%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM403+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:33:36 AM UTC 2026
% Result : Theorem 36.82s 6.53s
% Output : CNFRefutation 36.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 23
% Syntax : Number of formulae : 387 ( 167 unt; 0 typ; 0 def)
% Number of atoms : 2719 ( 768 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 4778 (1292 ~; 816 |; 63 &;2526 @)
% ( 18 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 6 con; 0-3 aty)
% Number of variables : 819 ( 0 ^; 810 !; 9 ?; 819 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_ordinal_subset,type,
ordinal_subset: $i > $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_relation_non_empty,type,
relation_non_empty: $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY59,type,
sK4_SY59: $i > $i ).
thf(tp_sK5_SY75,type,
sK5_SY75: $i > $i > $i ).
thf(tp_sK6_SY81,type,
sK6_SY81: $i > $i > $i ).
thf(tp_sK7_SY82,type,
sK7_SY82: $i > $i > $i > $i ).
thf(tp_sK8_SY85,type,
sK8_SY85: $i > $i > $i ).
thf(tp_sK9_SY85,type,
sK9_SY85: $i > $i > $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_succ,type,
succ: $i > $i ).
thf(tp_union,type,
union: $i > $i ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(7,axiom,
! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( ordinal @ B ) )
=> ( ordinal @ ( union @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_ordinal1) ).
thf(8,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ ( succ @ B ) )
<=> ( ordinal_subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_ordinal1) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(10,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ordinal @ ( succ @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_ordinal1) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(13,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ordinal_subset @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
<=> ( subset @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
thf(19,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
thf(27,axiom,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(31,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ ( union @ A ) )
& ( epsilon_connected @ ( union @ A ) )
& ( ordinal @ ( union @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_ordinal1) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
| ( ordinal_subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
thf(46,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
thf(47,axiom,
! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(50,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(53,conjecture,
! [A: $i] :
~ ( ! [B: $i] :
( ( in @ B @ A )
=> ( ordinal @ B ) )
& ! [B: $i] :
( ( ordinal @ B )
=> ~ ( subset @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_ordinal1) ).
thf(54,negated_conjecture,
( ( ! [A: $i] :
~ ( ! [B: $i] :
( ( in @ B @ A )
=> ( ordinal @ B ) )
& ! [B: $i] :
( ( ordinal @ B )
=> ~ ( subset @ A @ B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[53]) ).
thf(55,plain,
( ( ! [A: $i] :
~ ( ! [B: $i] :
( ( in @ B @ A )
=> ( ordinal @ B ) )
& ! [B: $i] :
( ( ordinal @ B )
=> ~ ( subset @ A @ B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[54]) ).
thf(56,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(57,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(58,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(59,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(60,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( ordinal @ B ) )
=> ( ordinal @ ( union @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(61,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ ( succ @ B ) )
<=> ( ordinal_subset @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(62,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(63,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ordinal @ ( succ @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(64,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(65,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(66,plain,
( ( ! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ordinal_subset @ A @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
<=> ( subset @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(68,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(69,plain,
( ( ? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(70,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ ( union @ A ) )
& ( epsilon_connected @ ( union @ A ) )
& ( ordinal @ ( union @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(71,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(72,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(73,plain,
( ( ! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
| ( ordinal_subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(74,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(75,plain,
( ( ! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(76,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(77,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(78,plain,
( ( ~ ( ! [SY45: $i] :
( ( in @ SY45 @ sK1_A )
=> ( ordinal @ SY45 ) )
& ! [SY46: $i] :
( ( ordinal @ SY46 )
=> ~ ( subset @ sK1_A @ SY46 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[55]) ).
thf(79,plain,
( ( ! [SY45: $i] :
( ( in @ SY45 @ sK1_A )
=> ( ordinal @ SY45 ) )
& ! [SY46: $i] :
( ( ordinal @ SY46 )
=> ~ ( subset @ sK1_A @ SY46 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[78]) ).
thf(80,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(81,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(82,plain,
( ( ! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(83,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(84,plain,
( ( ! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
| ( ordinal_subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(85,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(86,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(87,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ ( union @ A ) )
& ( epsilon_connected @ ( union @ A ) )
& ( ordinal @ ( union @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(88,plain,
( ( ? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(89,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(90,plain,
( ( ! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
<=> ( subset @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(91,plain,
( ( ! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ordinal_subset @ A @ A ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(92,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(93,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(94,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ordinal @ ( succ @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(95,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(96,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ ( succ @ B ) )
<=> ( ordinal_subset @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(97,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( ordinal @ B ) )
=> ( ordinal @ ( union @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(98,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(99,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(100,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(101,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(102,plain,
( ( ! [SY45: $i] :
( ( in @ SY45 @ sK1_A )
=> ( ordinal @ SY45 ) )
& ! [SY46: $i] :
( ( ordinal @ SY46 )
=> ~ ( subset @ sK1_A @ SY46 ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(103,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( union @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(104,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( epsilon_transitive @ SX0 )
| ~ ( epsilon_connected @ SX0 ) )
| ~ ( ordinal @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(105,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ~ ( ~ ( epsilon_transitive @ SX0 )
| ~ ( epsilon_connected @ SX0 ) )
| ~ ( ordinal @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(106,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ SX1 )
| ( empty @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(107,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(108,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ( element @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(109,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( ordinal @ SX1 ) )
| ( ordinal @ ( union @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(110,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 ) )
| ( ordinal_subset @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(111,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 ) )
| ( ordinal_subset @ SX0 @ SX1 )
| ( ordinal_subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(112,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ~ ~ ( ~ ( epsilon_transitive @ ( union @ SX0 ) )
| ~ ( epsilon_connected @ ( union @ SX0 ) ) )
| ~ ( ordinal @ ( union @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(113,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 ) )
| ~ ( ~ ( ~ ( ordinal_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( ordinal_subset @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(114,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)],[98]) ).
thf(115,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ~ ( empty @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(116,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)],[85]) ).
thf(117,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( ordinal @ ( succ @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(118,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ~ ( epsilon_transitive @ SX0 )
| ~ ( epsilon_connected @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(119,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ! [SX1: $i] :
( ~ ( ordinal @ SX1 )
| ~ ( ~ ( ~ ( in @ SX0 @ ( succ @ SX1 ) )
| ( ordinal_subset @ SX0 @ SX1 ) )
| ~ ( ~ ( ordinal_subset @ SX0 @ SX1 )
| ( in @ SX0 @ ( succ @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(120,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(121,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( epsilon_transitive @ SX0 ) )
| ~ ( epsilon_connected @ SX0 ) )
| ~ ( ordinal @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(122,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( epsilon_transitive @ SX0 )
| ~ ( epsilon_connected @ SX0 ) )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(123,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_A )
| ( ordinal @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( subset @ sK1_A @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(124,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(125,plain,
! [SV1: $i] :
( ( ! [SY47: $i] : ( subset @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(126,plain,
! [SV2: $i] :
( ( ! [SY48: $i] :
~ ( ~ ( ( SY48
!= ( union @ SV2 ) )
| ! [SY49: $i] :
~ ( ~ ( ~ ( in @ SY49 @ SY48 )
| ~ ! [SY50: $i] :
~ ~ ( ~ ( in @ SY49 @ SY50 )
| ~ ( in @ SY50 @ SV2 ) ) )
| ~ ( ~ ~ ! [SY51: $i] :
~ ~ ( ~ ( in @ SY49 @ SY51 )
| ~ ( in @ SY51 @ SV2 ) )
| ( in @ SY49 @ SY48 ) ) ) )
| ~ ( ~ ! [SY52: $i] :
~ ( ~ ( ~ ( in @ SY52 @ SY48 )
| ~ ! [SY53: $i] :
~ ~ ( ~ ( in @ SY52 @ SY53 )
| ~ ( in @ SY53 @ SV2 ) ) )
| ~ ( ~ ~ ! [SY54: $i] :
~ ~ ( ~ ( in @ SY52 @ SY54 )
| ~ ( in @ SY54 @ SV2 ) )
| ( in @ SY52 @ SY48 ) ) )
| ( SY48
= ( union @ SV2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(127,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( epsilon_transitive @ SX0 )
| ~ ( epsilon_connected @ SX0 ) )
| ~ ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(128,plain,
! [SV3: $i] :
( ( ~ ( empty @ SV3 )
| ~ ( ~ ~ ( ~ ( epsilon_transitive @ SV3 )
| ~ ( epsilon_connected @ SV3 ) )
| ~ ( ordinal @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(129,plain,
! [SV4: $i] :
( ( ! [SY55: $i] :
( ~ ( element @ SV4 @ SY55 )
| ( empty @ SY55 )
| ( in @ SV4 @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(130,plain,
! [SV5: $i] :
( ( ! [SY56: $i] :
( ~ ( in @ SV5 @ SY56 )
| ( element @ SV5 @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(131,plain,
! [SV6: $i] :
( ( ! [SY57: $i,SY58: $i] :
( ~ ~ ( ~ ( in @ SV6 @ SY57 )
| ~ ( element @ SY57 @ ( powerset @ SY58 ) ) )
| ( element @ SV6 @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(132,plain,
! [SV7: $i] :
( ( ~ ! [SY59: $i] :
( ~ ( in @ SY59 @ SV7 )
| ( ordinal @ SY59 ) )
| ( ordinal @ ( union @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(133,plain,
! [SV8: $i] :
( ( ! [SY60: $i] :
( ~ ~ ( ~ ( ordinal @ SV8 )
| ~ ( ordinal @ SY60 ) )
| ( ordinal_subset @ SV8 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(134,plain,
! [SV9: $i] :
( ( ! [SY61: $i] :
( ~ ~ ( ~ ( ordinal @ SV9 )
| ~ ( ordinal @ SY61 ) )
| ( ordinal_subset @ SV9 @ SY61 )
| ( ordinal_subset @ SY61 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(135,plain,
! [SV10: $i] :
( ( ~ ( ordinal @ SV10 )
| ~ ( ~ ~ ( ~ ( epsilon_transitive @ ( union @ SV10 ) )
| ~ ( epsilon_connected @ ( union @ SV10 ) ) )
| ~ ( ordinal @ ( union @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(136,plain,
! [SV11: $i] :
( ( ! [SY62: $i] :
( ~ ~ ( ~ ( ordinal @ SV11 )
| ~ ( ordinal @ SY62 ) )
| ~ ( ~ ( ~ ( ordinal_subset @ SV11 @ SY62 )
| ( subset @ SV11 @ SY62 ) )
| ~ ( ~ ( subset @ SV11 @ SY62 )
| ( ordinal_subset @ SV11 @ SY62 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(137,plain,
! [SV12: $i] :
( ( ! [SY63: $i] :
~ ( ~ ( ~ ( element @ SV12 @ ( powerset @ SY63 ) )
| ( subset @ SV12 @ SY63 ) )
| ~ ( ~ ( subset @ SV12 @ SY63 )
| ( element @ SV12 @ ( powerset @ SY63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(138,plain,
! [SV13: $i] :
( ( ! [SY64: $i,SY65: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV13 @ SY64 )
| ~ ( element @ SY64 @ ( powerset @ SY65 ) ) )
| ~ ( empty @ SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(139,plain,
! [SV14: $i] :
( ( ! [SY66: $i] :
~ ( ~ ( ~ ( subset @ SV14 @ SY66 )
| ! [SY67: $i] :
( ~ ( in @ SY67 @ SV14 )
| ( in @ SY67 @ SY66 ) ) )
| ~ ( ~ ! [SY68: $i] :
( ~ ( in @ SY68 @ SV14 )
| ( in @ SY68 @ SY66 ) )
| ( subset @ SV14 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(140,plain,
! [SV15: $i] :
( ( ~ ( ordinal @ SV15 )
| ( ordinal @ ( succ @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(141,plain,
! [SV16: $i] :
( ( ~ ( ordinal @ SV16 )
| ~ ( ~ ( epsilon_transitive @ SV16 )
| ~ ( epsilon_connected @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(142,plain,
! [SV17: $i] :
( ( ~ ( ordinal @ SV17 )
| ! [SY69: $i] :
( ~ ( ordinal @ SY69 )
| ~ ( ~ ( ~ ( in @ SV17 @ ( succ @ SY69 ) )
| ( ordinal_subset @ SV17 @ SY69 ) )
| ~ ( ~ ( ordinal_subset @ SV17 @ SY69 )
| ( in @ SV17 @ ( succ @ SY69 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(143,plain,
! [SV18: $i] :
( ( ! [SY70: $i] :
~ ~ ( ~ ( in @ SV18 @ SY70 )
| ~ ( empty @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(144,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( epsilon_transitive @ SX0 ) )
| ~ ( epsilon_connected @ SX0 ) )
| ~ ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(145,plain,
! [SV19: $i] :
( ( ~ ~ ( ~ ( epsilon_transitive @ SV19 )
| ~ ( epsilon_connected @ SV19 ) )
| ( ordinal @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(146,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_A )
| ( ordinal @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( subset @ sK1_A @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(147,plain,
! [SV20: $i] :
( ( ! [SY71: $i] :
( ~ ( in @ SV20 @ SY71 )
| ~ ( in @ SY71 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(148,plain,
! [SV1: $i] :
( ( subset @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(149,plain,
! [SV2: $i,SV22: $i] :
( ( ~ ( ~ ( ( SV22
!= ( union @ SV2 ) )
| ! [SY72: $i] :
~ ( ~ ( ~ ( in @ SY72 @ SV22 )
| ~ ! [SY50: $i] :
~ ~ ( ~ ( in @ SY72 @ SY50 )
| ~ ( in @ SY50 @ SV2 ) ) )
| ~ ( ~ ~ ! [SY51: $i] :
~ ~ ( ~ ( in @ SY72 @ SY51 )
| ~ ( in @ SY51 @ SV2 ) )
| ( in @ SY72 @ SV22 ) ) ) )
| ~ ( ~ ! [SY75: $i] :
~ ( ~ ( ~ ( in @ SY75 @ SV22 )
| ~ ! [SY53: $i] :
~ ~ ( ~ ( in @ SY75 @ SY53 )
| ~ ( in @ SY53 @ SV2 ) ) )
| ~ ( ~ ~ ! [SY54: $i] :
~ ~ ( ~ ( in @ SY75 @ SY54 )
| ~ ( in @ SY54 @ SV2 ) )
| ( in @ SY75 @ SV22 ) ) )
| ( SV22
= ( union @ SV2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(150,plain,
( ( ~ ~ ( ~ ~ ( ~ ( epsilon_transitive @ sK2_SX0 )
| ~ ( epsilon_connected @ sK2_SX0 ) )
| ~ ( ordinal @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[127]) ).
thf(151,plain,
! [SV3: $i] :
( ( ( ~ ( empty @ SV3 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( epsilon_transitive @ SV3 )
| ~ ( epsilon_connected @ SV3 ) )
| ~ ( ordinal @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(152,plain,
! [SV23: $i,SV4: $i] :
( ( ~ ( element @ SV4 @ SV23 )
| ( empty @ SV23 )
| ( in @ SV4 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(153,plain,
! [SV24: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ SV24 )
| ( element @ SV5 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(154,plain,
! [SV25: $i,SV6: $i] :
( ( ! [SY78: $i] :
( ~ ~ ( ~ ( in @ SV6 @ SV25 )
| ~ ( element @ SV25 @ ( powerset @ SY78 ) ) )
| ( element @ SV6 @ SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(155,plain,
! [SV7: $i] :
( ( ( ~ ! [SY59: $i] :
( ~ ( in @ SY59 @ SV7 )
| ( ordinal @ SY59 ) ) )
= $true )
| ( ( ordinal @ ( union @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(156,plain,
! [SV26: $i,SV8: $i] :
( ( ~ ~ ( ~ ( ordinal @ SV8 )
| ~ ( ordinal @ SV26 ) )
| ( ordinal_subset @ SV8 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(157,plain,
! [SV27: $i,SV9: $i] :
( ( ~ ~ ( ~ ( ordinal @ SV9 )
| ~ ( ordinal @ SV27 ) )
| ( ordinal_subset @ SV9 @ SV27 )
| ( ordinal_subset @ SV27 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(158,plain,
! [SV10: $i] :
( ( ( ~ ( ordinal @ SV10 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( epsilon_transitive @ ( union @ SV10 ) )
| ~ ( epsilon_connected @ ( union @ SV10 ) ) )
| ~ ( ordinal @ ( union @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(159,plain,
! [SV28: $i,SV11: $i] :
( ( ~ ~ ( ~ ( ordinal @ SV11 )
| ~ ( ordinal @ SV28 ) )
| ~ ( ~ ( ~ ( ordinal_subset @ SV11 @ SV28 )
| ( subset @ SV11 @ SV28 ) )
| ~ ( ~ ( subset @ SV11 @ SV28 )
| ( ordinal_subset @ SV11 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(160,plain,
! [SV29: $i,SV12: $i] :
( ( ~ ( ~ ( ~ ( element @ SV12 @ ( powerset @ SV29 ) )
| ( subset @ SV12 @ SV29 ) )
| ~ ( ~ ( subset @ SV12 @ SV29 )
| ( element @ SV12 @ ( powerset @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(161,plain,
! [SV30: $i,SV13: $i] :
( ( ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV13 @ SV30 )
| ~ ( element @ SV30 @ ( powerset @ SY79 ) ) )
| ~ ( empty @ SY79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(162,plain,
! [SV31: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV14 @ SV31 )
| ! [SY80: $i] :
( ~ ( in @ SY80 @ SV14 )
| ( in @ SY80 @ SV31 ) ) )
| ~ ( ~ ! [SY81: $i] :
( ~ ( in @ SY81 @ SV14 )
| ( in @ SY81 @ SV31 ) )
| ( subset @ SV14 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(163,plain,
! [SV15: $i] :
( ( ( ~ ( ordinal @ SV15 ) )
= $true )
| ( ( ordinal @ ( succ @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(164,plain,
! [SV16: $i] :
( ( ( ~ ( ordinal @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( epsilon_transitive @ SV16 )
| ~ ( epsilon_connected @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(165,plain,
! [SV17: $i] :
( ( ( ~ ( ordinal @ SV17 ) )
= $true )
| ( ( ! [SY69: $i] :
( ~ ( ordinal @ SY69 )
| ~ ( ~ ( ~ ( in @ SV17 @ ( succ @ SY69 ) )
| ( ordinal_subset @ SV17 @ SY69 ) )
| ~ ( ~ ( ordinal_subset @ SV17 @ SY69 )
| ( in @ SV17 @ ( succ @ SY69 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(166,plain,
! [SV32: $i,SV18: $i] :
( ( ~ ~ ( ~ ( in @ SV18 @ SV32 )
| ~ ( empty @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(167,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( epsilon_transitive @ sK3_SX0 ) )
| ~ ( epsilon_connected @ sK3_SX0 ) )
| ~ ( ordinal @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[144]) ).
thf(168,plain,
! [SV19: $i] :
( ( ( ~ ~ ( ~ ( epsilon_transitive @ SV19 )
| ~ ( epsilon_connected @ SV19 ) ) )
= $true )
| ( ( ordinal @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(169,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_A )
| ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(170,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( subset @ sK1_A @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(171,plain,
! [SV33: $i,SV20: $i] :
( ( ~ ( in @ SV20 @ SV33 )
| ~ ( in @ SV33 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(172,plain,
! [SV2: $i,SV22: $i] :
( ( ~ ( ( SV22
!= ( union @ SV2 ) )
| ! [SY72: $i] :
~ ( ~ ( ~ ( in @ SY72 @ SV22 )
| ~ ! [SY50: $i] :
~ ~ ( ~ ( in @ SY72 @ SY50 )
| ~ ( in @ SY50 @ SV2 ) ) )
| ~ ( ~ ~ ! [SY51: $i] :
~ ~ ( ~ ( in @ SY72 @ SY51 )
| ~ ( in @ SY51 @ SV2 ) )
| ( in @ SY72 @ SV22 ) ) ) )
| ~ ( ~ ! [SY75: $i] :
~ ( ~ ( ~ ( in @ SY75 @ SV22 )
| ~ ! [SY53: $i] :
~ ~ ( ~ ( in @ SY75 @ SY53 )
| ~ ( in @ SY53 @ SV2 ) ) )
| ~ ( ~ ~ ! [SY54: $i] :
~ ~ ( ~ ( in @ SY75 @ SY54 )
| ~ ( in @ SY54 @ SV2 ) )
| ( in @ SY75 @ SV22 ) ) )
| ( SV22
= ( union @ SV2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(173,plain,
( ( ~ ( ~ ~ ( ~ ( epsilon_transitive @ sK2_SX0 )
| ~ ( epsilon_connected @ sK2_SX0 ) )
| ~ ( ordinal @ sK2_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(174,plain,
! [SV3: $i] :
( ( ( empty @ SV3 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( epsilon_transitive @ SV3 )
| ~ ( epsilon_connected @ SV3 ) )
| ~ ( ordinal @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(175,plain,
! [SV23: $i,SV4: $i] :
( ( ( ~ ( element @ SV4 @ SV23 ) )
= $true )
| ( ( ( empty @ SV23 )
| ( in @ SV4 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(176,plain,
! [SV24: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV24 ) )
= $true )
| ( ( element @ SV5 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(177,plain,
! [SV34: $i,SV25: $i,SV6: $i] :
( ( ~ ~ ( ~ ( in @ SV6 @ SV25 )
| ~ ( element @ SV25 @ ( powerset @ SV34 ) ) )
| ( element @ SV6 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(178,plain,
! [SV7: $i] :
( ( ( ! [SY59: $i] :
( ~ ( in @ SY59 @ SV7 )
| ( ordinal @ SY59 ) ) )
= $false )
| ( ( ordinal @ ( union @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(179,plain,
! [SV26: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( ordinal @ SV8 )
| ~ ( ordinal @ SV26 ) ) )
= $true )
| ( ( ordinal_subset @ SV8 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(180,plain,
! [SV27: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( ordinal @ SV9 )
| ~ ( ordinal @ SV27 ) ) )
= $true )
| ( ( ( ordinal_subset @ SV9 @ SV27 )
| ( ordinal_subset @ SV27 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(181,plain,
! [SV10: $i] :
( ( ( ordinal @ SV10 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( epsilon_transitive @ ( union @ SV10 ) )
| ~ ( epsilon_connected @ ( union @ SV10 ) ) )
| ~ ( ordinal @ ( union @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(182,plain,
! [SV28: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( ordinal @ SV11 )
| ~ ( ordinal @ SV28 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ordinal_subset @ SV11 @ SV28 )
| ( subset @ SV11 @ SV28 ) )
| ~ ( ~ ( subset @ SV11 @ SV28 )
| ( ordinal_subset @ SV11 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(183,plain,
! [SV29: $i,SV12: $i] :
( ( ~ ( ~ ( element @ SV12 @ ( powerset @ SV29 ) )
| ( subset @ SV12 @ SV29 ) )
| ~ ( ~ ( subset @ SV12 @ SV29 )
| ( element @ SV12 @ ( powerset @ SV29 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(184,plain,
! [SV35: $i,SV30: $i,SV13: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV13 @ SV30 )
| ~ ( element @ SV30 @ ( powerset @ SV35 ) ) )
| ~ ( empty @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(185,plain,
! [SV31: $i,SV14: $i] :
( ( ~ ( ~ ( subset @ SV14 @ SV31 )
| ! [SY80: $i] :
( ~ ( in @ SY80 @ SV14 )
| ( in @ SY80 @ SV31 ) ) )
| ~ ( ~ ! [SY81: $i] :
( ~ ( in @ SY81 @ SV14 )
| ( in @ SY81 @ SV31 ) )
| ( subset @ SV14 @ SV31 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(186,plain,
! [SV15: $i] :
( ( ( ordinal @ SV15 )
= $false )
| ( ( ordinal @ ( succ @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(187,plain,
! [SV16: $i] :
( ( ( ordinal @ SV16 )
= $false )
| ( ( ~ ( ~ ( epsilon_transitive @ SV16 )
| ~ ( epsilon_connected @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(188,plain,
! [SV17: $i] :
( ( ( ordinal @ SV17 )
= $false )
| ( ( ! [SY69: $i] :
( ~ ( ordinal @ SY69 )
| ~ ( ~ ( ~ ( in @ SV17 @ ( succ @ SY69 ) )
| ( ordinal_subset @ SV17 @ SY69 ) )
| ~ ( ~ ( ordinal_subset @ SV17 @ SY69 )
| ( in @ SV17 @ ( succ @ SY69 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(189,plain,
! [SV32: $i,SV18: $i] :
( ( ~ ( ~ ( in @ SV18 @ SV32 )
| ~ ( empty @ SV32 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(190,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( epsilon_transitive @ sK3_SX0 ) )
| ~ ( epsilon_connected @ sK3_SX0 ) )
| ~ ( ordinal @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(191,plain,
! [SV19: $i] :
( ( ( ~ ( ~ ( epsilon_transitive @ SV19 )
| ~ ( epsilon_connected @ SV19 ) ) )
= $false )
| ( ( ordinal @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(192,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_A )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(193,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( subset @ sK1_A @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(194,plain,
! [SV33: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV33 ) )
= $true )
| ( ( ~ ( in @ SV33 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(195,plain,
! [SV2: $i,SV22: $i] :
( ( ~ ( ( SV22
!= ( union @ SV2 ) )
| ! [SY72: $i] :
~ ( ~ ( ~ ( in @ SY72 @ SV22 )
| ~ ! [SY50: $i] :
~ ~ ( ~ ( in @ SY72 @ SY50 )
| ~ ( in @ SY50 @ SV2 ) ) )
| ~ ( ~ ~ ! [SY51: $i] :
~ ~ ( ~ ( in @ SY72 @ SY51 )
| ~ ( in @ SY51 @ SV2 ) )
| ( in @ SY72 @ SV22 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(196,plain,
! [SV2: $i,SV22: $i] :
( ( ~ ( ~ ! [SY75: $i] :
~ ( ~ ( ~ ( in @ SY75 @ SV22 )
| ~ ! [SY53: $i] :
~ ~ ( ~ ( in @ SY75 @ SY53 )
| ~ ( in @ SY53 @ SV2 ) ) )
| ~ ( ~ ~ ! [SY54: $i] :
~ ~ ( ~ ( in @ SY75 @ SY54 )
| ~ ( in @ SY54 @ SV2 ) )
| ( in @ SY75 @ SV22 ) ) )
| ( SV22
= ( union @ SV2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(197,plain,
( ( ~ ~ ( ~ ( epsilon_transitive @ sK2_SX0 )
| ~ ( epsilon_connected @ sK2_SX0 ) )
| ~ ( ordinal @ sK2_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(198,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ( epsilon_transitive @ SV3 )
| ~ ( epsilon_connected @ SV3 ) )
| ~ ( ordinal @ SV3 ) )
= $false )
| ( ( empty @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(199,plain,
! [SV23: $i,SV4: $i] :
( ( ( element @ SV4 @ SV23 )
= $false )
| ( ( ( empty @ SV23 )
| ( in @ SV4 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(200,plain,
! [SV24: $i,SV5: $i] :
( ( ( in @ SV5 @ SV24 )
= $false )
| ( ( element @ SV5 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(201,plain,
! [SV34: $i,SV25: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( in @ SV6 @ SV25 )
| ~ ( element @ SV25 @ ( powerset @ SV34 ) ) ) )
= $true )
| ( ( element @ SV6 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(202,plain,
! [SV7: $i] :
( ( ( ~ ( in @ ( sK4_SY59 @ SV7 ) @ SV7 )
| ( ordinal @ ( sK4_SY59 @ SV7 ) ) )
= $false )
| ( ( ordinal @ ( union @ SV7 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[178]) ).
thf(203,plain,
! [SV26: $i,SV8: $i] :
( ( ( ~ ( ~ ( ordinal @ SV8 )
| ~ ( ordinal @ SV26 ) ) )
= $false )
| ( ( ordinal_subset @ SV8 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(204,plain,
! [SV27: $i,SV9: $i] :
( ( ( ~ ( ~ ( ordinal @ SV9 )
| ~ ( ordinal @ SV27 ) ) )
= $false )
| ( ( ( ordinal_subset @ SV9 @ SV27 )
| ( ordinal_subset @ SV27 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(205,plain,
! [SV10: $i] :
( ( ( ~ ~ ( ~ ( epsilon_transitive @ ( union @ SV10 ) )
| ~ ( epsilon_connected @ ( union @ SV10 ) ) )
| ~ ( ordinal @ ( union @ SV10 ) ) )
= $false )
| ( ( ordinal @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(206,plain,
! [SV28: $i,SV11: $i] :
( ( ( ~ ( ~ ( ordinal @ SV11 )
| ~ ( ordinal @ SV28 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( ordinal_subset @ SV11 @ SV28 )
| ( subset @ SV11 @ SV28 ) )
| ~ ( ~ ( subset @ SV11 @ SV28 )
| ( ordinal_subset @ SV11 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(207,plain,
! [SV29: $i,SV12: $i] :
( ( ~ ( ~ ( element @ SV12 @ ( powerset @ SV29 ) )
| ( subset @ SV12 @ SV29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(208,plain,
! [SV29: $i,SV12: $i] :
( ( ~ ( ~ ( subset @ SV12 @ SV29 )
| ( element @ SV12 @ ( powerset @ SV29 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(209,plain,
! [SV35: $i,SV30: $i,SV13: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV13 @ SV30 )
| ~ ( element @ SV30 @ ( powerset @ SV35 ) ) )
| ~ ( empty @ SV35 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(210,plain,
! [SV31: $i,SV14: $i] :
( ( ~ ( ~ ( subset @ SV14 @ SV31 )
| ! [SY80: $i] :
( ~ ( in @ SY80 @ SV14 )
| ( in @ SY80 @ SV31 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(211,plain,
! [SV31: $i,SV14: $i] :
( ( ~ ( ~ ! [SY81: $i] :
( ~ ( in @ SY81 @ SV14 )
| ( in @ SY81 @ SV31 ) )
| ( subset @ SV14 @ SV31 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(212,plain,
! [SV16: $i] :
( ( ( ~ ( epsilon_transitive @ SV16 )
| ~ ( epsilon_connected @ SV16 ) )
= $false )
| ( ( ordinal @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(213,plain,
! [SV17: $i,SV36: $i] :
( ( ( ~ ( ordinal @ SV36 )
| ~ ( ~ ( ~ ( in @ SV17 @ ( succ @ SV36 ) )
| ( ordinal_subset @ SV17 @ SV36 ) )
| ~ ( ~ ( ordinal_subset @ SV17 @ SV36 )
| ( in @ SV17 @ ( succ @ SV36 ) ) ) ) )
= $true )
| ( ( ordinal @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(214,plain,
! [SV32: $i,SV18: $i] :
( ( ~ ( in @ SV18 @ SV32 )
| ~ ( empty @ SV32 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(215,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( epsilon_transitive @ sK3_SX0 ) )
| ~ ( epsilon_connected @ sK3_SX0 ) )
| ~ ( ordinal @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(216,plain,
! [SV19: $i] :
( ( ( ~ ( epsilon_transitive @ SV19 )
| ~ ( epsilon_connected @ SV19 ) )
= $true )
| ( ( ordinal @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(217,plain,
! [SV37: $i] :
( ( ~ ( in @ SV37 @ sK1_A )
| ( ordinal @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(218,plain,
! [SV38: $i] :
( ( ~ ( ordinal @ SV38 )
| ~ ( subset @ sK1_A @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(219,plain,
! [SV33: $i,SV20: $i] :
( ( ( in @ SV20 @ SV33 )
= $false )
| ( ( ~ ( in @ SV33 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(220,plain,
! [SV2: $i,SV22: $i] :
( ( ( SV22
!= ( union @ SV2 ) )
| ! [SY72: $i] :
~ ( ~ ( ~ ( in @ SY72 @ SV22 )
| ~ ! [SY50: $i] :
~ ~ ( ~ ( in @ SY72 @ SY50 )
| ~ ( in @ SY50 @ SV2 ) ) )
| ~ ( ~ ~ ! [SY51: $i] :
~ ~ ( ~ ( in @ SY72 @ SY51 )
| ~ ( in @ SY51 @ SV2 ) )
| ( in @ SY72 @ SV22 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(221,plain,
! [SV2: $i,SV22: $i] :
( ( ~ ! [SY75: $i] :
~ ( ~ ( ~ ( in @ SY75 @ SV22 )
| ~ ! [SY53: $i] :
~ ~ ( ~ ( in @ SY75 @ SY53 )
| ~ ( in @ SY53 @ SV2 ) ) )
| ~ ( ~ ~ ! [SY54: $i] :
~ ~ ( ~ ( in @ SY75 @ SY54 )
| ~ ( in @ SY54 @ SV2 ) )
| ( in @ SY75 @ SV22 ) ) )
| ( SV22
= ( union @ SV2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(222,plain,
( ( ~ ~ ( ~ ( epsilon_transitive @ sK2_SX0 )
| ~ ( epsilon_connected @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(223,plain,
( ( ~ ( ordinal @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(224,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ( epsilon_transitive @ SV3 )
| ~ ( epsilon_connected @ SV3 ) ) )
= $false )
| ( ( empty @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(225,plain,
! [SV3: $i] :
( ( ( ~ ( ordinal @ SV3 ) )
= $false )
| ( ( empty @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(226,plain,
! [SV4: $i,SV23: $i] :
( ( ( empty @ SV23 )
= $true )
| ( ( in @ SV4 @ SV23 )
= $true )
| ( ( element @ SV4 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(227,plain,
! [SV34: $i,SV25: $i,SV6: $i] :
( ( ( ~ ( ~ ( in @ SV6 @ SV25 )
| ~ ( element @ SV25 @ ( powerset @ SV34 ) ) ) )
= $false )
| ( ( element @ SV6 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(228,plain,
! [SV7: $i] :
( ( ( ~ ( in @ ( sK4_SY59 @ SV7 ) @ SV7 ) )
= $false )
| ( ( ordinal @ ( union @ SV7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(229,plain,
! [SV7: $i] :
( ( ( ordinal @ ( sK4_SY59 @ SV7 ) )
= $false )
| ( ( ordinal @ ( union @ SV7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(230,plain,
! [SV26: $i,SV8: $i] :
( ( ( ~ ( ordinal @ SV8 )
| ~ ( ordinal @ SV26 ) )
= $true )
| ( ( ordinal_subset @ SV8 @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(231,plain,
! [SV27: $i,SV9: $i] :
( ( ( ~ ( ordinal @ SV9 )
| ~ ( ordinal @ SV27 ) )
= $true )
| ( ( ( ordinal_subset @ SV9 @ SV27 )
| ( ordinal_subset @ SV27 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(232,plain,
! [SV10: $i] :
( ( ( ~ ~ ( ~ ( epsilon_transitive @ ( union @ SV10 ) )
| ~ ( epsilon_connected @ ( union @ SV10 ) ) ) )
= $false )
| ( ( ordinal @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(233,plain,
! [SV10: $i] :
( ( ( ~ ( ordinal @ ( union @ SV10 ) ) )
= $false )
| ( ( ordinal @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(234,plain,
! [SV28: $i,SV11: $i] :
( ( ( ~ ( ordinal @ SV11 )
| ~ ( ordinal @ SV28 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ordinal_subset @ SV11 @ SV28 )
| ( subset @ SV11 @ SV28 ) )
| ~ ( ~ ( subset @ SV11 @ SV28 )
| ( ordinal_subset @ SV11 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(235,plain,
! [SV29: $i,SV12: $i] :
( ( ~ ( element @ SV12 @ ( powerset @ SV29 ) )
| ( subset @ SV12 @ SV29 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(236,plain,
! [SV29: $i,SV12: $i] :
( ( ~ ( subset @ SV12 @ SV29 )
| ( element @ SV12 @ ( powerset @ SV29 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(237,plain,
! [SV35: $i,SV30: $i,SV13: $i] :
( ( ~ ~ ( ~ ( in @ SV13 @ SV30 )
| ~ ( element @ SV30 @ ( powerset @ SV35 ) ) )
| ~ ( empty @ SV35 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(238,plain,
! [SV31: $i,SV14: $i] :
( ( ~ ( subset @ SV14 @ SV31 )
| ! [SY80: $i] :
( ~ ( in @ SY80 @ SV14 )
| ( in @ SY80 @ SV31 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(239,plain,
! [SV31: $i,SV14: $i] :
( ( ~ ! [SY81: $i] :
( ~ ( in @ SY81 @ SV14 )
| ( in @ SY81 @ SV31 ) )
| ( subset @ SV14 @ SV31 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(240,plain,
! [SV16: $i] :
( ( ( ~ ( epsilon_transitive @ SV16 ) )
= $false )
| ( ( ordinal @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(241,plain,
! [SV16: $i] :
( ( ( ~ ( epsilon_connected @ SV16 ) )
= $false )
| ( ( ordinal @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(242,plain,
! [SV17: $i,SV36: $i] :
( ( ( ~ ( ordinal @ SV36 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV17 @ ( succ @ SV36 ) )
| ( ordinal_subset @ SV17 @ SV36 ) )
| ~ ( ~ ( ordinal_subset @ SV17 @ SV36 )
| ( in @ SV17 @ ( succ @ SV36 ) ) ) ) )
= $true )
| ( ( ordinal @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(243,plain,
! [SV32: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ SV32 ) )
= $true )
| ( ( ~ ( empty @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(244,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( epsilon_transitive @ sK3_SX0 ) )
| ~ ( epsilon_connected @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(245,plain,
( ( ~ ( ordinal @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(246,plain,
! [SV19: $i] :
( ( ( ~ ( epsilon_transitive @ SV19 ) )
= $true )
| ( ( ~ ( epsilon_connected @ SV19 ) )
= $true )
| ( ( ordinal @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(247,plain,
! [SV37: $i] :
( ( ( ~ ( in @ SV37 @ sK1_A ) )
= $true )
| ( ( ordinal @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(248,plain,
! [SV38: $i] :
( ( ( ~ ( ordinal @ SV38 ) )
= $true )
| ( ( ~ ( subset @ sK1_A @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(249,plain,
! [SV20: $i,SV33: $i] :
( ( ( in @ SV33 @ SV20 )
= $false )
| ( ( in @ SV20 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(250,plain,
! [SV2: $i,SV22: $i] :
( ( ( SV22
!= ( union @ SV2 ) )
= $true )
| ( ( ! [SY72: $i] :
~ ( ~ ( ~ ( in @ SY72 @ SV22 )
| ~ ! [SY50: $i] :
~ ~ ( ~ ( in @ SY72 @ SY50 )
| ~ ( in @ SY50 @ SV2 ) ) )
| ~ ( ~ ~ ! [SY51: $i] :
~ ~ ( ~ ( in @ SY72 @ SY51 )
| ~ ( in @ SY51 @ SV2 ) )
| ( in @ SY72 @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(251,plain,
! [SV2: $i,SV22: $i] :
( ( ( ~ ! [SY75: $i] :
~ ( ~ ( ~ ( in @ SY75 @ SV22 )
| ~ ! [SY53: $i] :
~ ~ ( ~ ( in @ SY75 @ SY53 )
| ~ ( in @ SY53 @ SV2 ) ) )
| ~ ( ~ ~ ! [SY54: $i] :
~ ~ ( ~ ( in @ SY75 @ SY54 )
| ~ ( in @ SY54 @ SV2 ) )
| ( in @ SY75 @ SV22 ) ) ) )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(252,plain,
( ( ~ ( ~ ( epsilon_transitive @ sK2_SX0 )
| ~ ( epsilon_connected @ sK2_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(253,plain,
( ( ordinal @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(254,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ( epsilon_transitive @ SV3 )
| ~ ( epsilon_connected @ SV3 ) ) )
= $true )
| ( ( empty @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(255,plain,
! [SV3: $i] :
( ( ( ordinal @ SV3 )
= $true )
| ( ( empty @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(256,plain,
! [SV34: $i,SV25: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV25 )
| ~ ( element @ SV25 @ ( powerset @ SV34 ) ) )
= $true )
| ( ( element @ SV6 @ SV34 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(257,plain,
! [SV7: $i] :
( ( ( in @ ( sK4_SY59 @ SV7 ) @ SV7 )
= $true )
| ( ( ordinal @ ( union @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(258,plain,
! [SV26: $i,SV8: $i] :
( ( ( ~ ( ordinal @ SV8 ) )
= $true )
| ( ( ~ ( ordinal @ SV26 ) )
= $true )
| ( ( ordinal_subset @ SV8 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(259,plain,
! [SV27: $i,SV9: $i] :
( ( ( ~ ( ordinal @ SV9 ) )
= $true )
| ( ( ~ ( ordinal @ SV27 ) )
= $true )
| ( ( ( ordinal_subset @ SV9 @ SV27 )
| ( ordinal_subset @ SV27 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(260,plain,
! [SV10: $i] :
( ( ( ~ ( ~ ( epsilon_transitive @ ( union @ SV10 ) )
| ~ ( epsilon_connected @ ( union @ SV10 ) ) ) )
= $true )
| ( ( ordinal @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(261,plain,
! [SV10: $i] :
( ( ( ordinal @ ( union @ SV10 ) )
= $true )
| ( ( ordinal @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(262,plain,
! [SV28: $i,SV11: $i] :
( ( ( ~ ( ordinal @ SV11 ) )
= $true )
| ( ( ~ ( ordinal @ SV28 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ordinal_subset @ SV11 @ SV28 )
| ( subset @ SV11 @ SV28 ) )
| ~ ( ~ ( subset @ SV11 @ SV28 )
| ( ordinal_subset @ SV11 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(263,plain,
! [SV29: $i,SV12: $i] :
( ( ( ~ ( element @ SV12 @ ( powerset @ SV29 ) ) )
= $true )
| ( ( subset @ SV12 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(264,plain,
! [SV29: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV29 ) )
= $true )
| ( ( element @ SV12 @ ( powerset @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(265,plain,
! [SV35: $i,SV30: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( in @ SV13 @ SV30 )
| ~ ( element @ SV30 @ ( powerset @ SV35 ) ) ) )
= $true )
| ( ( ~ ( empty @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(266,plain,
! [SV31: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV31 ) )
= $true )
| ( ( ! [SY80: $i] :
( ~ ( in @ SY80 @ SV14 )
| ( in @ SY80 @ SV31 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(267,plain,
! [SV31: $i,SV14: $i] :
( ( ( ~ ! [SY81: $i] :
( ~ ( in @ SY81 @ SV14 )
| ( in @ SY81 @ SV31 ) ) )
= $true )
| ( ( subset @ SV14 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(268,plain,
! [SV16: $i] :
( ( ( epsilon_transitive @ SV16 )
= $true )
| ( ( ordinal @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(269,plain,
! [SV16: $i] :
( ( ( epsilon_connected @ SV16 )
= $true )
| ( ( ordinal @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(270,plain,
! [SV17: $i,SV36: $i] :
( ( ( ordinal @ SV36 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV17 @ ( succ @ SV36 ) )
| ( ordinal_subset @ SV17 @ SV36 ) )
| ~ ( ~ ( ordinal_subset @ SV17 @ SV36 )
| ( in @ SV17 @ ( succ @ SV36 ) ) ) ) )
= $true )
| ( ( ordinal @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(271,plain,
! [SV32: $i,SV18: $i] :
( ( ( in @ SV18 @ SV32 )
= $false )
| ( ( ~ ( empty @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(272,plain,
( ( ~ ( ~ ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( epsilon_transitive @ sK3_SX0 ) )
| ~ ( epsilon_connected @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(273,plain,
( ( ordinal @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(274,plain,
! [SV19: $i] :
( ( ( epsilon_transitive @ SV19 )
= $false )
| ( ( ~ ( epsilon_connected @ SV19 ) )
= $true )
| ( ( ordinal @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(275,plain,
! [SV37: $i] :
( ( ( in @ SV37 @ sK1_A )
= $false )
| ( ( ordinal @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(276,plain,
! [SV38: $i] :
( ( ( ordinal @ SV38 )
= $false )
| ( ( ~ ( subset @ sK1_A @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(277,plain,
! [SV2: $i,SV22: $i] :
( ( ( SV22
= ( union @ SV2 ) )
= $false )
| ( ( ! [SY72: $i] :
~ ( ~ ( ~ ( in @ SY72 @ SV22 )
| ~ ! [SY50: $i] :
~ ~ ( ~ ( in @ SY72 @ SY50 )
| ~ ( in @ SY50 @ SV2 ) ) )
| ~ ( ~ ~ ! [SY51: $i] :
~ ~ ( ~ ( in @ SY72 @ SY51 )
| ~ ( in @ SY51 @ SV2 ) )
| ( in @ SY72 @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(278,plain,
! [SV2: $i,SV22: $i] :
( ( ( ! [SY75: $i] :
~ ( ~ ( ~ ( in @ SY75 @ SV22 )
| ~ ! [SY53: $i] :
~ ~ ( ~ ( in @ SY75 @ SY53 )
| ~ ( in @ SY53 @ SV2 ) ) )
| ~ ( ~ ~ ! [SY54: $i] :
~ ~ ( ~ ( in @ SY75 @ SY54 )
| ~ ( in @ SY54 @ SV2 ) )
| ( in @ SY75 @ SV22 ) ) ) )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(279,plain,
( ( ~ ( epsilon_transitive @ sK2_SX0 )
| ~ ( epsilon_connected @ sK2_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(280,plain,
! [SV3: $i] :
( ( ( ~ ( epsilon_transitive @ SV3 )
| ~ ( epsilon_connected @ SV3 ) )
= $false )
| ( ( empty @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(281,plain,
! [SV34: $i,SV25: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV25 ) )
= $true )
| ( ( ~ ( element @ SV25 @ ( powerset @ SV34 ) ) )
= $true )
| ( ( element @ SV6 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(282,plain,
! [SV26: $i,SV8: $i] :
( ( ( ordinal @ SV8 )
= $false )
| ( ( ~ ( ordinal @ SV26 ) )
= $true )
| ( ( ordinal_subset @ SV8 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(283,plain,
! [SV27: $i,SV9: $i] :
( ( ( ordinal @ SV9 )
= $false )
| ( ( ~ ( ordinal @ SV27 ) )
= $true )
| ( ( ( ordinal_subset @ SV9 @ SV27 )
| ( ordinal_subset @ SV27 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(284,plain,
! [SV10: $i] :
( ( ( ~ ( epsilon_transitive @ ( union @ SV10 ) )
| ~ ( epsilon_connected @ ( union @ SV10 ) ) )
= $false )
| ( ( ordinal @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(285,plain,
! [SV28: $i,SV11: $i] :
( ( ( ordinal @ SV11 )
= $false )
| ( ( ~ ( ordinal @ SV28 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ordinal_subset @ SV11 @ SV28 )
| ( subset @ SV11 @ SV28 ) )
| ~ ( ~ ( subset @ SV11 @ SV28 )
| ( ordinal_subset @ SV11 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(286,plain,
! [SV29: $i,SV12: $i] :
( ( ( element @ SV12 @ ( powerset @ SV29 ) )
= $false )
| ( ( subset @ SV12 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(287,plain,
! [SV29: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV29 )
= $false )
| ( ( element @ SV12 @ ( powerset @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(288,plain,
! [SV35: $i,SV30: $i,SV13: $i] :
( ( ( ~ ( ~ ( in @ SV13 @ SV30 )
| ~ ( element @ SV30 @ ( powerset @ SV35 ) ) ) )
= $false )
| ( ( ~ ( empty @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(289,plain,
! [SV31: $i,SV14: $i] :
( ( ( subset @ SV14 @ SV31 )
= $false )
| ( ( ! [SY80: $i] :
( ~ ( in @ SY80 @ SV14 )
| ( in @ SY80 @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(290,plain,
! [SV31: $i,SV14: $i] :
( ( ( ! [SY81: $i] :
( ~ ( in @ SY81 @ SV14 )
| ( in @ SY81 @ SV31 ) ) )
= $false )
| ( ( subset @ SV14 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(291,plain,
! [SV36: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ SV17 @ ( succ @ SV36 ) )
| ( ordinal_subset @ SV17 @ SV36 ) )
| ~ ( ~ ( ordinal_subset @ SV17 @ SV36 )
| ( in @ SV17 @ ( succ @ SV36 ) ) ) )
= $false )
| ( ( ordinal @ SV36 )
= $false )
| ( ( ordinal @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(292,plain,
! [SV18: $i,SV32: $i] :
( ( ( empty @ SV32 )
= $false )
| ( ( in @ SV18 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(293,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( epsilon_transitive @ sK3_SX0 ) )
| ~ ( epsilon_connected @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(294,plain,
! [SV19: $i] :
( ( ( epsilon_connected @ SV19 )
= $false )
| ( ( epsilon_transitive @ SV19 )
= $false )
| ( ( ordinal @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(295,plain,
! [SV38: $i] :
( ( ( subset @ sK1_A @ SV38 )
= $false )
| ( ( ordinal @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(296,plain,
! [SV2: $i,SV22: $i,SV39: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV39 @ SV22 )
| ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ SV39 @ SY82 )
| ~ ( in @ SY82 @ SV2 ) ) )
| ~ ( ~ ~ ! [SY83: $i] :
~ ~ ( ~ ( in @ SV39 @ SY83 )
| ~ ( in @ SY83 @ SV2 ) )
| ( in @ SV39 @ SV22 ) ) ) )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(297,plain,
! [SV22: $i,SV2: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 )
| ~ ! [SY84: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY84 )
| ~ ( in @ SY84 @ SV2 ) ) )
| ~ ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY85 )
| ~ ( in @ SY85 @ SV2 ) )
| ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 ) ) ) )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[278]) ).
thf(298,plain,
( ( ~ ( epsilon_transitive @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(299,plain,
( ( ~ ( epsilon_connected @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(300,plain,
! [SV3: $i] :
( ( ( ~ ( epsilon_transitive @ SV3 ) )
= $false )
| ( ( empty @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(301,plain,
! [SV3: $i] :
( ( ( ~ ( epsilon_connected @ SV3 ) )
= $false )
| ( ( empty @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(302,plain,
! [SV34: $i,SV25: $i,SV6: $i] :
( ( ( in @ SV6 @ SV25 )
= $false )
| ( ( ~ ( element @ SV25 @ ( powerset @ SV34 ) ) )
= $true )
| ( ( element @ SV6 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(303,plain,
! [SV8: $i,SV26: $i] :
( ( ( ordinal @ SV26 )
= $false )
| ( ( ordinal @ SV8 )
= $false )
| ( ( ordinal_subset @ SV8 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(304,plain,
! [SV9: $i,SV27: $i] :
( ( ( ordinal @ SV27 )
= $false )
| ( ( ordinal @ SV9 )
= $false )
| ( ( ( ordinal_subset @ SV9 @ SV27 )
| ( ordinal_subset @ SV27 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(305,plain,
! [SV10: $i] :
( ( ( ~ ( epsilon_transitive @ ( union @ SV10 ) ) )
= $false )
| ( ( ordinal @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(306,plain,
! [SV10: $i] :
( ( ( ~ ( epsilon_connected @ ( union @ SV10 ) ) )
= $false )
| ( ( ordinal @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(307,plain,
! [SV11: $i,SV28: $i] :
( ( ( ordinal @ SV28 )
= $false )
| ( ( ordinal @ SV11 )
= $false )
| ( ( ~ ( ~ ( ~ ( ordinal_subset @ SV11 @ SV28 )
| ( subset @ SV11 @ SV28 ) )
| ~ ( ~ ( subset @ SV11 @ SV28 )
| ( ordinal_subset @ SV11 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(308,plain,
! [SV35: $i,SV30: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV30 )
| ~ ( element @ SV30 @ ( powerset @ SV35 ) ) )
= $true )
| ( ( ~ ( empty @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(309,plain,
! [SV31: $i,SV14: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ SV14 )
| ( in @ SV40 @ SV31 ) )
= $true )
| ( ( subset @ SV14 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(310,plain,
! [SV14: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK6_SY81 @ SV31 @ SV14 ) @ SV14 )
| ( in @ ( sK6_SY81 @ SV31 @ SV14 ) @ SV31 ) )
= $false )
| ( ( subset @ SV14 @ SV31 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[290]) ).
thf(311,plain,
! [SV36: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ SV17 @ ( succ @ SV36 ) )
| ( ordinal_subset @ SV17 @ SV36 ) ) )
= $false )
| ( ( ordinal @ SV36 )
= $false )
| ( ( ordinal @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(312,plain,
! [SV36: $i,SV17: $i] :
( ( ( ~ ( ~ ( ordinal_subset @ SV17 @ SV36 )
| ( in @ SV17 @ ( succ @ SV36 ) ) ) )
= $false )
| ( ( ordinal @ SV36 )
= $false )
| ( ( ordinal @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(313,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( epsilon_transitive @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(314,plain,
( ( ~ ( epsilon_connected @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(315,plain,
! [SV2: $i,SV22: $i,SV39: $i] :
( ( ( ~ ( ~ ( in @ SV39 @ SV22 )
| ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ SV39 @ SY82 )
| ~ ( in @ SY82 @ SV2 ) ) )
| ~ ( ~ ~ ! [SY83: $i] :
~ ~ ( ~ ( in @ SV39 @ SY83 )
| ~ ( in @ SY83 @ SV2 ) )
| ( in @ SV39 @ SV22 ) ) )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(316,plain,
! [SV22: $i,SV2: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 )
| ~ ! [SY84: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY84 )
| ~ ( in @ SY84 @ SV2 ) ) )
| ~ ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY85 )
| ~ ( in @ SY85 @ SV2 ) )
| ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(317,plain,
( ( epsilon_transitive @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(318,plain,
( ( epsilon_connected @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(319,plain,
! [SV3: $i] :
( ( ( epsilon_transitive @ SV3 )
= $true )
| ( ( empty @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(320,plain,
! [SV3: $i] :
( ( ( epsilon_connected @ SV3 )
= $true )
| ( ( empty @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(321,plain,
! [SV6: $i,SV34: $i,SV25: $i] :
( ( ( element @ SV25 @ ( powerset @ SV34 ) )
= $false )
| ( ( in @ SV6 @ SV25 )
= $false )
| ( ( element @ SV6 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(322,plain,
! [SV27: $i,SV9: $i] :
( ( ( ordinal_subset @ SV9 @ SV27 )
= $true )
| ( ( ordinal_subset @ SV27 @ SV9 )
= $true )
| ( ( ordinal @ SV9 )
= $false )
| ( ( ordinal @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(323,plain,
! [SV10: $i] :
( ( ( epsilon_transitive @ ( union @ SV10 ) )
= $true )
| ( ( ordinal @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(324,plain,
! [SV10: $i] :
( ( ( epsilon_connected @ ( union @ SV10 ) )
= $true )
| ( ( ordinal @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(325,plain,
! [SV28: $i,SV11: $i] :
( ( ( ~ ( ~ ( ordinal_subset @ SV11 @ SV28 )
| ( subset @ SV11 @ SV28 ) )
| ~ ( ~ ( subset @ SV11 @ SV28 )
| ( ordinal_subset @ SV11 @ SV28 ) ) )
= $false )
| ( ( ordinal @ SV11 )
= $false )
| ( ( ordinal @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(326,plain,
! [SV35: $i,SV30: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV30 ) )
= $true )
| ( ( ~ ( element @ SV30 @ ( powerset @ SV35 ) ) )
= $true )
| ( ( ~ ( empty @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(327,plain,
! [SV31: $i,SV14: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ SV14 ) )
= $true )
| ( ( in @ SV40 @ SV31 )
= $true )
| ( ( subset @ SV14 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(328,plain,
! [SV14: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK6_SY81 @ SV31 @ SV14 ) @ SV14 ) )
= $false )
| ( ( subset @ SV14 @ SV31 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(329,plain,
! [SV14: $i,SV31: $i] :
( ( ( in @ ( sK6_SY81 @ SV31 @ SV14 ) @ SV31 )
= $false )
| ( ( subset @ SV14 @ SV31 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(330,plain,
! [SV36: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ ( succ @ SV36 ) )
| ( ordinal_subset @ SV17 @ SV36 ) )
= $true )
| ( ( ordinal @ SV36 )
= $false )
| ( ( ordinal @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(331,plain,
! [SV36: $i,SV17: $i] :
( ( ( ~ ( ordinal_subset @ SV17 @ SV36 )
| ( in @ SV17 @ ( succ @ SV36 ) ) )
= $true )
| ( ( ordinal @ SV36 )
= $false )
| ( ( ordinal @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(332,plain,
( ( ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( epsilon_transitive @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(333,plain,
( ( epsilon_connected @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[314]) ).
thf(334,plain,
! [SV2: $i,SV22: $i,SV39: $i] :
( ( ( ~ ( ~ ( in @ SV39 @ SV22 )
| ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ SV39 @ SY82 )
| ~ ( in @ SY82 @ SV2 ) ) ) )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[315]) ).
thf(335,plain,
! [SV22: $i,SV2: $i,SV39: $i] :
( ( ( ~ ( ~ ~ ! [SY83: $i] :
~ ~ ( ~ ( in @ SV39 @ SY83 )
| ~ ( in @ SY83 @ SV2 ) )
| ( in @ SV39 @ SV22 ) ) )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[315]) ).
thf(336,plain,
! [SV22: $i,SV2: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 )
| ~ ! [SY84: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY84 )
| ~ ( in @ SY84 @ SV2 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY85 )
| ~ ( in @ SY85 @ SV2 ) )
| ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(337,plain,
! [SV28: $i,SV11: $i] :
( ( ( ~ ( ~ ( ordinal_subset @ SV11 @ SV28 )
| ( subset @ SV11 @ SV28 ) ) )
= $false )
| ( ( ordinal @ SV11 )
= $false )
| ( ( ordinal @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(338,plain,
! [SV28: $i,SV11: $i] :
( ( ( ~ ( ~ ( subset @ SV11 @ SV28 )
| ( ordinal_subset @ SV11 @ SV28 ) ) )
= $false )
| ( ( ordinal @ SV11 )
= $false )
| ( ( ordinal @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(339,plain,
! [SV35: $i,SV30: $i,SV13: $i] :
( ( ( in @ SV13 @ SV30 )
= $false )
| ( ( ~ ( element @ SV30 @ ( powerset @ SV35 ) ) )
= $true )
| ( ( ~ ( empty @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(340,plain,
! [SV31: $i,SV14: $i,SV40: $i] :
( ( ( in @ SV40 @ SV14 )
= $false )
| ( ( in @ SV40 @ SV31 )
= $true )
| ( ( subset @ SV14 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(341,plain,
! [SV14: $i,SV31: $i] :
( ( ( in @ ( sK6_SY81 @ SV31 @ SV14 ) @ SV14 )
= $true )
| ( ( subset @ SV14 @ SV31 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(342,plain,
! [SV36: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ ( succ @ SV36 ) ) )
= $true )
| ( ( ordinal_subset @ SV17 @ SV36 )
= $true )
| ( ( ordinal @ SV36 )
= $false )
| ( ( ordinal @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(343,plain,
! [SV36: $i,SV17: $i] :
( ( ( ~ ( ordinal_subset @ SV17 @ SV36 ) )
= $true )
| ( ( in @ SV17 @ ( succ @ SV36 ) )
= $true )
| ( ( ordinal @ SV36 )
= $false )
| ( ( ordinal @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(344,plain,
( ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( epsilon_transitive @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(345,plain,
! [SV2: $i,SV22: $i,SV39: $i] :
( ( ( ~ ( in @ SV39 @ SV22 )
| ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ SV39 @ SY82 )
| ~ ( in @ SY82 @ SV2 ) ) )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(346,plain,
! [SV22: $i,SV2: $i,SV39: $i] :
( ( ( ~ ~ ! [SY83: $i] :
~ ~ ( ~ ( in @ SV39 @ SY83 )
| ~ ( in @ SY83 @ SV2 ) )
| ( in @ SV39 @ SV22 ) )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(347,plain,
! [SV22: $i,SV2: $i] :
( ( ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 )
| ~ ! [SY84: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY84 )
| ~ ( in @ SY84 @ SV2 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY85 )
| ~ ( in @ SY85 @ SV2 ) )
| ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(348,plain,
! [SV28: $i,SV11: $i] :
( ( ( ~ ( ordinal_subset @ SV11 @ SV28 )
| ( subset @ SV11 @ SV28 ) )
= $true )
| ( ( ordinal @ SV11 )
= $false )
| ( ( ordinal @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(349,plain,
! [SV28: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV28 )
| ( ordinal_subset @ SV11 @ SV28 ) )
= $true )
| ( ( ordinal @ SV11 )
= $false )
| ( ( ordinal @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(350,plain,
! [SV13: $i,SV35: $i,SV30: $i] :
( ( ( element @ SV30 @ ( powerset @ SV35 ) )
= $false )
| ( ( in @ SV13 @ SV30 )
= $false )
| ( ( ~ ( empty @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(351,plain,
! [SV36: $i,SV17: $i] :
( ( ( in @ SV17 @ ( succ @ SV36 ) )
= $false )
| ( ( ordinal_subset @ SV17 @ SV36 )
= $true )
| ( ( ordinal @ SV36 )
= $false )
| ( ( ordinal @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(352,plain,
! [SV36: $i,SV17: $i] :
( ( ( ordinal_subset @ SV17 @ SV36 )
= $false )
| ( ( in @ SV17 @ ( succ @ SV36 ) )
= $true )
| ( ( ordinal @ SV36 )
= $false )
| ( ( ordinal @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(353,plain,
( ( ~ ~ ( empty @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(354,plain,
( ( ~ ( epsilon_transitive @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(355,plain,
! [SV2: $i,SV22: $i,SV39: $i] :
( ( ( ~ ( in @ SV39 @ SV22 ) )
= $true )
| ( ( ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ SV39 @ SY82 )
| ~ ( in @ SY82 @ SV2 ) ) )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(356,plain,
! [SV22: $i,SV2: $i,SV39: $i] :
( ( ( ~ ~ ! [SY83: $i] :
~ ~ ( ~ ( in @ SV39 @ SY83 )
| ~ ( in @ SY83 @ SV2 ) ) )
= $true )
| ( ( in @ SV39 @ SV22 )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(357,plain,
! [SV22: $i,SV2: $i] :
( ( ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY85 )
| ~ ( in @ SY85 @ SV2 ) )
| ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[347]) ).
thf(358,plain,
! [SV22: $i,SV2: $i] :
( ( ( ~ ! [SY84: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY84 )
| ~ ( in @ SY84 @ SV2 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY85 )
| ~ ( in @ SY85 @ SV2 ) )
| ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[347]) ).
thf(359,plain,
! [SV28: $i,SV11: $i] :
( ( ( ~ ( ordinal_subset @ SV11 @ SV28 ) )
= $true )
| ( ( subset @ SV11 @ SV28 )
= $true )
| ( ( ordinal @ SV11 )
= $false )
| ( ( ordinal @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(360,plain,
! [SV28: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV28 ) )
= $true )
| ( ( ordinal_subset @ SV11 @ SV28 )
= $true )
| ( ( ordinal @ SV11 )
= $false )
| ( ( ordinal @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(361,plain,
! [SV30: $i,SV13: $i,SV35: $i] :
( ( ( empty @ SV35 )
= $false )
| ( ( in @ SV13 @ SV30 )
= $false )
| ( ( element @ SV30 @ ( powerset @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(362,plain,
( ( ~ ( empty @ sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(363,plain,
( ( epsilon_transitive @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(364,plain,
! [SV2: $i,SV22: $i,SV39: $i] :
( ( ( in @ SV39 @ SV22 )
= $false )
| ( ( ~ ! [SY82: $i] :
~ ~ ( ~ ( in @ SV39 @ SY82 )
| ~ ( in @ SY82 @ SV2 ) ) )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(365,plain,
! [SV22: $i,SV2: $i,SV39: $i] :
( ( ( ~ ! [SY83: $i] :
~ ~ ( ~ ( in @ SV39 @ SY83 )
| ~ ( in @ SY83 @ SV2 ) ) )
= $false )
| ( ( in @ SV39 @ SV22 )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(366,plain,
! [SV22: $i,SV2: $i] :
( ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 )
= $true )
| ( ( ~ ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY85 )
| ~ ( in @ SY85 @ SV2 ) )
| ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[357]) ).
thf(367,plain,
! [SV22: $i,SV2: $i] :
( ( ( ! [SY84: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY84 )
| ~ ( in @ SY84 @ SV2 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY85 )
| ~ ( in @ SY85 @ SV2 ) )
| ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[358]) ).
thf(368,plain,
! [SV28: $i,SV11: $i] :
( ( ( ordinal_subset @ SV11 @ SV28 )
= $false )
| ( ( subset @ SV11 @ SV28 )
= $true )
| ( ( ordinal @ SV11 )
= $false )
| ( ( ordinal @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(369,plain,
! [SV28: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV28 )
= $false )
| ( ( ordinal_subset @ SV11 @ SV28 )
= $true )
| ( ( ordinal @ SV11 )
= $false )
| ( ( ordinal @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(370,plain,
( ( empty @ sK3_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(371,plain,
! [SV22: $i,SV2: $i,SV39: $i] :
( ( ( ! [SY82: $i] :
~ ~ ( ~ ( in @ SV39 @ SY82 )
| ~ ( in @ SY82 @ SV2 ) ) )
= $false )
| ( ( in @ SV39 @ SV22 )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(372,plain,
! [SV22: $i,SV2: $i,SV39: $i] :
( ( ( ! [SY83: $i] :
~ ~ ( ~ ( in @ SV39 @ SY83 )
| ~ ( in @ SY83 @ SV2 ) ) )
= $true )
| ( ( in @ SV39 @ SV22 )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(373,plain,
! [SV22: $i,SV2: $i] :
( ( ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY85 )
| ~ ( in @ SY85 @ SV2 ) )
| ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 ) )
= $false )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(374,plain,
! [SV41: $i,SV22: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV41 )
| ~ ( in @ SV41 @ SV2 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY85 )
| ~ ( in @ SY85 @ SV2 ) )
| ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(375,plain,
! [SV2: $i,SV22: $i,SV39: $i] :
( ( ( ~ ~ ( ~ ( in @ SV39 @ ( sK7_SY82 @ SV22 @ SV2 @ SV39 ) )
| ~ ( in @ ( sK7_SY82 @ SV22 @ SV2 @ SV39 ) @ SV2 ) ) )
= $false )
| ( ( in @ SV39 @ SV22 )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[371]) ).
thf(376,plain,
! [SV22: $i,SV2: $i,SV42: $i,SV39: $i] :
( ( ( ~ ~ ( ~ ( in @ SV39 @ SV42 )
| ~ ( in @ SV42 @ SV2 ) ) )
= $true )
| ( ( in @ SV39 @ SV22 )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(377,plain,
! [SV22: $i,SV2: $i] :
( ( ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY85 )
| ~ ( in @ SY85 @ SV2 ) ) )
= $false )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[373]) ).
thf(378,plain,
! [SV22: $i,SV2: $i] :
( ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 )
= $false )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[373]) ).
thf(379,plain,
! [SV41: $i,SV22: $i,SV2: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV41 )
| ~ ( in @ SV41 @ SV2 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY85 )
| ~ ( in @ SY85 @ SV2 ) )
| ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(380,plain,
! [SV2: $i,SV22: $i,SV39: $i] :
( ( ( ~ ( ~ ( in @ SV39 @ ( sK7_SY82 @ SV22 @ SV2 @ SV39 ) )
| ~ ( in @ ( sK7_SY82 @ SV22 @ SV2 @ SV39 ) @ SV2 ) ) )
= $true )
| ( ( in @ SV39 @ SV22 )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[375]) ).
thf(381,plain,
! [SV22: $i,SV2: $i,SV42: $i,SV39: $i] :
( ( ( ~ ( ~ ( in @ SV39 @ SV42 )
| ~ ( in @ SV42 @ SV2 ) ) )
= $false )
| ( ( in @ SV39 @ SV22 )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(382,plain,
! [SV22: $i,SV2: $i] :
( ( ( ~ ! [SY85: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY85 )
| ~ ( in @ SY85 @ SV2 ) ) )
= $true )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(383,plain,
! [SV41: $i,SV22: $i,SV2: $i] :
( ( ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV41 )
| ~ ( in @ SV41 @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY85 )
| ~ ( in @ SY85 @ SV2 ) )
| ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[379]) ).
thf(384,plain,
! [SV2: $i,SV22: $i,SV39: $i] :
( ( ( ~ ( in @ SV39 @ ( sK7_SY82 @ SV22 @ SV2 @ SV39 ) )
| ~ ( in @ ( sK7_SY82 @ SV22 @ SV2 @ SV39 ) @ SV2 ) )
= $false )
| ( ( in @ SV39 @ SV22 )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(385,plain,
! [SV22: $i,SV2: $i,SV42: $i,SV39: $i] :
( ( ( ~ ( in @ SV39 @ SV42 )
| ~ ( in @ SV42 @ SV2 ) )
= $true )
| ( ( in @ SV39 @ SV22 )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[381]) ).
thf(386,plain,
! [SV22: $i,SV2: $i] :
( ( ( ! [SY85: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY85 )
| ~ ( in @ SY85 @ SV2 ) ) )
= $false )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(387,plain,
! [SV41: $i,SV22: $i,SV2: $i] :
( ( ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV41 ) )
= $true )
| ( ( ~ ( in @ SV41 @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY85 )
| ~ ( in @ SY85 @ SV2 ) )
| ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(388,plain,
! [SV2: $i,SV22: $i,SV39: $i] :
( ( ( ~ ( in @ SV39 @ ( sK7_SY82 @ SV22 @ SV2 @ SV39 ) ) )
= $false )
| ( ( in @ SV39 @ SV22 )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[384]) ).
thf(389,plain,
! [SV39: $i,SV2: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK7_SY82 @ SV22 @ SV2 @ SV39 ) @ SV2 ) )
= $false )
| ( ( in @ SV39 @ SV22 )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[384]) ).
thf(390,plain,
! [SV22: $i,SV2: $i,SV42: $i,SV39: $i] :
( ( ( ~ ( in @ SV39 @ SV42 ) )
= $true )
| ( ( ~ ( in @ SV42 @ SV2 ) )
= $true )
| ( ( in @ SV39 @ SV22 )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(391,plain,
! [SV22: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ ( sK8_SY85 @ SV22 @ SV2 ) )
| ~ ( in @ ( sK8_SY85 @ SV22 @ SV2 ) @ SV2 ) ) )
= $false )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[386]) ).
thf(392,plain,
! [SV41: $i,SV22: $i,SV2: $i] :
( ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV41 )
= $false )
| ( ( ~ ( in @ SV41 @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY85 )
| ~ ( in @ SY85 @ SV2 ) )
| ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(393,plain,
! [SV2: $i,SV22: $i,SV39: $i] :
( ( ( in @ SV39 @ ( sK7_SY82 @ SV22 @ SV2 @ SV39 ) )
= $true )
| ( ( in @ SV39 @ SV22 )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(394,plain,
! [SV39: $i,SV2: $i,SV22: $i] :
( ( ( in @ ( sK7_SY82 @ SV22 @ SV2 @ SV39 ) @ SV2 )
= $true )
| ( ( in @ SV39 @ SV22 )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[389]) ).
thf(395,plain,
! [SV22: $i,SV2: $i,SV42: $i,SV39: $i] :
( ( ( in @ SV39 @ SV42 )
= $false )
| ( ( ~ ( in @ SV42 @ SV2 ) )
= $true )
| ( ( in @ SV39 @ SV22 )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(396,plain,
! [SV22: $i,SV2: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ ( sK8_SY85 @ SV22 @ SV2 ) )
| ~ ( in @ ( sK8_SY85 @ SV22 @ SV2 ) @ SV2 ) ) )
= $true )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(397,plain,
! [SV22: $i,SV2: $i,SV41: $i] :
( ( ( in @ SV41 @ SV2 )
= $false )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV41 )
= $false )
| ( ( ~ ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY85 )
| ~ ( in @ SY85 @ SV2 ) )
| ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(398,plain,
! [SV22: $i,SV39: $i,SV2: $i,SV42: $i] :
( ( ( in @ SV42 @ SV2 )
= $false )
| ( ( in @ SV39 @ SV42 )
= $false )
| ( ( in @ SV39 @ SV22 )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(399,plain,
! [SV22: $i,SV2: $i] :
( ( ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ ( sK8_SY85 @ SV22 @ SV2 ) )
| ~ ( in @ ( sK8_SY85 @ SV22 @ SV2 ) @ SV2 ) )
= $false )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(400,plain,
! [SV41: $i,SV22: $i,SV2: $i] :
( ( ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY85 )
| ~ ( in @ SY85 @ SV2 ) )
| ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 ) )
= $false )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV41 )
= $false )
| ( ( in @ SV41 @ SV2 )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(401,plain,
! [SV22: $i,SV2: $i] :
( ( ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ ( sK8_SY85 @ SV22 @ SV2 ) ) )
= $false )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[399]) ).
thf(402,plain,
! [SV2: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK8_SY85 @ SV22 @ SV2 ) @ SV2 ) )
= $false )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[399]) ).
thf(403,plain,
! [SV41: $i,SV22: $i,SV2: $i] :
( ( ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY85 )
| ~ ( in @ SY85 @ SV2 ) ) )
= $false )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV41 )
= $false )
| ( ( in @ SV41 @ SV2 )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(404,plain,
! [SV41: $i,SV22: $i,SV2: $i] :
( ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 )
= $false )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV41 )
= $false )
| ( ( in @ SV41 @ SV2 )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(405,plain,
! [SV22: $i,SV2: $i] :
( ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ ( sK8_SY85 @ SV22 @ SV2 ) )
= $true )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[401]) ).
thf(406,plain,
! [SV2: $i,SV22: $i] :
( ( ( in @ ( sK8_SY85 @ SV22 @ SV2 ) @ SV2 )
= $true )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[402]) ).
thf(407,plain,
! [SV41: $i,SV22: $i,SV2: $i] :
( ( ( ~ ! [SY85: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY85 )
| ~ ( in @ SY85 @ SV2 ) ) )
= $true )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV41 )
= $false )
| ( ( in @ SV41 @ SV2 )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[403]) ).
thf(408,plain,
! [SV41: $i,SV22: $i,SV2: $i] :
( ( ( ! [SY85: $i] :
~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SY85 )
| ~ ( in @ SY85 @ SV2 ) ) )
= $false )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV41 )
= $false )
| ( ( in @ SV41 @ SV2 )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(409,plain,
! [SV41: $i,SV22: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ ( sK9_SY85 @ SV41 @ SV22 @ SV2 ) )
| ~ ( in @ ( sK9_SY85 @ SV41 @ SV22 @ SV2 ) @ SV2 ) ) )
= $false )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV41 )
= $false )
| ( ( in @ SV41 @ SV2 )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[408]) ).
thf(410,plain,
! [SV41: $i,SV22: $i,SV2: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ ( sK9_SY85 @ SV41 @ SV22 @ SV2 ) )
| ~ ( in @ ( sK9_SY85 @ SV41 @ SV22 @ SV2 ) @ SV2 ) ) )
= $true )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV41 )
= $false )
| ( ( in @ SV41 @ SV2 )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[409]) ).
thf(411,plain,
! [SV41: $i,SV22: $i,SV2: $i] :
( ( ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ ( sK9_SY85 @ SV41 @ SV22 @ SV2 ) )
| ~ ( in @ ( sK9_SY85 @ SV41 @ SV22 @ SV2 ) @ SV2 ) )
= $false )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV41 )
= $false )
| ( ( in @ SV41 @ SV2 )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(412,plain,
! [SV41: $i,SV22: $i,SV2: $i] :
( ( ( ~ ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ ( sK9_SY85 @ SV41 @ SV22 @ SV2 ) ) )
= $false )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV41 )
= $false )
| ( ( in @ SV41 @ SV2 )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(413,plain,
! [SV2: $i,SV22: $i,SV41: $i] :
( ( ( ~ ( in @ ( sK9_SY85 @ SV41 @ SV22 @ SV2 ) @ SV2 ) )
= $false )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV41 )
= $false )
| ( ( in @ SV41 @ SV2 )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(414,plain,
! [SV41: $i,SV22: $i,SV2: $i] :
( ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ ( sK9_SY85 @ SV41 @ SV22 @ SV2 ) )
= $true )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV41 )
= $false )
| ( ( in @ SV41 @ SV2 )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[412]) ).
thf(415,plain,
! [SV2: $i,SV22: $i,SV41: $i] :
( ( ( in @ ( sK9_SY85 @ SV41 @ SV22 @ SV2 ) @ SV2 )
= $true )
| ( ( in @ ( sK5_SY75 @ SV2 @ SV22 ) @ SV41 )
= $false )
| ( ( in @ SV41 @ SV2 )
= $false )
| ( ( SV22
= ( union @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[413]) ).
thf(416,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[148,415,414,406,405,404,398,394,393,378,370,369,368,363,361,352,351,341,340,333,329,324,323,322,321,320,319,318,317,303,295,294,292,287,286,275,273,269,268,261,257,255,253,249,229,226,200,186]) ).
thf(417,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[416]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM403+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 13:07:15 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.82/6.53
% 36.82/6.53 No.of.Axioms: 22
% 36.82/6.53
% 36.82/6.53 Length.of.Defs: 0
% 36.82/6.53
% 36.82/6.53 Contains.Choice.Funs: false
% 36.82/6.53 ..........
% 36.82/6.53
% 36.82/6.53 ********************************
% 36.82/6.53 * All subproblems solved! *
% 36.82/6.53 ********************************
% 36.82/6.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:22,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:416,loop_count:0,foatp_calls:1,translation:fof_full)
% 36.82/6.53
% 36.82/6.53 %**** Beginning of derivation protocol ****
% 36.82/6.53 % SZS output start CNFRefutation
% See solution above
% 36.82/6.53
% 36.82/6.53 %**** End of derivation protocol ****
% 36.82/6.53 %**** no. of clauses in derivation: 387 ****
% 36.82/6.53 %**** clause counter: 416 ****
% 36.82/6.53
% 36.82/6.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:22,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:416,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------