 ) @ SY53 ) )
| ( SV13
= ( sK3_SY46 @ SV11 @ SV9 @ SV13 @ SV3 ) ) ) )
= $false )
| ( ( SV13
= ( pair_first @ SV3 ) )
= $true )
| ( ( SV3
= ( ordered_pair @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[461]) ).
thf(466,plain,
! [SV12: $i,SV10: $i,SV14: $i,SV16: $i,SV4: $i] :
( ( ( ! [SY54: $i] :
( ( SV4
!= ( ordered_pair @ SV16 @ SY54 ) )
| ( SV14 = SY54 ) ) )
= $true )
| ( ( SV14
= ( pair_second @ SV4 ) )
= $false )
| ( ( SV4
= ( ordered_pair @ SV10 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(467,plain,
! [SV14: $i,SV10: $i,SV12: $i,SV4: $i] :
( ( ( ! [SY55: $i] :
( ( SV4
!= ( ordered_pair @ ( sK4_SY50 @ SV12 @ SV10 @ SV14 @ SV4 ) @ SY55 ) )
| ( SV14 = SY55 ) ) )
= $false )
| ( ( SV14
= ( pair_second @ SV4 ) )
= $true )
| ( ( SV4
= ( ordered_pair @ SV10 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[463]) ).
thf(468,plain,
! [SV11: $i,SV9: $i,SV13: $i,SV17: $i,SV15: $i,SV3: $i] :
( ( ( ( SV3
!= ( ordered_pair @ SV15 @ SV17 ) )
| ( SV13 = SV15 ) )
= $true )
| ( ( SV13
= ( pair_first @ SV3 ) )
= $false )
| ( ( SV3
= ( ordered_pair @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(469,plain,
! [SV13: $i,SV9: $i,SV11: $i,SV3: $i] :
( ( ( ( SV3
!= ( ordered_pair @ ( sK3_SY46 @ SV11 @ SV9 @ SV13 @ SV3 ) @ ( sK5_SY53 @ SV13 @ SV9 @ SV11 @ SV3 ) ) )
| ( SV13
= ( sK3_SY46 @ SV11 @ SV9 @ SV13 @ SV3 ) ) )
= $false )
| ( ( SV13
= ( pair_first @ SV3 ) )
= $true )
| ( ( SV3
= ( ordered_pair @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[465]) ).
thf(470,plain,
! [SV12: $i,SV10: $i,SV14: $i,SV18: $i,SV16: $i,SV4: $i] :
( ( ( ( SV4
!= ( ordered_pair @ SV16 @ SV18 ) )
| ( SV14 = SV18 ) )
= $true )
| ( ( SV14
= ( pair_second @ SV4 ) )
= $false )
| ( ( SV4
= ( ordered_pair @ SV10 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(471,plain,
! [SV14: $i,SV10: $i,SV12: $i,SV4: $i] :
( ( ( ( SV4
!= ( ordered_pair @ ( sK4_SY50 @ SV12 @ SV10 @ SV14 @ SV4 ) @ ( sK6_SY55 @ SV14 @ SV10 @ SV12 @ SV4 ) ) )
| ( SV14
= ( sK6_SY55 @ SV14 @ SV10 @ SV12 @ SV4 ) ) )
= $false )
| ( ( SV14
= ( pair_second @ SV4 ) )
= $true )
| ( ( SV4
= ( ordered_pair @ SV10 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[467]) ).
thf(472,plain,
! [SV11: $i,SV9: $i,SV13: $i,SV17: $i,SV15: $i,SV3: $i] :
( ( ( SV3
!= ( ordered_pair @ SV15 @ SV17 ) )
= $true )
| ( ( SV13 = SV15 )
= $true )
| ( ( SV13
= ( pair_first @ SV3 ) )
= $false )
| ( ( SV3
= ( ordered_pair @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(473,plain,
! [SV13: $i,SV9: $i,SV11: $i,SV3: $i] :
( ( ( SV3
!= ( ordered_pair @ ( sK3_SY46 @ SV11 @ SV9 @ SV13 @ SV3 ) @ ( sK5_SY53 @ SV13 @ SV9 @ SV11 @ SV3 ) ) )
= $false )
| ( ( SV13
= ( pair_first @ SV3 ) )
= $true )
| ( ( SV3
= ( ordered_pair @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[469]) ).
thf(474,plain,
! [SV3: $i,SV9: $i,SV11: $i,SV13: $i] :
( ( ( SV13
= ( sK3_SY46 @ SV11 @ SV9 @ SV13 @ SV3 ) )
= $false )
| ( ( SV13
= ( pair_first @ SV3 ) )
= $true )
| ( ( SV3
= ( ordered_pair @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[469]) ).
thf(475,plain,
! [SV12: $i,SV10: $i,SV14: $i,SV18: $i,SV16: $i,SV4: $i] :
( ( ( SV4
!= ( ordered_pair @ SV16 @ SV18 ) )
= $true )
| ( ( SV14 = SV18 )
= $true )
| ( ( SV14
= ( pair_second @ SV4 ) )
= $false )
| ( ( SV4
= ( ordered_pair @ SV10 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(476,plain,
! [SV14: $i,SV10: $i,SV12: $i,SV4: $i] :
( ( ( SV4
!= ( ordered_pair @ ( sK4_SY50 @ SV12 @ SV10 @ SV14 @ SV4 ) @ ( sK6_SY55 @ SV14 @ SV10 @ SV12 @ SV4 ) ) )
= $false )
| ( ( SV14
= ( pair_second @ SV4 ) )
= $true )
| ( ( SV4
= ( ordered_pair @ SV10 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[471]) ).
thf(477,plain,
! [SV4: $i,SV12: $i,SV10: $i,SV14: $i] :
( ( ( SV14
= ( sK6_SY55 @ SV14 @ SV10 @ SV12 @ SV4 ) )
= $false )
| ( ( SV14
= ( pair_second @ SV4 ) )
= $true )
| ( ( SV4
= ( ordered_pair @ SV10 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[471]) ).
thf(478,plain,
! [SV11: $i,SV9: $i,SV13: $i,SV17: $i,SV15: $i,SV3: $i] :
( ( ( SV3
= ( ordered_pair @ SV15 @ SV17 ) )
= $false )
| ( ( SV13 = SV15 )
= $true )
| ( ( SV13
= ( pair_first @ SV3 ) )
= $false )
| ( ( SV3
= ( ordered_pair @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(479,plain,
! [SV13: $i,SV9: $i,SV11: $i,SV3: $i] :
( ( ( SV3
= ( ordered_pair @ ( sK3_SY46 @ SV11 @ SV9 @ SV13 @ SV3 ) @ ( sK5_SY53 @ SV13 @ SV9 @ SV11 @ SV3 ) ) )
= $true )
| ( ( SV13
= ( pair_first @ SV3 ) )
= $true )
| ( ( SV3
= ( ordered_pair @ SV9 @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(480,plain,
! [SV12: $i,SV10: $i,SV14: $i,SV18: $i,SV16: $i,SV4: $i] :
( ( ( SV4
= ( ordered_pair @ SV16 @ SV18 ) )
= $false )
| ( ( SV14 = SV18 )
= $true )
| ( ( SV14
= ( pair_second @ SV4 ) )
= $false )
| ( ( SV4
= ( ordered_pair @ SV10 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(481,plain,
! [SV14: $i,SV10: $i,SV12: $i,SV4: $i] :
( ( ( SV4
= ( ordered_pair @ ( sK4_SY50 @ SV12 @ SV10 @ SV14 @ SV4 ) @ ( sK6_SY55 @ SV14 @ SV10 @ SV12 @ SV4 ) ) )
= $true )
| ( ( SV14
= ( pair_second @ SV4 ) )
= $true )
| ( ( SV4
= ( ordered_pair @ SV10 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[476]) ).
thf(482,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[382,481,480,479,478,477,474,441,440,420,412,405,404,403,402,401,400,399,398,397,396,395,394,393,392,391,390,389,388,387,386,385,384,383]) ).
thf(483,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(484,plain,
( ( ! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( ordered_pair @ B @ C ) )
=> ! [B: $i] :
( ( B
= ( pair_first @ A ) )
<=> ! [C: $i,D: $i] :
( ( A
= ( ordered_pair @ C @ D ) )
=> ( B = C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(485,plain,
( ( ! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( ordered_pair @ B @ C ) )
=> ! [B: $i] :
( ( B
= ( pair_second @ A ) )
<=> ! [C: $i,D: $i] :
( ( A
= ( ordered_pair @ C @ D ) )
=> ( B = D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(486,plain,
$true = $true,
inference(copy,[status(thm)],[369]) ).
thf(487,plain,
$true = $true,
inference(copy,[status(thm)],[368]) ).
thf(488,plain,
$true = $true,
inference(copy,[status(thm)],[367]) ).
thf(489,plain,
$true = $true,
inference(copy,[status(thm)],[366]) ).
thf(490,plain,
$true = $true,
inference(copy,[status(thm)],[365]) ).
thf(491,plain,
$true = $true,
inference(copy,[status(thm)],[364]) ).
thf(492,plain,
$true = $true,
inference(copy,[status(thm)],[363]) ).
thf(493,plain,
$true = $true,
inference(copy,[status(thm)],[362]) ).
thf(494,plain,
$true = $true,
inference(copy,[status(thm)],[361]) ).
thf(495,plain,
$true = $true,
inference(copy,[status(thm)],[360]) ).
thf(496,plain,
$true = $true,
inference(copy,[status(thm)],[359]) ).
thf(497,plain,
$true = $true,
inference(copy,[status(thm)],[358]) ).
thf(498,plain,
$true = $true,
inference(copy,[status(thm)],[357]) ).
thf(499,plain,
$true = $true,
inference(copy,[status(thm)],[356]) ).
thf(500,plain,
$true = $true,
inference(copy,[status(thm)],[355]) ).
thf(501,plain,
$true = $true,
inference(copy,[status(thm)],[354]) ).
thf(502,plain,
$true = $true,
inference(copy,[status(thm)],[353]) ).
thf(503,plain,
$true = $true,
inference(copy,[status(thm)],[352]) ).
thf(504,plain,
$true = $true,
inference(copy,[status(thm)],[351]) ).
thf(505,plain,
$true = $true,
inference(copy,[status(thm)],[350]) ).
thf(506,plain,
$true = $true,
inference(copy,[status(thm)],[349]) ).
thf(507,plain,
$true = $true,
inference(copy,[status(thm)],[348]) ).
thf(508,plain,
$true = $true,
inference(copy,[status(thm)],[347]) ).
thf(509,plain,
$true = $true,
inference(copy,[status(thm)],[346]) ).
thf(510,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(511,plain,
( ( ( pair_second @ ( ordered_pair @ sK1_A @ sK2_SY20 ) )
!= sK2_SY20 )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(512,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[483]) ).
thf(513,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
( SX0
!= ( ordered_pair @ SX1 @ SX2 ) )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( pair_second @ SX0 ) )
| ! [SX2: $i,SX3: $i] :
( ( SX0
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX0
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) )
| ( SX1
= ( pair_second @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485]) ).
thf(514,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
( SX0
!= ( ordered_pair @ SX1 @ SX2 ) )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( pair_first @ SX0 ) )
| ! [SX2: $i,SX3: $i] :
( ( SX0
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX1 = SX2 ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX0
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX1 = SX2 ) )
| ( SX1
= ( pair_first @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484]) ).
thf(515,plain,
! [SV19: $i] :
( ( ! [SY56: $i] :
~ ( empty @ ( ordered_pair @ SV19 @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(516,plain,
( ( ( pair_second @ ( ordered_pair @ sK1_A @ sK2_SY20 ) )
= sK2_SY20 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(517,plain,
! [SV20: $i] :
( ( ! [SY57: $i,SY58: $i,SY59: $i] :
( ( ( ordered_pair @ SV20 @ SY57 )
!= ( ordered_pair @ SY58 @ SY59 ) )
| ~ ( ( SV20 != SY58 )
| ( SY57 != SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(518,plain,
! [SV21: $i] :
( ( ~ ~ ! [SY60: $i] :
~ ~ ! [SY61: $i] :
( SV21
!= ( ordered_pair @ SY60 @ SY61 ) )
| ! [SY62: $i] :
~ ( ~ ( ( SY62
!= ( pair_second @ SV21 ) )
| ! [SY63: $i,SY64: $i] :
( ( SV21
!= ( ordered_pair @ SY63 @ SY64 ) )
| ( SY62 = SY64 ) ) )
| ~ ( ~ ! [SY65: $i,SY66: $i] :
( ( SV21
!= ( ordered_pair @ SY65 @ SY66 ) )
| ( SY62 = SY66 ) )
| ( SY62
= ( pair_second @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(519,plain,
! [SV22: $i] :
( ( ~ ~ ! [SY67: $i] :
~ ~ ! [SY68: $i] :
( SV22
!= ( ordered_pair @ SY67 @ SY68 ) )
| ! [SY69: $i] :
~ ( ~ ( ( SY69
!= ( pair_first @ SV22 ) )
| ! [SY70: $i,SY71: $i] :
( ( SV22
!= ( ordered_pair @ SY70 @ SY71 ) )
| ( SY69 = SY70 ) ) )
| ~ ( ~ ! [SY72: $i,SY73: $i] :
( ( SV22
!= ( ordered_pair @ SY72 @ SY73 ) )
| ( SY69 = SY72 ) )
| ( SY69
= ( pair_first @ SV22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(520,plain,
! [SV23: $i,SV19: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV19 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(521,plain,
! [SV24: $i,SV20: $i] :
( ( ! [SY74: $i,SY75: $i] :
( ( ( ordered_pair @ SV20 @ SV24 )
!= ( ordered_pair @ SY74 @ SY75 ) )
| ~ ( ( SV20 != SY74 )
| ( SV24 != SY75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(522,plain,
! [SV21: $i] :
( ( ( ~ ~ ! [SY60: $i] :
~ ~ ! [SY61: $i] :
( SV21
!= ( ordered_pair @ SY60 @ SY61 ) ) )
= $true )
| ( ( ! [SY62: $i] :
~ ( ~ ( ( SY62
!= ( pair_second @ SV21 ) )
| ! [SY63: $i,SY64: $i] :
( ( SV21
!= ( ordered_pair @ SY63 @ SY64 ) )
| ( SY62 = SY64 ) ) )
| ~ ( ~ ! [SY65: $i,SY66: $i] :
( ( SV21
!= ( ordered_pair @ SY65 @ SY66 ) )
| ( SY62 = SY66 ) )
| ( SY62
= ( pair_second @ SV21 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[518]) ).
thf(523,plain,
! [SV22: $i] :
( ( ( ~ ~ ! [SY67: $i] :
~ ~ ! [SY68: $i] :
( SV22
!= ( ordered_pair @ SY67 @ SY68 ) ) )
= $true )
| ( ( ! [SY69: $i] :
~ ( ~ ( ( SY69
!= ( pair_first @ SV22 ) )
| ! [SY70: $i,SY71: $i] :
( ( SV22
!= ( ordered_pair @ SY70 @ SY71 ) )
| ( SY69 = SY70 ) ) )
| ~ ( ~ ! [SY72: $i,SY73: $i] :
( ( SV22
!= ( ordered_pair @ SY72 @ SY73 ) )
| ( SY69 = SY72 ) )
| ( SY69
= ( pair_first @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(524,plain,
! [SV23: $i,SV19: $i] :
( ( empty @ ( ordered_pair @ SV19 @ SV23 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(525,plain,
! [SV25: $i,SV24: $i,SV20: $i] :
( ( ! [SY76: $i] :
( ( ( ordered_pair @ SV20 @ SV24 )
!= ( ordered_pair @ SV25 @ SY76 ) )
| ~ ( ( SV20 != SV25 )
| ( SV24 != SY76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(526,plain,
! [SV21: $i] :
( ( ( ~ ! [SY60: $i] :
~ ~ ! [SY61: $i] :
( SV21
!= ( ordered_pair @ SY60 @ SY61 ) ) )
= $false )
| ( ( ! [SY62: $i] :
~ ( ~ ( ( SY62
!= ( pair_second @ SV21 ) )
| ! [SY63: $i,SY64: $i] :
( ( SV21
!= ( ordered_pair @ SY63 @ SY64 ) )
| ( SY62 = SY64 ) ) )
| ~ ( ~ ! [SY65: $i,SY66: $i] :
( ( SV21
!= ( ordered_pair @ SY65 @ SY66 ) )
| ( SY62 = SY66 ) )
| ( SY62
= ( pair_second @ SV21 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(527,plain,
! [SV22: $i] :
( ( ( ~ ! [SY67: $i] :
~ ~ ! [SY68: $i] :
( SV22
!= ( ordered_pair @ SY67 @ SY68 ) ) )
= $false )
| ( ( ! [SY69: $i] :
~ ( ~ ( ( SY69
!= ( pair_first @ SV22 ) )
| ! [SY70: $i,SY71: $i] :
( ( SV22
!= ( ordered_pair @ SY70 @ SY71 ) )
| ( SY69 = SY70 ) ) )
| ~ ( ~ ! [SY72: $i,SY73: $i] :
( ( SV22
!= ( ordered_pair @ SY72 @ SY73 ) )
| ( SY69 = SY72 ) )
| ( SY69
= ( pair_first @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(528,plain,
! [SV26: $i,SV25: $i,SV24: $i,SV20: $i] :
( ( ( ( ordered_pair @ SV20 @ SV24 )
!= ( ordered_pair @ SV25 @ SV26 ) )
| ~ ( ( SV20 != SV25 )
| ( SV24 != SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(529,plain,
! [SV21: $i] :
( ( ( ! [SY60: $i] :
~ ~ ! [SY61: $i] :
( SV21
!= ( ordered_pair @ SY60 @ SY61 ) ) )
= $true )
| ( ( ! [SY62: $i] :
~ ( ~ ( ( SY62
!= ( pair_second @ SV21 ) )
| ! [SY63: $i,SY64: $i] :
( ( SV21
!= ( ordered_pair @ SY63 @ SY64 ) )
| ( SY62 = SY64 ) ) )
| ~ ( ~ ! [SY65: $i,SY66: $i] :
( ( SV21
!= ( ordered_pair @ SY65 @ SY66 ) )
| ( SY62 = SY66 ) )
| ( SY62
= ( pair_second @ SV21 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(530,plain,
! [SV22: $i] :
( ( ( ! [SY67: $i] :
~ ~ ! [SY68: $i] :
( SV22
!= ( ordered_pair @ SY67 @ SY68 ) ) )
= $true )
| ( ( ! [SY69: $i] :
~ ( ~ ( ( SY69
!= ( pair_first @ SV22 ) )
| ! [SY70: $i,SY71: $i] :
( ( SV22
!= ( ordered_pair @ SY70 @ SY71 ) )
| ( SY69 = SY70 ) ) )
| ~ ( ~ ! [SY72: $i,SY73: $i] :
( ( SV22
!= ( ordered_pair @ SY72 @ SY73 ) )
| ( SY69 = SY72 ) )
| ( SY69
= ( pair_first @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(531,plain,
! [SV26: $i,SV25: $i,SV24: $i,SV20: $i] :
( ( ( ( ordered_pair @ SV20 @ SV24 )
!= ( ordered_pair @ SV25 @ SV26 ) )
= $true )
| ( ( ~ ( ( SV20 != SV25 )
| ( SV24 != SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[528]) ).
thf(532,plain,
! [SV27: $i,SV21: $i] :
( ( ( ~ ~ ! [SY77: $i] :
( SV21
!= ( ordered_pair @ SV27 @ SY77 ) ) )
= $true )
| ( ( ! [SY62: $i] :
~ ( ~ ( ( SY62
!= ( pair_second @ SV21 ) )
| ! [SY63: $i,SY64: $i] :
( ( SV21
!= ( ordered_pair @ SY63 @ SY64 ) )
| ( SY62 = SY64 ) ) )
| ~ ( ~ ! [SY65: $i,SY66: $i] :
( ( SV21
!= ( ordered_pair @ SY65 @ SY66 ) )
| ( SY62 = SY66 ) )
| ( SY62
= ( pair_second @ SV21 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(533,plain,
! [SV28: $i,SV22: $i] :
( ( ( ~ ~ ! [SY78: $i] :
( SV22
!= ( ordered_pair @ SV28 @ SY78 ) ) )
= $true )
| ( ( ! [SY69: $i] :
~ ( ~ ( ( SY69
!= ( pair_first @ SV22 ) )
| ! [SY70: $i,SY71: $i] :
( ( SV22
!= ( ordered_pair @ SY70 @ SY71 ) )
| ( SY69 = SY70 ) ) )
| ~ ( ~ ! [SY72: $i,SY73: $i] :
( ( SV22
!= ( ordered_pair @ SY72 @ SY73 ) )
| ( SY69 = SY72 ) )
| ( SY69
= ( pair_first @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(534,plain,
! [SV26: $i,SV25: $i,SV24: $i,SV20: $i] :
( ( ( ( ordered_pair @ SV20 @ SV24 )
= ( ordered_pair @ SV25 @ SV26 ) )
= $false )
| ( ( ~ ( ( SV20 != SV25 )
| ( SV24 != SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(535,plain,
! [SV27: $i,SV21: $i] :
( ( ( ~ ! [SY77: $i] :
( SV21
!= ( ordered_pair @ SV27 @ SY77 ) ) )
= $false )
| ( ( ! [SY62: $i] :
~ ( ~ ( ( SY62
!= ( pair_second @ SV21 ) )
| ! [SY63: $i,SY64: $i] :
( ( SV21
!= ( ordered_pair @ SY63 @ SY64 ) )
| ( SY62 = SY64 ) ) )
| ~ ( ~ ! [SY65: $i,SY66: $i] :
( ( SV21
!= ( ordered_pair @ SY65 @ SY66 ) )
| ( SY62 = SY66 ) )
| ( SY62
= ( pair_second @ SV21 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(536,plain,
! [SV28: $i,SV22: $i] :
( ( ( ~ ! [SY78: $i] :
( SV22
!= ( ordered_pair @ SV28 @ SY78 ) ) )
= $false )
| ( ( ! [SY69: $i] :
~ ( ~ ( ( SY69
!= ( pair_first @ SV22 ) )
| ! [SY70: $i,SY71: $i] :
( ( SV22
!= ( ordered_pair @ SY70 @ SY71 ) )
| ( SY69 = SY70 ) ) )
| ~ ( ~ ! [SY72: $i,SY73: $i] :
( ( SV22
!= ( ordered_pair @ SY72 @ SY73 ) )
| ( SY69 = SY72 ) )
| ( SY69
= ( pair_first @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(537,plain,
! [SV26: $i,SV24: $i,SV25: $i,SV20: $i] :
( ( ( ( SV20 != SV25 )
| ( SV24 != SV26 ) )
= $false )
| ( ( ( ordered_pair @ SV20 @ SV24 )
= ( ordered_pair @ SV25 @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(538,plain,
! [SV27: $i,SV21: $i] :
( ( ( ! [SY77: $i] :
( SV21
!= ( ordered_pair @ SV27 @ SY77 ) ) )
= $true )
| ( ( ! [SY62: $i] :
~ ( ~ ( ( SY62
!= ( pair_second @ SV21 ) )
| ! [SY63: $i,SY64: $i] :
( ( SV21
!= ( ordered_pair @ SY63 @ SY64 ) )
| ( SY62 = SY64 ) ) )
| ~ ( ~ ! [SY65: $i,SY66: $i] :
( ( SV21
!= ( ordered_pair @ SY65 @ SY66 ) )
| ( SY62 = SY66 ) )
| ( SY62
= ( pair_second @ SV21 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[535]) ).
thf(539,plain,
! [SV28: $i,SV22: $i] :
( ( ( ! [SY78: $i] :
( SV22
!= ( ordered_pair @ SV28 @ SY78 ) ) )
= $true )
| ( ( ! [SY69: $i] :
~ ( ~ ( ( SY69
!= ( pair_first @ SV22 ) )
| ! [SY70: $i,SY71: $i] :
( ( SV22
!= ( ordered_pair @ SY70 @ SY71 ) )
| ( SY69 = SY70 ) ) )
| ~ ( ~ ! [SY72: $i,SY73: $i] :
( ( SV22
!= ( ordered_pair @ SY72 @ SY73 ) )
| ( SY69 = SY72 ) )
| ( SY69
= ( pair_first @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[536]) ).
thf(540,plain,
! [SV26: $i,SV24: $i,SV25: $i,SV20: $i] :
( ( ( SV20 != SV25 )
= $false )
| ( ( ( ordered_pair @ SV20 @ SV24 )
= ( ordered_pair @ SV25 @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(541,plain,
! [SV25: $i,SV20: $i,SV26: $i,SV24: $i] :
( ( ( SV24 != SV26 )
= $false )
| ( ( ( ordered_pair @ SV20 @ SV24 )
= ( ordered_pair @ SV25 @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(542,plain,
! [SV29: $i,SV27: $i,SV21: $i] :
( ( ( SV21
!= ( ordered_pair @ SV27 @ SV29 ) )
= $true )
| ( ( ! [SY62: $i] :
~ ( ~ ( ( SY62
!= ( pair_second @ SV21 ) )
| ! [SY63: $i,SY64: $i] :
( ( SV21
!= ( ordered_pair @ SY63 @ SY64 ) )
| ( SY62 = SY64 ) ) )
| ~ ( ~ ! [SY65: $i,SY66: $i] :
( ( SV21
!= ( ordered_pair @ SY65 @ SY66 ) )
| ( SY62 = SY66 ) )
| ( SY62
= ( pair_second @ SV21 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(543,plain,
! [SV30: $i,SV28: $i,SV22: $i] :
( ( ( SV22
!= ( ordered_pair @ SV28 @ SV30 ) )
= $true )
| ( ( ! [SY69: $i] :
~ ( ~ ( ( SY69
!= ( pair_first @ SV22 ) )
| ! [SY70: $i,SY71: $i] :
( ( SV22
!= ( ordered_pair @ SY70 @ SY71 ) )
| ( SY69 = SY70 ) ) )
| ~ ( ~ ! [SY72: $i,SY73: $i] :
( ( SV22
!= ( ordered_pair @ SY72 @ SY73 ) )
| ( SY69 = SY72 ) )
| ( SY69
= ( pair_first @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(544,plain,
! [SV26: $i,SV24: $i,SV25: $i,SV20: $i] :
( ( ( SV20 = SV25 )
= $true )
| ( ( ( ordered_pair @ SV20 @ SV24 )
= ( ordered_pair @ SV25 @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[540]) ).
thf(545,plain,
! [SV25: $i,SV20: $i,SV26: $i,SV24: $i] :
( ( ( SV24 = SV26 )
= $true )
| ( ( ( ordered_pair @ SV20 @ SV24 )
= ( ordered_pair @ SV25 @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[541]) ).
thf(546,plain,
! [SV29: $i,SV27: $i,SV21: $i] :
( ( ( SV21
= ( ordered_pair @ SV27 @ SV29 ) )
= $false )
| ( ( ! [SY62: $i] :
~ ( ~ ( ( SY62
!= ( pair_second @ SV21 ) )
| ! [SY63: $i,SY64: $i] :
( ( SV21
!= ( ordered_pair @ SY63 @ SY64 ) )
| ( SY62 = SY64 ) ) )
| ~ ( ~ ! [SY65: $i,SY66: $i] :
( ( SV21
!= ( ordered_pair @ SY65 @ SY66 ) )
| ( SY62 = SY66 ) )
| ( SY62
= ( pair_second @ SV21 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(547,plain,
! [SV30: $i,SV28: $i,SV22: $i] :
( ( ( SV22
= ( ordered_pair @ SV28 @ SV30 ) )
= $false )
| ( ( ! [SY69: $i] :
~ ( ~ ( ( SY69
!= ( pair_first @ SV22 ) )
| ! [SY70: $i,SY71: $i] :
( ( SV22
!= ( ordered_pair @ SY70 @ SY71 ) )
| ( SY69 = SY70 ) ) )
| ~ ( ~ ! [SY72: $i,SY73: $i] :
( ( SV22
!= ( ordered_pair @ SY72 @ SY73 ) )
| ( SY69 = SY72 ) )
| ( SY69
= ( pair_first @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(548,plain,
! [SV29: $i,SV27: $i,SV21: $i,SV31: $i] :
( ( ( ~ ( ~ ( ( SV31
!= ( pair_second @ SV21 ) )
| ! [SY79: $i,SY80: $i] :
( ( SV21
!= ( ordered_pair @ SY79 @ SY80 ) )
| ( SV31 = SY80 ) ) )
| ~ ( ~ ! [SY81: $i,SY82: $i] :
( ( SV21
!= ( ordered_pair @ SY81 @ SY82 ) )
| ( SV31 = SY82 ) )
| ( SV31
= ( pair_second @ SV21 ) ) ) ) )
= $true )
| ( ( SV21
= ( ordered_pair @ SV27 @ SV29 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(549,plain,
! [SV30: $i,SV28: $i,SV22: $i,SV32: $i] :
( ( ( ~ ( ~ ( ( SV32
!= ( pair_first @ SV22 ) )
| ! [SY83: $i,SY84: $i] :
( ( SV22
!= ( ordered_pair @ SY83 @ SY84 ) )
| ( SV32 = SY83 ) ) )
| ~ ( ~ ! [SY85: $i,SY86: $i] :
( ( SV22
!= ( ordered_pair @ SY85 @ SY86 ) )
| ( SV32 = SY85 ) )
| ( SV32
= ( pair_first @ SV22 ) ) ) ) )
= $true )
| ( ( SV22
= ( ordered_pair @ SV28 @ SV30 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(550,plain,
! [SV29: $i,SV27: $i,SV21: $i,SV31: $i] :
( ( ( ~ ( ( SV31
!= ( pair_second @ SV21 ) )
| ! [SY79: $i,SY80: $i] :
( ( SV21
!= ( ordered_pair @ SY79 @ SY80 ) )
| ( SV31 = SY80 ) ) )
| ~ ( ~ ! [SY81: $i,SY82: $i] :
( ( SV21
!= ( ordered_pair @ SY81 @ SY82 ) )
| ( SV31 = SY82 ) )
| ( SV31
= ( pair_second @ SV21 ) ) ) )
= $false )
| ( ( SV21
= ( ordered_pair @ SV27 @ SV29 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(551,plain,
! [SV30: $i,SV28: $i,SV22: $i,SV32: $i] :
( ( ( ~ ( ( SV32
!= ( pair_first @ SV22 ) )
| ! [SY83: $i,SY84: $i] :
( ( SV22
!= ( ordered_pair @ SY83 @ SY84 ) )
| ( SV32 = SY83 ) ) )
| ~ ( ~ ! [SY85: $i,SY86: $i] :
( ( SV22
!= ( ordered_pair @ SY85 @ SY86 ) )
| ( SV32 = SY85 ) )
| ( SV32
= ( pair_first @ SV22 ) ) ) )
= $false )
| ( ( SV22
= ( ordered_pair @ SV28 @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(552,plain,
! [SV29: $i,SV27: $i,SV21: $i,SV31: $i] :
( ( ( ~ ( ( SV31
!= ( pair_second @ SV21 ) )
| ! [SY79: $i,SY80: $i] :
( ( SV21
!= ( ordered_pair @ SY79 @ SY80 ) )
| ( SV31 = SY80 ) ) ) )
= $false )
| ( ( SV21
= ( ordered_pair @ SV27 @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[550]) ).
thf(553,plain,
! [SV29: $i,SV27: $i,SV31: $i,SV21: $i] :
( ( ( ~ ( ~ ! [SY81: $i,SY82: $i] :
( ( SV21
!= ( ordered_pair @ SY81 @ SY82 ) )
| ( SV31 = SY82 ) )
| ( SV31
= ( pair_second @ SV21 ) ) ) )
= $false )
| ( ( SV21
= ( ordered_pair @ SV27 @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[550]) ).
thf(554,plain,
! [SV30: $i,SV28: $i,SV22: $i,SV32: $i] :
( ( ( ~ ( ( SV32
!= ( pair_first @ SV22 ) )
| ! [SY83: $i,SY84: $i] :
( ( SV22
!= ( ordered_pair @ SY83 @ SY84 ) )
| ( SV32 = SY83 ) ) ) )
= $false )
| ( ( SV22
= ( ordered_pair @ SV28 @ SV30 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[551]) ).
thf(555,plain,
! [SV30: $i,SV28: $i,SV32: $i,SV22: $i] :
( ( ( ~ ( ~ ! [SY85: $i,SY86: $i] :
( ( SV22
!= ( ordered_pair @ SY85 @ SY86 ) )
| ( SV32 = SY85 ) )
| ( SV32
= ( pair_first @ SV22 ) ) ) )
= $false )
| ( ( SV22
= ( ordered_pair @ SV28 @ SV30 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[551]) ).
thf(556,plain,
! [SV29: $i,SV27: $i,SV21: $i,SV31: $i] :
( ( ( ( SV31
!= ( pair_second @ SV21 ) )
| ! [SY79: $i,SY80: $i] :
( ( SV21
!= ( ordered_pair @ SY79 @ SY80 ) )
| ( SV31 = SY80 ) ) )
= $true )
| ( ( SV21
= ( ordered_pair @ SV27 @ SV29 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(557,plain,
! [SV29: $i,SV27: $i,SV31: $i,SV21: $i] :
( ( ( ~ ! [SY81: $i,SY82: $i] :
( ( SV21
!= ( ordered_pair @ SY81 @ SY82 ) )
| ( SV31 = SY82 ) )
| ( SV31
= ( pair_second @ SV21 ) ) )
= $true )
| ( ( SV21
= ( ordered_pair @ SV27 @ SV29 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[553]) ).
thf(558,plain,
! [SV30: $i,SV28: $i,SV22: $i,SV32: $i] :
( ( ( ( SV32
!= ( pair_first @ SV22 ) )
| ! [SY83: $i,SY84: $i] :
( ( SV22
!= ( ordered_pair @ SY83 @ SY84 ) )
| ( SV32 = SY83 ) ) )
= $true )
| ( ( SV22
= ( ordered_pair @ SV28 @ SV30 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[554]) ).
thf(559,plain,
! [SV30: $i,SV28: $i,SV32: $i,SV22: $i] :
( ( ( ~ ! [SY85: $i,SY86: $i] :
( ( SV22
!= ( ordered_pair @ SY85 @ SY86 ) )
| ( SV32 = SY85 ) )
| ( SV32
= ( pair_first @ SV22 ) ) )
= $true )
| ( ( SV22
= ( ordered_pair @ SV28 @ SV30 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[555]) ).
thf(560,plain,
! [SV29: $i,SV27: $i,SV21: $i,SV31: $i] :
( ( ( SV31
!= ( pair_second @ SV21 ) )
= $true )
| ( ( ! [SY79: $i,SY80: $i] :
( ( SV21
!= ( ordered_pair @ SY79 @ SY80 ) )
| ( SV31 = SY80 ) ) )
= $true )
| ( ( SV21
= ( ordered_pair @ SV27 @ SV29 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(561,plain,
! [SV29: $i,SV27: $i,SV31: $i,SV21: $i] :
( ( ( ~ ! [SY81: $i,SY82: $i] :
( ( SV21
!= ( ordered_pair @ SY81 @ SY82 ) )
| ( SV31 = SY82 ) ) )
= $true )
| ( ( SV31
= ( pair_second @ SV21 ) )
= $true )
| ( ( SV21
= ( ordered_pair @ SV27 @ SV29 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(562,plain,
! [SV30: $i,SV28: $i,SV22: $i,SV32: $i] :
( ( ( SV32
!= ( pair_first @ SV22 ) )
= $true )
| ( ( ! [SY83: $i,SY84: $i] :
( ( SV22
!= ( ordered_pair @ SY83 @ SY84 ) )
| ( SV32 = SY83 ) ) )
= $true )
| ( ( SV22
= ( ordered_pair @ SV28 @ SV30 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(563,plain,
! [SV30: $i,SV28: $i,SV32: $i,SV22: $i] :
( ( ( ~ ! [SY85: $i,SY86: $i] :
( ( SV22
!= ( ordered_pair @ SY85 @ SY86 ) )
| ( SV32 = SY85 ) ) )
= $true )
| ( ( SV32
= ( pair_first @ SV22 ) )
= $true )
| ( ( SV22
= ( ordered_pair @ SV28 @ SV30 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[559]) ).
thf(564,plain,
! [SV29: $i,SV27: $i,SV21: $i,SV31: $i] :
( ( ( SV31
= ( pair_second @ SV21 ) )
= $false )
| ( ( ! [SY79: $i,SY80: $i] :
( ( SV21
!= ( ordered_pair @ SY79 @ SY80 ) )
| ( SV31 = SY80 ) ) )
= $true )
| ( ( SV21
= ( ordered_pair @ SV27 @ SV29 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(565,plain,
! [SV29: $i,SV27: $i,SV31: $i,SV21: $i] :
( ( ( ! [SY81: $i,SY82: $i] :
( ( SV21
!= ( ordered_pair @ SY81 @ SY82 ) )
| ( SV31 = SY82 ) ) )
= $false )
| ( ( SV31
= ( pair_second @ SV21 ) )
= $true )
| ( ( SV21
= ( ordered_pair @ SV27 @ SV29 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(566,plain,
! [SV30: $i,SV28: $i,SV22: $i,SV32: $i] :
( ( ( SV32
= ( pair_first @ SV22 ) )
= $false )
| ( ( ! [SY83: $i,SY84: $i] :
( ( SV22
!= ( ordered_pair @ SY83 @ SY84 ) )
| ( SV32 = SY83 ) ) )
= $true )
| ( ( SV22
= ( ordered_pair @ SV28 @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(567,plain,
! [SV30: $i,SV28: $i,SV32: $i,SV22: $i] :
( ( ( ! [SY85: $i,SY86: $i] :
( ( SV22
!= ( ordered_pair @ SY85 @ SY86 ) )
| ( SV32 = SY85 ) ) )
= $false )
| ( ( SV32
= ( pair_first @ SV22 ) )
= $true )
| ( ( SV22
= ( ordered_pair @ SV28 @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(568,plain,
! [SV29: $i,SV27: $i,SV31: $i,SV33: $i,SV21: $i] :
( ( ( ! [SY87: $i] :
( ( SV21
!= ( ordered_pair @ SV33 @ SY87 ) )
| ( SV31 = SY87 ) ) )
= $true )
| ( ( SV31
= ( pair_second @ SV21 ) )
= $false )
| ( ( SV21
= ( ordered_pair @ SV27 @ SV29 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(569,plain,
! [SV31: $i,SV27: $i,SV29: $i,SV21: $i] :
( ( ( ! [SY88: $i] :
( ( SV21
!= ( ordered_pair @ ( sK7_SY81 @ SV29 @ SV27 @ SV31 @ SV21 ) @ SY88 ) )
| ( SV31 = SY88 ) ) )
= $false )
| ( ( SV31
= ( pair_second @ SV21 ) )
= $true )
| ( ( SV21
= ( ordered_pair @ SV27 @ SV29 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[565]) ).
thf(570,plain,
! [SV30: $i,SV28: $i,SV32: $i,SV34: $i,SV22: $i] :
( ( ( ! [SY89: $i] :
( ( SV22
!= ( ordered_pair @ SV34 @ SY89 ) )
| ( SV32 = SV34 ) ) )
= $true )
| ( ( SV32
= ( pair_first @ SV22 ) )
= $false )
| ( ( SV22
= ( ordered_pair @ SV28 @ SV30 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(571,plain,
! [SV32: $i,SV28: $i,SV30: $i,SV22: $i] :
( ( ( ! [SY90: $i] :
( ( SV22
!= ( ordered_pair @ ( sK8_SY85 @ SV30 @ SV28 @ SV32 @ SV22 ) @ SY90 ) )
| ( SV32
= ( sK8_SY85 @ SV30 @ SV28 @ SV32 @ SV22 ) ) ) )
= $false )
| ( ( SV32
= ( pair_first @ SV22 ) )
= $true )
| ( ( SV22
= ( ordered_pair @ SV28 @ SV30 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[567]) ).
thf(572,plain,
! [SV29: $i,SV27: $i,SV31: $i,SV35: $i,SV33: $i,SV21: $i] :
( ( ( ( SV21
!= ( ordered_pair @ SV33 @ SV35 ) )
| ( SV31 = SV35 ) )
= $true )
| ( ( SV31
= ( pair_second @ SV21 ) )
= $false )
| ( ( SV21
= ( ordered_pair @ SV27 @ SV29 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(573,plain,
! [SV31: $i,SV27: $i,SV29: $i,SV21: $i] :
( ( ( ( SV21
!= ( ordered_pair @ ( sK7_SY81 @ SV29 @ SV27 @ SV31 @ SV21 ) @ ( sK9_SY88 @ SV31 @ SV27 @ SV29 @ SV21 ) ) )
| ( SV31
= ( sK9_SY88 @ SV31 @ SV27 @ SV29 @ SV21 ) ) )
= $false )
| ( ( SV31
= ( pair_second @ SV21 ) )
= $true )
| ( ( SV21
= ( ordered_pair @ SV27 @ SV29 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[569]) ).
thf(574,plain,
! [SV30: $i,SV28: $i,SV32: $i,SV36: $i,SV34: $i,SV22: $i] :
( ( ( ( SV22
!= ( ordered_pair @ SV34 @ SV36 ) )
| ( SV32 = SV34 ) )
= $true )
| ( ( SV32
= ( pair_first @ SV22 ) )
= $false )
| ( ( SV22
= ( ordered_pair @ SV28 @ SV30 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(575,plain,
! [SV32: $i,SV28: $i,SV30: $i,SV22: $i] :
( ( ( ( SV22
!= ( ordered_pair @ ( sK8_SY85 @ SV30 @ SV28 @ SV32 @ SV22 ) @ ( sK10_SY90 @ SV32 @ SV28 @ SV30 @ SV22 ) ) )
| ( SV32
= ( sK8_SY85 @ SV30 @ SV28 @ SV32 @ SV22 ) ) )
= $false )
| ( ( SV32
= ( pair_first @ SV22 ) )
= $true )
| ( ( SV22
= ( ordered_pair @ SV28 @ SV30 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[571]) ).
thf(576,plain,
! [SV29: $i,SV27: $i,SV31: $i,SV35: $i,SV33: $i,SV21: $i] :
( ( ( SV21
!= ( ordered_pair @ SV33 @ SV35 ) )
= $true )
| ( ( SV31 = SV35 )
= $true )
| ( ( SV31
= ( pair_second @ SV21 ) )
= $false )
| ( ( SV21
= ( ordered_pair @ SV27 @ SV29 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(577,plain,
! [SV31: $i,SV27: $i,SV29: $i,SV21: $i] :
( ( ( SV21
!= ( ordered_pair @ ( sK7_SY81 @ SV29 @ SV27 @ SV31 @ SV21 ) @ ( sK9_SY88 @ SV31 @ SV27 @ SV29 @ SV21 ) ) )
= $false )
| ( ( SV31
= ( pair_second @ SV21 ) )
= $true )
| ( ( SV21
= ( ordered_pair @ SV27 @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[573]) ).
thf(578,plain,
! [SV21: $i,SV29: $i,SV27: $i,SV31: $i] :
( ( ( SV31
= ( sK9_SY88 @ SV31 @ SV27 @ SV29 @ SV21 ) )
= $false )
| ( ( SV31
= ( pair_second @ SV21 ) )
= $true )
| ( ( SV21
= ( ordered_pair @ SV27 @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[573]) ).
thf(579,plain,
! [SV30: $i,SV28: $i,SV32: $i,SV36: $i,SV34: $i,SV22: $i] :
( ( ( SV22
!= ( ordered_pair @ SV34 @ SV36 ) )
= $true )
| ( ( SV32 = SV34 )
= $true )
| ( ( SV32
= ( pair_first @ SV22 ) )
= $false )
| ( ( SV22
= ( ordered_pair @ SV28 @ SV30 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[574]) ).
thf(580,plain,
! [SV32: $i,SV28: $i,SV30: $i,SV22: $i] :
( ( ( SV22
!= ( ordered_pair @ ( sK8_SY85 @ SV30 @ SV28 @ SV32 @ SV22 ) @ ( sK10_SY90 @ SV32 @ SV28 @ SV30 @ SV22 ) ) )
= $false )
| ( ( SV32
= ( pair_first @ SV22 ) )
= $true )
| ( ( SV22
= ( ordered_pair @ SV28 @ SV30 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[575]) ).
thf(581,plain,
! [SV22: $i,SV28: $i,SV30: $i,SV32: $i] :
( ( ( SV32
= ( sK8_SY85 @ SV30 @ SV28 @ SV32 @ SV22 ) )
= $false )
| ( ( SV32
= ( pair_first @ SV22 ) )
= $true )
| ( ( SV22
= ( ordered_pair @ SV28 @ SV30 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[575]) ).
thf(582,plain,
! [SV29: $i,SV27: $i,SV31: $i,SV35: $i,SV33: $i,SV21: $i] :
( ( ( SV21
= ( ordered_pair @ SV33 @ SV35 ) )
= $false )
| ( ( SV31 = SV35 )
= $true )
| ( ( SV31
= ( pair_second @ SV21 ) )
= $false )
| ( ( SV21
= ( ordered_pair @ SV27 @ SV29 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(583,plain,
! [SV31: $i,SV27: $i,SV29: $i,SV21: $i] :
( ( ( SV21
= ( ordered_pair @ ( sK7_SY81 @ SV29 @ SV27 @ SV31 @ SV21 ) @ ( sK9_SY88 @ SV31 @ SV27 @ SV29 @ SV21 ) ) )
= $true )
| ( ( SV31
= ( pair_second @ SV21 ) )
= $true )
| ( ( SV21
= ( ordered_pair @ SV27 @ SV29 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[577]) ).
thf(584,plain,
! [SV30: $i,SV28: $i,SV32: $i,SV36: $i,SV34: $i,SV22: $i] :
( ( ( SV22
= ( ordered_pair @ SV34 @ SV36 ) )
= $false )
| ( ( SV32 = SV34 )
= $true )
| ( ( SV32
= ( pair_first @ SV22 ) )
= $false )
| ( ( SV22
= ( ordered_pair @ SV28 @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(585,plain,
! [SV32: $i,SV28: $i,SV30: $i,SV22: $i] :
( ( ( SV22
= ( ordered_pair @ ( sK8_SY85 @ SV30 @ SV28 @ SV32 @ SV22 ) @ ( sK10_SY90 @ SV32 @ SV28 @ SV30 @ SV22 ) ) )
= $true )
| ( ( SV32
= ( pair_first @ SV22 ) )
= $true )
| ( ( SV22
= ( ordered_pair @ SV28 @ SV30 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[580]) ).
thf(586,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[486,585,584,583,582,581,578,545,544,524,516,509,508,507,506,505,504,503,502,501,500,499,498,497,496,495,494,493,492,491,490,489,488,487]) ).
thf(587,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[586,482]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU267+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.23 % Computer : n015.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Oct 6 15:13:43 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.12/0.56 ..
% 1.12/0.56
% 1.12/0.56 No.of.Axioms: 28
% 1.12/0.56
% 1.12/0.56 Length.of.Defs: 0
% 1.12/0.56
% 1.12/0.56 Contains.Choice.Funs: false
% 1.12/0.56 ...........
% 1.12/0.56
% 1.12/0.56 ********************************
% 1.12/0.56 * All subproblems solved! *
% 1.12/0.56 ********************************
% 1.12/0.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:28,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:586,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.12/0.56
% 1.12/0.56 %**** Beginning of derivation protocol ****
% 1.12/0.56 % SZS output start CNFRefutation
% See solution above
% 1.12/0.57
% 1.12/0.57 %**** End of derivation protocol ****
% 1.12/0.57 %**** no. of clauses in derivation: 274 ****
% 1.12/0.57 %**** clause counter: 586 ****
% 1.12/0.57
% 1.12/0.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:28,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:586,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------