%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM404+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 : n018.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 1.12s 0.47s
% Output : CNFRefutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 18
% Syntax : Number of formulae : 325 ( 146 unt; 0 typ; 0 def)
% Number of atoms : 2244 ( 643 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 3755 (1289 ~; 658 |; 60 &;1691 @)
% ( 18 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 6 con; 0-2 aty)
% Number of variables : 566 ( 0 ^; 560 !; 6 ?; 566 :)
% 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_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_SY39,type,
sK4_SY39: $i > $i ).
thf(tp_sK5_SY43,type,
sK5_SY43: $i > $i ).
thf(tp_sK6_SY59,type,
sK6_SY59: $i > $i ).
thf(tp_sK7_SY57,type,
sK7_SY57: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
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(7,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(8,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ~ ( ~ ( in @ A @ B )
& ( A != B )
& ~ ( in @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
=> ( ordinal @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_ordinal1) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(15,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
thf(23,axiom,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(30,axiom,
! [A: $i] :
( ( ordinal @ A )
<=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_ordinal1) ).
thf(31,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(32,axiom,
! [A: $i] :
( ( epsilon_connected @ A )
<=> ! [B: $i,C: $i] :
~ ( ( in @ B @ A )
& ( in @ C @ A )
& ~ ( in @ B @ C )
& ( B != C )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_ordinal1) ).
thf(33,axiom,
! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
thf(34,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
thf(35,axiom,
! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(38,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(41,conjecture,
! [A: $i] :
~ ! [B: $i] :
( ( in @ B @ A )
<=> ( ordinal @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_ordinal1) ).
thf(42,negated_conjecture,
( ( ! [A: $i] :
~ ! [B: $i] :
( ( in @ B @ A )
<=> ( ordinal @ B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[41]) ).
thf(43,plain,
( ( ! [A: $i] :
~ ! [B: $i] :
( ( in @ B @ A )
<=> ( ordinal @ B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[42]) ).
thf(44,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(45,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(46,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(47,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(48,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ~ ( ~ ( in @ A @ B )
& ( A != B )
& ~ ( in @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
=> ( ordinal @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(50,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(51,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(52,plain,
( ( ? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(53,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
<=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(54,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(55,plain,
( ( ! [A: $i] :
( ( epsilon_connected @ A )
<=> ! [B: $i,C: $i] :
~ ( ( in @ B @ A )
& ( in @ C @ A )
& ~ ( in @ B @ C )
& ( B != C )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(56,plain,
( ( ! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(57,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(58,plain,
( ( ! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(59,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(60,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(61,plain,
( ( ~ ! [SY34: $i] :
( ( in @ SY34 @ sK1_A )
<=> ( ordinal @ SY34 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[43]) ).
thf(62,plain,
( ( ! [SY34: $i] :
( ( in @ SY34 @ sK1_A )
<=> ( ordinal @ SY34 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[61]) ).
thf(63,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(64,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(65,plain,
( ( ! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(66,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(67,plain,
( ( ! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(68,plain,
( ( ! [A: $i] :
( ( epsilon_connected @ A )
<=> ! [B: $i,C: $i] :
~ ( ( in @ B @ A )
& ( in @ C @ A )
& ~ ( in @ B @ C )
& ( B != C )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(69,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(70,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
<=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(71,plain,
( ( ? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(72,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(73,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(74,plain,
( ( ! [A: $i,B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
=> ( ordinal @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(75,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ~ ( ~ ( in @ A @ B )
& ( A != B )
& ~ ( in @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(76,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(77,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(78,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(80,plain,
( ( ! [SY34: $i] :
( ( in @ SY34 @ sK1_A )
<=> ( ordinal @ SY34 ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(81,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ~ ( ~ ( epsilon_transitive @ SX0 )
| ~ ( epsilon_connected @ SX0 ) )
| ~ ( ordinal @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(82,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ~ ( epsilon_transitive @ SX0 )
| ~ ( epsilon_connected @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(83,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( epsilon_transitive @ SX0 ) )
| ~ ( epsilon_connected @ SX0 ) )
| ~ ( ordinal @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(84,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(85,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( epsilon_transitive @ SX0 )
| ~ ( epsilon_connected @ SX0 ) )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(86,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( epsilon_transitive @ SX0 )
| ~ ( epsilon_connected @ SX0 ) )
| ~ ( ordinal @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(87,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ! [SX1: $i] :
( ~ ( ordinal @ SX1 )
| ~ ~ ( ~ ~ ( ~ ~ ( in @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ~ ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(88,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX1 )
| ~ ( in @ SX0 @ SX1 )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(89,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) )
| ( epsilon_transitive @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(90,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(91,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( epsilon_connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ~ ( in @ SX1 @ SX2 ) )
| ~ ( ( SX1 != SX2 ) ) )
| ~ ~ ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ~ ( in @ SX1 @ SX2 ) )
| ~ ( ( SX1 != SX2 ) ) )
| ~ ~ ( in @ SX2 @ SX1 ) )
| ( epsilon_connected @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(92,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ SX1 )
| ( empty @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(93,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ordinal @ SX0 )
| ~ ( ~ ( epsilon_transitive @ SX0 )
| ~ ( epsilon_connected @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( epsilon_transitive @ SX0 )
| ~ ( epsilon_connected @ SX0 ) )
| ( ordinal @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(94,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ( element @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(95,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ~ ( empty @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(96,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)],[69]) ).
thf(97,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(98,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( in @ SX0 @ sK1_A )
| ( ordinal @ SX0 ) )
| ~ ( ~ ( ordinal @ SX0 )
| ( in @ SX0 @ sK1_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(99,plain,
! [SV1: $i] :
( ( ~ ( empty @ SV1 )
| ~ ( ~ ~ ( ~ ( epsilon_transitive @ SV1 )
| ~ ( epsilon_connected @ SV1 ) )
| ~ ( ordinal @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(100,plain,
! [SV2: $i] :
( ( ~ ( ordinal @ SV2 )
| ~ ( ~ ( epsilon_transitive @ SV2 )
| ~ ( epsilon_connected @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(101,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( epsilon_transitive @ SX0 ) )
| ~ ( epsilon_connected @ SX0 ) )
| ~ ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(102,plain,
! [SV3: $i] :
( ( ! [SY35: $i] :
( ~ ( in @ SV3 @ SY35 )
| ( element @ SV3 @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(103,plain,
! [SV4: $i] :
( ( ~ ~ ( ~ ( epsilon_transitive @ SV4 )
| ~ ( epsilon_connected @ SV4 ) )
| ( ordinal @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(104,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( epsilon_transitive @ SX0 )
| ~ ( epsilon_connected @ SX0 ) )
| ~ ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(105,plain,
! [SV5: $i] :
( ( ~ ( ordinal @ SV5 )
| ! [SY36: $i] :
( ~ ( ordinal @ SY36 )
| ~ ~ ( ~ ~ ( ~ ~ ( in @ SV5 @ SY36 )
| ~ ( ( SV5 != SY36 ) ) )
| ~ ~ ( in @ SY36 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(106,plain,
! [SV6: $i] :
( ( ! [SY37: $i] :
( ~ ( ordinal @ SY37 )
| ~ ( in @ SV6 @ SY37 )
| ( ordinal @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(107,plain,
! [SV7: $i] :
( ( ~ ( ~ ( ~ ( epsilon_transitive @ SV7 )
| ! [SY38: $i] :
( ~ ( in @ SY38 @ SV7 )
| ( subset @ SY38 @ SV7 ) ) )
| ~ ( ~ ! [SY39: $i] :
( ~ ( in @ SY39 @ SV7 )
| ( subset @ SY39 @ SV7 ) )
| ( epsilon_transitive @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(108,plain,
! [SV8: $i] :
( ( ! [SY40: $i] :
( ~ ( in @ SV8 @ SY40 )
| ~ ( in @ SY40 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(109,plain,
! [SV9: $i] :
( ( ~ ( ~ ( ~ ( epsilon_connected @ SV9 )
| ! [SY41: $i,SY42: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY41 @ SV9 )
| ~ ( in @ SY42 @ SV9 ) )
| ~ ~ ( in @ SY41 @ SY42 ) )
| ~ ( ( SY41 != SY42 ) ) )
| ~ ~ ( in @ SY42 @ SY41 ) ) )
| ~ ( ~ ! [SY43: $i,SY44: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY43 @ SV9 )
| ~ ( in @ SY44 @ SV9 ) )
| ~ ~ ( in @ SY43 @ SY44 ) )
| ~ ( ( SY43 != SY44 ) ) )
| ~ ~ ( in @ SY44 @ SY43 ) )
| ( epsilon_connected @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(110,plain,
! [SV10: $i] :
( ( ! [SY45: $i] :
( ~ ( element @ SV10 @ SY45 )
| ( empty @ SY45 )
| ( in @ SV10 @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(111,plain,
! [SV11: $i] :
( ( ~ ( ~ ( ~ ( ordinal @ SV11 )
| ~ ( ~ ( epsilon_transitive @ SV11 )
| ~ ( epsilon_connected @ SV11 ) ) )
| ~ ( ~ ~ ( ~ ( epsilon_transitive @ SV11 )
| ~ ( epsilon_connected @ SV11 ) )
| ( ordinal @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(112,plain,
! [SV12: $i] :
( ( ! [SY46: $i,SY47: $i] :
( ~ ~ ( ~ ( in @ SV12 @ SY46 )
| ~ ( element @ SY46 @ ( powerset @ SY47 ) ) )
| ( element @ SV12 @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(113,plain,
! [SV13: $i] :
( ( ! [SY48: $i,SY49: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV13 @ SY48 )
| ~ ( element @ SY48 @ ( powerset @ SY49 ) ) )
| ~ ( empty @ SY49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(114,plain,
! [SV14: $i] :
( ( ! [SY50: $i] :
~ ( ~ ( ~ ( subset @ SV14 @ SY50 )
| ! [SY51: $i] :
( ~ ( in @ SY51 @ SV14 )
| ( in @ SY51 @ SY50 ) ) )
| ~ ( ~ ! [SY52: $i] :
( ~ ( in @ SY52 @ SV14 )
| ( in @ SY52 @ SY50 ) )
| ( subset @ SV14 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(115,plain,
! [SV15: $i] :
( ( ! [SY53: $i] :
~ ~ ( ~ ( in @ SV15 @ SY53 )
| ~ ( empty @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(116,plain,
! [SV16: $i] :
( ( ~ ( ~ ( ~ ( in @ SV16 @ sK1_A )
| ( ordinal @ SV16 ) )
| ~ ( ~ ( ordinal @ SV16 )
| ( in @ SV16 @ sK1_A ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(117,plain,
! [SV1: $i] :
( ( ( ~ ( empty @ SV1 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( epsilon_transitive @ SV1 )
| ~ ( epsilon_connected @ SV1 ) )
| ~ ( ordinal @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(118,plain,
! [SV2: $i] :
( ( ( ~ ( ordinal @ SV2 ) )
= $true )
| ( ( ~ ( ~ ( epsilon_transitive @ SV2 )
| ~ ( epsilon_connected @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(119,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK2_SX0 )
| ~ ( epsilon_transitive @ sK2_SX0 ) )
| ~ ( epsilon_connected @ sK2_SX0 ) )
| ~ ( ordinal @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[101]) ).
thf(120,plain,
! [SV17: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ SV17 )
| ( element @ SV3 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(121,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ( epsilon_transitive @ SV4 )
| ~ ( epsilon_connected @ SV4 ) ) )
= $true )
| ( ( ordinal @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(122,plain,
( ( ~ ~ ( ~ ~ ( ~ ( epsilon_transitive @ sK3_SX0 )
| ~ ( epsilon_connected @ sK3_SX0 ) )
| ~ ( ordinal @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[104]) ).
thf(123,plain,
! [SV5: $i] :
( ( ( ~ ( ordinal @ SV5 ) )
= $true )
| ( ( ! [SY36: $i] :
( ~ ( ordinal @ SY36 )
| ~ ~ ( ~ ~ ( ~ ~ ( in @ SV5 @ SY36 )
| ~ ( ( SV5 != SY36 ) ) )
| ~ ~ ( in @ SY36 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(124,plain,
! [SV6: $i,SV18: $i] :
( ( ~ ( ordinal @ SV18 )
| ~ ( in @ SV6 @ SV18 )
| ( ordinal @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(125,plain,
! [SV7: $i] :
( ( ~ ( ~ ( epsilon_transitive @ SV7 )
| ! [SY38: $i] :
( ~ ( in @ SY38 @ SV7 )
| ( subset @ SY38 @ SV7 ) ) )
| ~ ( ~ ! [SY39: $i] :
( ~ ( in @ SY39 @ SV7 )
| ( subset @ SY39 @ SV7 ) )
| ( epsilon_transitive @ SV7 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(126,plain,
! [SV19: $i,SV8: $i] :
( ( ~ ( in @ SV8 @ SV19 )
| ~ ( in @ SV19 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(127,plain,
! [SV9: $i] :
( ( ~ ( ~ ( epsilon_connected @ SV9 )
| ! [SY41: $i,SY42: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY41 @ SV9 )
| ~ ( in @ SY42 @ SV9 ) )
| ~ ~ ( in @ SY41 @ SY42 ) )
| ~ ( ( SY41 != SY42 ) ) )
| ~ ~ ( in @ SY42 @ SY41 ) ) )
| ~ ( ~ ! [SY43: $i,SY44: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY43 @ SV9 )
| ~ ( in @ SY44 @ SV9 ) )
| ~ ~ ( in @ SY43 @ SY44 ) )
| ~ ( ( SY43 != SY44 ) ) )
| ~ ~ ( in @ SY44 @ SY43 ) )
| ( epsilon_connected @ SV9 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(128,plain,
! [SV20: $i,SV10: $i] :
( ( ~ ( element @ SV10 @ SV20 )
| ( empty @ SV20 )
| ( in @ SV10 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(129,plain,
! [SV11: $i] :
( ( ~ ( ~ ( ordinal @ SV11 )
| ~ ( ~ ( epsilon_transitive @ SV11 )
| ~ ( epsilon_connected @ SV11 ) ) )
| ~ ( ~ ~ ( ~ ( epsilon_transitive @ SV11 )
| ~ ( epsilon_connected @ SV11 ) )
| ( ordinal @ SV11 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(130,plain,
! [SV21: $i,SV12: $i] :
( ( ! [SY54: $i] :
( ~ ~ ( ~ ( in @ SV12 @ SV21 )
| ~ ( element @ SV21 @ ( powerset @ SY54 ) ) )
| ( element @ SV12 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(131,plain,
! [SV22: $i,SV13: $i] :
( ( ! [SY55: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV13 @ SV22 )
| ~ ( element @ SV22 @ ( powerset @ SY55 ) ) )
| ~ ( empty @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(132,plain,
! [SV23: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV14 @ SV23 )
| ! [SY56: $i] :
( ~ ( in @ SY56 @ SV14 )
| ( in @ SY56 @ SV23 ) ) )
| ~ ( ~ ! [SY57: $i] :
( ~ ( in @ SY57 @ SV14 )
| ( in @ SY57 @ SV23 ) )
| ( subset @ SV14 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(133,plain,
! [SV24: $i,SV15: $i] :
( ( ~ ~ ( ~ ( in @ SV15 @ SV24 )
| ~ ( empty @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(134,plain,
! [SV16: $i] :
( ( ~ ( ~ ( in @ SV16 @ sK1_A )
| ( ordinal @ SV16 ) )
| ~ ( ~ ( ordinal @ SV16 )
| ( in @ SV16 @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(135,plain,
! [SV1: $i] :
( ( ( empty @ SV1 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( epsilon_transitive @ SV1 )
| ~ ( epsilon_connected @ SV1 ) )
| ~ ( ordinal @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(136,plain,
! [SV2: $i] :
( ( ( ordinal @ SV2 )
= $false )
| ( ( ~ ( ~ ( epsilon_transitive @ SV2 )
| ~ ( epsilon_connected @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(137,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK2_SX0 )
| ~ ( epsilon_transitive @ sK2_SX0 ) )
| ~ ( epsilon_connected @ sK2_SX0 ) )
| ~ ( ordinal @ sK2_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(138,plain,
! [SV17: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV17 ) )
= $true )
| ( ( element @ SV3 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(139,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ( epsilon_transitive @ SV4 )
| ~ ( epsilon_connected @ SV4 ) ) )
= $false )
| ( ( ordinal @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(140,plain,
( ( ~ ( ~ ~ ( ~ ( epsilon_transitive @ sK3_SX0 )
| ~ ( epsilon_connected @ sK3_SX0 ) )
| ~ ( ordinal @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(141,plain,
! [SV5: $i] :
( ( ( ordinal @ SV5 )
= $false )
| ( ( ! [SY36: $i] :
( ~ ( ordinal @ SY36 )
| ~ ~ ( ~ ~ ( ~ ~ ( in @ SV5 @ SY36 )
| ~ ( ( SV5 != SY36 ) ) )
| ~ ~ ( in @ SY36 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(142,plain,
! [SV6: $i,SV18: $i] :
( ( ( ~ ( ordinal @ SV18 ) )
= $true )
| ( ( ~ ( in @ SV6 @ SV18 )
| ( ordinal @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(143,plain,
! [SV7: $i] :
( ( ~ ( ~ ( epsilon_transitive @ SV7 )
| ! [SY38: $i] :
( ~ ( in @ SY38 @ SV7 )
| ( subset @ SY38 @ SV7 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(144,plain,
! [SV7: $i] :
( ( ~ ( ~ ! [SY39: $i] :
( ~ ( in @ SY39 @ SV7 )
| ( subset @ SY39 @ SV7 ) )
| ( epsilon_transitive @ SV7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(145,plain,
! [SV19: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV19 ) )
= $true )
| ( ( ~ ( in @ SV19 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(146,plain,
! [SV9: $i] :
( ( ~ ( ~ ( epsilon_connected @ SV9 )
| ! [SY41: $i,SY42: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY41 @ SV9 )
| ~ ( in @ SY42 @ SV9 ) )
| ~ ~ ( in @ SY41 @ SY42 ) )
| ~ ( ( SY41 != SY42 ) ) )
| ~ ~ ( in @ SY42 @ SY41 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(147,plain,
! [SV9: $i] :
( ( ~ ( ~ ! [SY43: $i,SY44: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY43 @ SV9 )
| ~ ( in @ SY44 @ SV9 ) )
| ~ ~ ( in @ SY43 @ SY44 ) )
| ~ ( ( SY43 != SY44 ) ) )
| ~ ~ ( in @ SY44 @ SY43 ) )
| ( epsilon_connected @ SV9 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(148,plain,
! [SV20: $i,SV10: $i] :
( ( ( ~ ( element @ SV10 @ SV20 ) )
= $true )
| ( ( ( empty @ SV20 )
| ( in @ SV10 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(149,plain,
! [SV11: $i] :
( ( ~ ( ~ ( ordinal @ SV11 )
| ~ ( ~ ( epsilon_transitive @ SV11 )
| ~ ( epsilon_connected @ SV11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(150,plain,
! [SV11: $i] :
( ( ~ ( ~ ~ ( ~ ( epsilon_transitive @ SV11 )
| ~ ( epsilon_connected @ SV11 ) )
| ( ordinal @ SV11 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(151,plain,
! [SV25: $i,SV21: $i,SV12: $i] :
( ( ~ ~ ( ~ ( in @ SV12 @ SV21 )
| ~ ( element @ SV21 @ ( powerset @ SV25 ) ) )
| ( element @ SV12 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(152,plain,
! [SV26: $i,SV22: $i,SV13: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV13 @ SV22 )
| ~ ( element @ SV22 @ ( powerset @ SV26 ) ) )
| ~ ( empty @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(153,plain,
! [SV23: $i,SV14: $i] :
( ( ~ ( ~ ( subset @ SV14 @ SV23 )
| ! [SY56: $i] :
( ~ ( in @ SY56 @ SV14 )
| ( in @ SY56 @ SV23 ) ) )
| ~ ( ~ ! [SY57: $i] :
( ~ ( in @ SY57 @ SV14 )
| ( in @ SY57 @ SV23 ) )
| ( subset @ SV14 @ SV23 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(154,plain,
! [SV24: $i,SV15: $i] :
( ( ~ ( ~ ( in @ SV15 @ SV24 )
| ~ ( empty @ SV24 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(155,plain,
! [SV16: $i] :
( ( ~ ( ~ ( in @ SV16 @ sK1_A )
| ( ordinal @ SV16 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(156,plain,
! [SV16: $i] :
( ( ~ ( ~ ( ordinal @ SV16 )
| ( in @ SV16 @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(157,plain,
! [SV1: $i] :
( ( ( ~ ~ ( ~ ( epsilon_transitive @ SV1 )
| ~ ( epsilon_connected @ SV1 ) )
| ~ ( ordinal @ SV1 ) )
= $false )
| ( ( empty @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(158,plain,
! [SV2: $i] :
( ( ( ~ ( epsilon_transitive @ SV2 )
| ~ ( epsilon_connected @ SV2 ) )
= $false )
| ( ( ordinal @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(159,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK2_SX0 )
| ~ ( epsilon_transitive @ sK2_SX0 ) )
| ~ ( epsilon_connected @ sK2_SX0 ) )
| ~ ( ordinal @ sK2_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(160,plain,
! [SV17: $i,SV3: $i] :
( ( ( in @ SV3 @ SV17 )
= $false )
| ( ( element @ SV3 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(161,plain,
! [SV4: $i] :
( ( ( ~ ( epsilon_transitive @ SV4 )
| ~ ( epsilon_connected @ SV4 ) )
= $true )
| ( ( ordinal @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(162,plain,
( ( ~ ~ ( ~ ( epsilon_transitive @ sK3_SX0 )
| ~ ( epsilon_connected @ sK3_SX0 ) )
| ~ ( ordinal @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(163,plain,
! [SV5: $i,SV27: $i] :
( ( ( ~ ( ordinal @ SV27 )
| ~ ~ ( ~ ~ ( ~ ~ ( in @ SV5 @ SV27 )
| ~ ( ( SV5 != SV27 ) ) )
| ~ ~ ( in @ SV27 @ SV5 ) ) )
= $true )
| ( ( ordinal @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(164,plain,
! [SV6: $i,SV18: $i] :
( ( ( ordinal @ SV18 )
= $false )
| ( ( ~ ( in @ SV6 @ SV18 )
| ( ordinal @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(165,plain,
! [SV7: $i] :
( ( ~ ( epsilon_transitive @ SV7 )
| ! [SY38: $i] :
( ~ ( in @ SY38 @ SV7 )
| ( subset @ SY38 @ SV7 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(166,plain,
! [SV7: $i] :
( ( ~ ! [SY39: $i] :
( ~ ( in @ SY39 @ SV7 )
| ( subset @ SY39 @ SV7 ) )
| ( epsilon_transitive @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(167,plain,
! [SV19: $i,SV8: $i] :
( ( ( in @ SV8 @ SV19 )
= $false )
| ( ( ~ ( in @ SV19 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(168,plain,
! [SV9: $i] :
( ( ~ ( epsilon_connected @ SV9 )
| ! [SY41: $i,SY42: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY41 @ SV9 )
| ~ ( in @ SY42 @ SV9 ) )
| ~ ~ ( in @ SY41 @ SY42 ) )
| ~ ( ( SY41 != SY42 ) ) )
| ~ ~ ( in @ SY42 @ SY41 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(169,plain,
! [SV9: $i] :
( ( ~ ! [SY43: $i,SY44: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY43 @ SV9 )
| ~ ( in @ SY44 @ SV9 ) )
| ~ ~ ( in @ SY43 @ SY44 ) )
| ~ ( ( SY43 != SY44 ) ) )
| ~ ~ ( in @ SY44 @ SY43 ) )
| ( epsilon_connected @ SV9 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(170,plain,
! [SV20: $i,SV10: $i] :
( ( ( element @ SV10 @ SV20 )
= $false )
| ( ( ( empty @ SV20 )
| ( in @ SV10 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(171,plain,
! [SV11: $i] :
( ( ~ ( ordinal @ SV11 )
| ~ ( ~ ( epsilon_transitive @ SV11 )
| ~ ( epsilon_connected @ SV11 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(172,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ( epsilon_transitive @ SV11 )
| ~ ( epsilon_connected @ SV11 ) )
| ( ordinal @ SV11 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(173,plain,
! [SV25: $i,SV21: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( in @ SV12 @ SV21 )
| ~ ( element @ SV21 @ ( powerset @ SV25 ) ) ) )
= $true )
| ( ( element @ SV12 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(174,plain,
! [SV26: $i,SV22: $i,SV13: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV13 @ SV22 )
| ~ ( element @ SV22 @ ( powerset @ SV26 ) ) )
| ~ ( empty @ SV26 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(175,plain,
! [SV23: $i,SV14: $i] :
( ( ~ ( ~ ( subset @ SV14 @ SV23 )
| ! [SY56: $i] :
( ~ ( in @ SY56 @ SV14 )
| ( in @ SY56 @ SV23 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(176,plain,
! [SV23: $i,SV14: $i] :
( ( ~ ( ~ ! [SY57: $i] :
( ~ ( in @ SY57 @ SV14 )
| ( in @ SY57 @ SV23 ) )
| ( subset @ SV14 @ SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(177,plain,
! [SV24: $i,SV15: $i] :
( ( ~ ( in @ SV15 @ SV24 )
| ~ ( empty @ SV24 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(178,plain,
! [SV16: $i] :
( ( ~ ( in @ SV16 @ sK1_A )
| ( ordinal @ SV16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(179,plain,
! [SV16: $i] :
( ( ~ ( ordinal @ SV16 )
| ( in @ SV16 @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(180,plain,
! [SV1: $i] :
( ( ( ~ ~ ( ~ ( epsilon_transitive @ SV1 )
| ~ ( epsilon_connected @ SV1 ) ) )
= $false )
| ( ( empty @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(181,plain,
! [SV1: $i] :
( ( ( ~ ( ordinal @ SV1 ) )
= $false )
| ( ( empty @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(182,plain,
! [SV2: $i] :
( ( ( ~ ( epsilon_transitive @ SV2 ) )
= $false )
| ( ( ordinal @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(183,plain,
! [SV2: $i] :
( ( ( ~ ( epsilon_connected @ SV2 ) )
= $false )
| ( ( ordinal @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(184,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK2_SX0 )
| ~ ( epsilon_transitive @ sK2_SX0 ) )
| ~ ( epsilon_connected @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(185,plain,
( ( ~ ( ordinal @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(186,plain,
! [SV4: $i] :
( ( ( ~ ( epsilon_transitive @ SV4 ) )
= $true )
| ( ( ~ ( epsilon_connected @ SV4 ) )
= $true )
| ( ( ordinal @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(187,plain,
( ( ~ ~ ( ~ ( epsilon_transitive @ sK3_SX0 )
| ~ ( epsilon_connected @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[162]) ).
thf(188,plain,
( ( ~ ( ordinal @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[162]) ).
thf(189,plain,
! [SV5: $i,SV27: $i] :
( ( ( ~ ( ordinal @ SV27 ) )
= $true )
| ( ( ~ ~ ( ~ ~ ( ~ ~ ( in @ SV5 @ SV27 )
| ~ ( ( SV5 != SV27 ) ) )
| ~ ~ ( in @ SV27 @ SV5 ) ) )
= $true )
| ( ( ordinal @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(190,plain,
! [SV18: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV18 ) )
= $true )
| ( ( ordinal @ SV6 )
= $true )
| ( ( ordinal @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(191,plain,
! [SV7: $i] :
( ( ( ~ ( epsilon_transitive @ SV7 ) )
= $true )
| ( ( ! [SY38: $i] :
( ~ ( in @ SY38 @ SV7 )
| ( subset @ SY38 @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(192,plain,
! [SV7: $i] :
( ( ( ~ ! [SY39: $i] :
( ~ ( in @ SY39 @ SV7 )
| ( subset @ SY39 @ SV7 ) ) )
= $true )
| ( ( epsilon_transitive @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(193,plain,
! [SV8: $i,SV19: $i] :
( ( ( in @ SV19 @ SV8 )
= $false )
| ( ( in @ SV8 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(194,plain,
! [SV9: $i] :
( ( ( ~ ( epsilon_connected @ SV9 ) )
= $true )
| ( ( ! [SY41: $i,SY42: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY41 @ SV9 )
| ~ ( in @ SY42 @ SV9 ) )
| ~ ~ ( in @ SY41 @ SY42 ) )
| ~ ( ( SY41 != SY42 ) ) )
| ~ ~ ( in @ SY42 @ SY41 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(195,plain,
! [SV9: $i] :
( ( ( ~ ! [SY43: $i,SY44: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY43 @ SV9 )
| ~ ( in @ SY44 @ SV9 ) )
| ~ ~ ( in @ SY43 @ SY44 ) )
| ~ ( ( SY43 != SY44 ) ) )
| ~ ~ ( in @ SY44 @ SY43 ) ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(196,plain,
! [SV10: $i,SV20: $i] :
( ( ( empty @ SV20 )
= $true )
| ( ( in @ SV10 @ SV20 )
= $true )
| ( ( element @ SV10 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(197,plain,
! [SV11: $i] :
( ( ( ~ ( ordinal @ SV11 ) )
= $true )
| ( ( ~ ( ~ ( epsilon_transitive @ SV11 )
| ~ ( epsilon_connected @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(198,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ( epsilon_transitive @ SV11 )
| ~ ( epsilon_connected @ SV11 ) ) )
= $true )
| ( ( ordinal @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(199,plain,
! [SV25: $i,SV21: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ SV12 @ SV21 )
| ~ ( element @ SV21 @ ( powerset @ SV25 ) ) ) )
= $false )
| ( ( element @ SV12 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(200,plain,
! [SV26: $i,SV22: $i,SV13: $i] :
( ( ~ ~ ( ~ ( in @ SV13 @ SV22 )
| ~ ( element @ SV22 @ ( powerset @ SV26 ) ) )
| ~ ( empty @ SV26 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(201,plain,
! [SV23: $i,SV14: $i] :
( ( ~ ( subset @ SV14 @ SV23 )
| ! [SY56: $i] :
( ~ ( in @ SY56 @ SV14 )
| ( in @ SY56 @ SV23 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(202,plain,
! [SV23: $i,SV14: $i] :
( ( ~ ! [SY57: $i] :
( ~ ( in @ SY57 @ SV14 )
| ( in @ SY57 @ SV23 ) )
| ( subset @ SV14 @ SV23 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(203,plain,
! [SV24: $i,SV15: $i] :
( ( ( ~ ( in @ SV15 @ SV24 ) )
= $true )
| ( ( ~ ( empty @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(204,plain,
! [SV16: $i] :
( ( ( ~ ( in @ SV16 @ sK1_A ) )
= $true )
| ( ( ordinal @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(205,plain,
! [SV16: $i] :
( ( ( ~ ( ordinal @ SV16 ) )
= $true )
| ( ( in @ SV16 @ sK1_A )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(206,plain,
! [SV1: $i] :
( ( ( ~ ( ~ ( epsilon_transitive @ SV1 )
| ~ ( epsilon_connected @ SV1 ) ) )
= $true )
| ( ( empty @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(207,plain,
! [SV1: $i] :
( ( ( ordinal @ SV1 )
= $true )
| ( ( empty @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(208,plain,
! [SV2: $i] :
( ( ( epsilon_transitive @ SV2 )
= $true )
| ( ( ordinal @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(209,plain,
! [SV2: $i] :
( ( ( epsilon_connected @ SV2 )
= $true )
| ( ( ordinal @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(210,plain,
( ( ~ ( ~ ~ ( ~ ~ ( empty @ sK2_SX0 )
| ~ ( epsilon_transitive @ sK2_SX0 ) )
| ~ ( epsilon_connected @ sK2_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(211,plain,
( ( ordinal @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(212,plain,
! [SV4: $i] :
( ( ( epsilon_transitive @ SV4 )
= $false )
| ( ( ~ ( epsilon_connected @ SV4 ) )
= $true )
| ( ( ordinal @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(213,plain,
( ( ~ ( ~ ( epsilon_transitive @ sK3_SX0 )
| ~ ( epsilon_connected @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(214,plain,
( ( ordinal @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(215,plain,
! [SV5: $i,SV27: $i] :
( ( ( ordinal @ SV27 )
= $false )
| ( ( ~ ~ ( ~ ~ ( ~ ~ ( in @ SV5 @ SV27 )
| ~ ( ( SV5 != SV27 ) ) )
| ~ ~ ( in @ SV27 @ SV5 ) ) )
= $true )
| ( ( ordinal @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(216,plain,
! [SV18: $i,SV6: $i] :
( ( ( in @ SV6 @ SV18 )
= $false )
| ( ( ordinal @ SV6 )
= $true )
| ( ( ordinal @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(217,plain,
! [SV7: $i] :
( ( ( epsilon_transitive @ SV7 )
= $false )
| ( ( ! [SY38: $i] :
( ~ ( in @ SY38 @ SV7 )
| ( subset @ SY38 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(218,plain,
! [SV7: $i] :
( ( ( ! [SY39: $i] :
( ~ ( in @ SY39 @ SV7 )
| ( subset @ SY39 @ SV7 ) ) )
= $false )
| ( ( epsilon_transitive @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(219,plain,
! [SV9: $i] :
( ( ( epsilon_connected @ SV9 )
= $false )
| ( ( ! [SY41: $i,SY42: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY41 @ SV9 )
| ~ ( in @ SY42 @ SV9 ) )
| ~ ~ ( in @ SY41 @ SY42 ) )
| ~ ( ( SY41 != SY42 ) ) )
| ~ ~ ( in @ SY42 @ SY41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(220,plain,
! [SV9: $i] :
( ( ( ! [SY43: $i,SY44: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY43 @ SV9 )
| ~ ( in @ SY44 @ SV9 ) )
| ~ ~ ( in @ SY43 @ SY44 ) )
| ~ ( ( SY43 != SY44 ) ) )
| ~ ~ ( in @ SY44 @ SY43 ) ) )
= $false )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(221,plain,
! [SV11: $i] :
( ( ( ordinal @ SV11 )
= $false )
| ( ( ~ ( ~ ( epsilon_transitive @ SV11 )
| ~ ( epsilon_connected @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(222,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ( epsilon_transitive @ SV11 )
| ~ ( epsilon_connected @ SV11 ) ) )
= $false )
| ( ( ordinal @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(223,plain,
! [SV25: $i,SV21: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV21 )
| ~ ( element @ SV21 @ ( powerset @ SV25 ) ) )
= $true )
| ( ( element @ SV12 @ SV25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(224,plain,
! [SV26: $i,SV22: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( in @ SV13 @ SV22 )
| ~ ( element @ SV22 @ ( powerset @ SV26 ) ) ) )
= $true )
| ( ( ~ ( empty @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(225,plain,
! [SV23: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV23 ) )
= $true )
| ( ( ! [SY56: $i] :
( ~ ( in @ SY56 @ SV14 )
| ( in @ SY56 @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(226,plain,
! [SV23: $i,SV14: $i] :
( ( ( ~ ! [SY57: $i] :
( ~ ( in @ SY57 @ SV14 )
| ( in @ SY57 @ SV23 ) ) )
= $true )
| ( ( subset @ SV14 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(227,plain,
! [SV24: $i,SV15: $i] :
( ( ( in @ SV15 @ SV24 )
= $false )
| ( ( ~ ( empty @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(228,plain,
! [SV16: $i] :
( ( ( in @ SV16 @ sK1_A )
= $false )
| ( ( ordinal @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(229,plain,
! [SV16: $i] :
( ( ( ordinal @ SV16 )
= $false )
| ( ( in @ SV16 @ sK1_A )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(230,plain,
! [SV1: $i] :
( ( ( ~ ( epsilon_transitive @ SV1 )
| ~ ( epsilon_connected @ SV1 ) )
= $false )
| ( ( empty @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(231,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK2_SX0 )
| ~ ( epsilon_transitive @ sK2_SX0 ) )
| ~ ( epsilon_connected @ sK2_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(232,plain,
! [SV4: $i] :
( ( ( epsilon_connected @ SV4 )
= $false )
| ( ( epsilon_transitive @ SV4 )
= $false )
| ( ( ordinal @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(233,plain,
( ( ~ ( epsilon_transitive @ sK3_SX0 )
| ~ ( epsilon_connected @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(234,plain,
! [SV27: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( in @ SV5 @ SV27 )
| ~ ( ( SV5 != SV27 ) ) )
| ~ ~ ( in @ SV27 @ SV5 ) ) )
= $false )
| ( ( ordinal @ SV27 )
= $false )
| ( ( ordinal @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(235,plain,
! [SV7: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ SV7 )
| ( subset @ SV28 @ SV7 ) )
= $true )
| ( ( epsilon_transitive @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(236,plain,
! [SV7: $i] :
( ( ( ~ ( in @ ( sK4_SY39 @ SV7 ) @ SV7 )
| ( subset @ ( sK4_SY39 @ SV7 ) @ SV7 ) )
= $false )
| ( ( epsilon_transitive @ SV7 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[218]) ).
thf(237,plain,
! [SV9: $i,SV29: $i] :
( ( ( ! [SY58: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV29 @ SV9 )
| ~ ( in @ SY58 @ SV9 ) )
| ~ ~ ( in @ SV29 @ SY58 ) )
| ~ ( ( SV29 != SY58 ) ) )
| ~ ~ ( in @ SY58 @ SV29 ) ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(238,plain,
! [SV9: $i] :
( ( ( ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK5_SY43 @ SV9 ) @ SV9 )
| ~ ( in @ SY59 @ SV9 ) )
| ~ ~ ( in @ ( sK5_SY43 @ SV9 ) @ SY59 ) )
| ~ ( ( ( sK5_SY43 @ SV9 )
!= SY59 ) ) )
| ~ ~ ( in @ SY59 @ ( sK5_SY43 @ SV9 ) ) ) )
= $false )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[220]) ).
thf(239,plain,
! [SV11: $i] :
( ( ( ~ ( epsilon_transitive @ SV11 )
| ~ ( epsilon_connected @ SV11 ) )
= $false )
| ( ( ordinal @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(240,plain,
! [SV11: $i] :
( ( ( ~ ( epsilon_transitive @ SV11 )
| ~ ( epsilon_connected @ SV11 ) )
= $true )
| ( ( ordinal @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(241,plain,
! [SV25: $i,SV21: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV21 ) )
= $true )
| ( ( ~ ( element @ SV21 @ ( powerset @ SV25 ) ) )
= $true )
| ( ( element @ SV12 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(242,plain,
! [SV26: $i,SV22: $i,SV13: $i] :
( ( ( ~ ( ~ ( in @ SV13 @ SV22 )
| ~ ( element @ SV22 @ ( powerset @ SV26 ) ) ) )
= $false )
| ( ( ~ ( empty @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(243,plain,
! [SV23: $i,SV14: $i] :
( ( ( subset @ SV14 @ SV23 )
= $false )
| ( ( ! [SY56: $i] :
( ~ ( in @ SY56 @ SV14 )
| ( in @ SY56 @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(244,plain,
! [SV23: $i,SV14: $i] :
( ( ( ! [SY57: $i] :
( ~ ( in @ SY57 @ SV14 )
| ( in @ SY57 @ SV23 ) ) )
= $false )
| ( ( subset @ SV14 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(245,plain,
! [SV15: $i,SV24: $i] :
( ( ( empty @ SV24 )
= $false )
| ( ( in @ SV15 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(246,plain,
! [SV1: $i] :
( ( ( ~ ( epsilon_transitive @ SV1 ) )
= $false )
| ( ( empty @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(247,plain,
! [SV1: $i] :
( ( ( ~ ( epsilon_connected @ SV1 ) )
= $false )
| ( ( empty @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(248,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK2_SX0 )
| ~ ( epsilon_transitive @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(249,plain,
( ( ~ ( epsilon_connected @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(250,plain,
( ( ~ ( epsilon_transitive @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(251,plain,
( ( ~ ( epsilon_connected @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(252,plain,
! [SV27: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( in @ SV5 @ SV27 )
| ~ ( ( SV5 != SV27 ) ) )
| ~ ~ ( in @ SV27 @ SV5 ) )
= $true )
| ( ( ordinal @ SV27 )
= $false )
| ( ( ordinal @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(253,plain,
! [SV7: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ SV7 ) )
= $true )
| ( ( subset @ SV28 @ SV7 )
= $true )
| ( ( epsilon_transitive @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(254,plain,
! [SV7: $i] :
( ( ( ~ ( in @ ( sK4_SY39 @ SV7 ) @ SV7 ) )
= $false )
| ( ( epsilon_transitive @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(255,plain,
! [SV7: $i] :
( ( ( subset @ ( sK4_SY39 @ SV7 ) @ SV7 )
= $false )
| ( ( epsilon_transitive @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(256,plain,
! [SV30: $i,SV9: $i,SV29: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV29 @ SV9 )
| ~ ( in @ SV30 @ SV9 ) )
| ~ ~ ( in @ SV29 @ SV30 ) )
| ~ ( ( SV29 != SV30 ) ) )
| ~ ~ ( in @ SV30 @ SV29 ) ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(257,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK5_SY43 @ SV9 ) @ SV9 )
| ~ ( in @ ( sK6_SY59 @ SV9 ) @ SV9 ) )
| ~ ~ ( in @ ( sK5_SY43 @ SV9 ) @ ( sK6_SY59 @ SV9 ) ) )
| ~ ( ( ( sK5_SY43 @ SV9 )
!= ( sK6_SY59 @ SV9 ) ) ) )
| ~ ~ ( in @ ( sK6_SY59 @ SV9 ) @ ( sK5_SY43 @ SV9 ) ) ) )
= $false )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[238]) ).
thf(258,plain,
! [SV11: $i] :
( ( ( ~ ( epsilon_transitive @ SV11 ) )
= $false )
| ( ( ordinal @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(259,plain,
! [SV11: $i] :
( ( ( ~ ( epsilon_connected @ SV11 ) )
= $false )
| ( ( ordinal @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(260,plain,
! [SV11: $i] :
( ( ( ~ ( epsilon_transitive @ SV11 ) )
= $true )
| ( ( ~ ( epsilon_connected @ SV11 ) )
= $true )
| ( ( ordinal @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(261,plain,
! [SV25: $i,SV21: $i,SV12: $i] :
( ( ( in @ SV12 @ SV21 )
= $false )
| ( ( ~ ( element @ SV21 @ ( powerset @ SV25 ) ) )
= $true )
| ( ( element @ SV12 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(262,plain,
! [SV26: $i,SV22: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV22 )
| ~ ( element @ SV22 @ ( powerset @ SV26 ) ) )
= $true )
| ( ( ~ ( empty @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(263,plain,
! [SV23: $i,SV14: $i,SV31: $i] :
( ( ( ~ ( in @ SV31 @ SV14 )
| ( in @ SV31 @ SV23 ) )
= $true )
| ( ( subset @ SV14 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(264,plain,
! [SV14: $i,SV23: $i] :
( ( ( ~ ( in @ ( sK7_SY57 @ SV23 @ SV14 ) @ SV14 )
| ( in @ ( sK7_SY57 @ SV23 @ SV14 ) @ SV23 ) )
= $false )
| ( ( subset @ SV14 @ SV23 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[244]) ).
thf(265,plain,
! [SV1: $i] :
( ( ( epsilon_transitive @ SV1 )
= $true )
| ( ( empty @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(266,plain,
! [SV1: $i] :
( ( ( epsilon_connected @ SV1 )
= $true )
| ( ( empty @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(267,plain,
( ( ~ ( ~ ~ ( empty @ sK2_SX0 )
| ~ ( epsilon_transitive @ sK2_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(268,plain,
( ( epsilon_connected @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(269,plain,
( ( epsilon_transitive @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(270,plain,
( ( epsilon_connected @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(271,plain,
! [SV27: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( in @ SV5 @ SV27 )
| ~ ( ( SV5 != SV27 ) ) ) )
= $true )
| ( ( ~ ~ ( in @ SV27 @ SV5 ) )
= $true )
| ( ( ordinal @ SV27 )
= $false )
| ( ( ordinal @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(272,plain,
! [SV7: $i,SV28: $i] :
( ( ( in @ SV28 @ SV7 )
= $false )
| ( ( subset @ SV28 @ SV7 )
= $true )
| ( ( epsilon_transitive @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(273,plain,
! [SV7: $i] :
( ( ( in @ ( sK4_SY39 @ SV7 ) @ SV7 )
= $true )
| ( ( epsilon_transitive @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(274,plain,
! [SV30: $i,SV9: $i,SV29: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV29 @ SV9 )
| ~ ( in @ SV30 @ SV9 ) )
| ~ ~ ( in @ SV29 @ SV30 ) )
| ~ ( ( SV29 != SV30 ) ) )
| ~ ~ ( in @ SV30 @ SV29 ) ) )
= $false )
| ( ( epsilon_connected @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(275,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK5_SY43 @ SV9 ) @ SV9 )
| ~ ( in @ ( sK6_SY59 @ SV9 ) @ SV9 ) )
| ~ ~ ( in @ ( sK5_SY43 @ SV9 ) @ ( sK6_SY59 @ SV9 ) ) )
| ~ ( ( ( sK5_SY43 @ SV9 )
!= ( sK6_SY59 @ SV9 ) ) ) )
| ~ ~ ( in @ ( sK6_SY59 @ SV9 ) @ ( sK5_SY43 @ SV9 ) ) ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(276,plain,
! [SV11: $i] :
( ( ( epsilon_transitive @ SV11 )
= $true )
| ( ( ordinal @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(277,plain,
! [SV11: $i] :
( ( ( epsilon_connected @ SV11 )
= $true )
| ( ( ordinal @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(278,plain,
! [SV11: $i] :
( ( ( epsilon_transitive @ SV11 )
= $false )
| ( ( ~ ( epsilon_connected @ SV11 ) )
= $true )
| ( ( ordinal @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(279,plain,
! [SV12: $i,SV25: $i,SV21: $i] :
( ( ( element @ SV21 @ ( powerset @ SV25 ) )
= $false )
| ( ( in @ SV12 @ SV21 )
= $false )
| ( ( element @ SV12 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(280,plain,
! [SV26: $i,SV22: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV22 ) )
= $true )
| ( ( ~ ( element @ SV22 @ ( powerset @ SV26 ) ) )
= $true )
| ( ( ~ ( empty @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(281,plain,
! [SV23: $i,SV14: $i,SV31: $i] :
( ( ( ~ ( in @ SV31 @ SV14 ) )
= $true )
| ( ( in @ SV31 @ SV23 )
= $true )
| ( ( subset @ SV14 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(282,plain,
! [SV14: $i,SV23: $i] :
( ( ( ~ ( in @ ( sK7_SY57 @ SV23 @ SV14 ) @ SV14 ) )
= $false )
| ( ( subset @ SV14 @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(283,plain,
! [SV14: $i,SV23: $i] :
( ( ( in @ ( sK7_SY57 @ SV23 @ SV14 ) @ SV23 )
= $false )
| ( ( subset @ SV14 @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(284,plain,
( ( ~ ~ ( empty @ sK2_SX0 )
| ~ ( epsilon_transitive @ sK2_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(285,plain,
! [SV27: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( in @ SV5 @ SV27 )
| ~ ( ( SV5 != SV27 ) ) ) )
= $false )
| ( ( ~ ~ ( in @ SV27 @ SV5 ) )
= $true )
| ( ( ordinal @ SV27 )
= $false )
| ( ( ordinal @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(286,plain,
! [SV30: $i,SV9: $i,SV29: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV29 @ SV9 )
| ~ ( in @ SV30 @ SV9 ) )
| ~ ~ ( in @ SV29 @ SV30 ) )
| ~ ( ( SV29 != SV30 ) ) )
| ~ ~ ( in @ SV30 @ SV29 ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(287,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK5_SY43 @ SV9 ) @ SV9 )
| ~ ( in @ ( sK6_SY59 @ SV9 ) @ SV9 ) )
| ~ ~ ( in @ ( sK5_SY43 @ SV9 ) @ ( sK6_SY59 @ SV9 ) ) )
| ~ ( ( ( sK5_SY43 @ SV9 )
!= ( sK6_SY59 @ SV9 ) ) ) )
| ~ ~ ( in @ ( sK6_SY59 @ SV9 ) @ ( sK5_SY43 @ SV9 ) ) )
= $false )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(288,plain,
! [SV11: $i] :
( ( ( epsilon_connected @ SV11 )
= $false )
| ( ( epsilon_transitive @ SV11 )
= $false )
| ( ( ordinal @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(289,plain,
! [SV26: $i,SV22: $i,SV13: $i] :
( ( ( in @ SV13 @ SV22 )
= $false )
| ( ( ~ ( element @ SV22 @ ( powerset @ SV26 ) ) )
= $true )
| ( ( ~ ( empty @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(290,plain,
! [SV23: $i,SV14: $i,SV31: $i] :
( ( ( in @ SV31 @ SV14 )
= $false )
| ( ( in @ SV31 @ SV23 )
= $true )
| ( ( subset @ SV14 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(291,plain,
! [SV14: $i,SV23: $i] :
( ( ( in @ ( sK7_SY57 @ SV23 @ SV14 ) @ SV14 )
= $true )
| ( ( subset @ SV14 @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(292,plain,
( ( ~ ~ ( empty @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(293,plain,
( ( ~ ( epsilon_transitive @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(294,plain,
! [SV27: $i,SV5: $i] :
( ( ( ~ ~ ( in @ SV5 @ SV27 )
| ~ ( ( SV5 != SV27 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV27 @ SV5 ) )
= $true )
| ( ( ordinal @ SV27 )
= $false )
| ( ( ordinal @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(295,plain,
! [SV30: $i,SV9: $i,SV29: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV29 @ SV9 )
| ~ ( in @ SV30 @ SV9 ) )
| ~ ~ ( in @ SV29 @ SV30 ) )
| ~ ( ( SV29 != SV30 ) ) ) )
= $true )
| ( ( ~ ~ ( in @ SV30 @ SV29 ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(296,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK5_SY43 @ SV9 ) @ SV9 )
| ~ ( in @ ( sK6_SY59 @ SV9 ) @ SV9 ) )
| ~ ~ ( in @ ( sK5_SY43 @ SV9 ) @ ( sK6_SY59 @ SV9 ) ) )
| ~ ( ( ( sK5_SY43 @ SV9 )
!= ( sK6_SY59 @ SV9 ) ) ) ) )
= $false )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[287]) ).
thf(297,plain,
! [SV9: $i] :
( ( ( ~ ~ ( in @ ( sK6_SY59 @ SV9 ) @ ( sK5_SY43 @ SV9 ) ) )
= $false )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[287]) ).
thf(298,plain,
! [SV13: $i,SV26: $i,SV22: $i] :
( ( ( element @ SV22 @ ( powerset @ SV26 ) )
= $false )
| ( ( in @ SV13 @ SV22 )
= $false )
| ( ( ~ ( empty @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(299,plain,
( ( ~ ( empty @ sK2_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(300,plain,
( ( epsilon_transitive @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(301,plain,
! [SV27: $i,SV5: $i] :
( ( ( ~ ~ ( in @ SV5 @ SV27 ) )
= $true )
| ( ( ~ ( ( SV5 != SV27 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV27 @ SV5 ) )
= $true )
| ( ( ordinal @ SV27 )
= $false )
| ( ( ordinal @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(302,plain,
! [SV30: $i,SV9: $i,SV29: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV29 @ SV9 )
| ~ ( in @ SV30 @ SV9 ) )
| ~ ~ ( in @ SV29 @ SV30 ) )
| ~ ( ( SV29 != SV30 ) ) ) )
= $false )
| ( ( ~ ~ ( in @ SV30 @ SV29 ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(303,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK5_SY43 @ SV9 ) @ SV9 )
| ~ ( in @ ( sK6_SY59 @ SV9 ) @ SV9 ) )
| ~ ~ ( in @ ( sK5_SY43 @ SV9 ) @ ( sK6_SY59 @ SV9 ) ) )
| ~ ( ( ( sK5_SY43 @ SV9 )
!= ( sK6_SY59 @ SV9 ) ) ) ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(304,plain,
! [SV9: $i] :
( ( ( ~ ( in @ ( sK6_SY59 @ SV9 ) @ ( sK5_SY43 @ SV9 ) ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(305,plain,
! [SV22: $i,SV13: $i,SV26: $i] :
( ( ( empty @ SV26 )
= $false )
| ( ( in @ SV13 @ SV22 )
= $false )
| ( ( element @ SV22 @ ( powerset @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(306,plain,
( ( empty @ sK2_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(307,plain,
! [SV27: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV27 ) )
= $false )
| ( ( ~ ( ( SV5 != SV27 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV27 @ SV5 ) )
= $true )
| ( ( ordinal @ SV27 )
= $false )
| ( ( ordinal @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(308,plain,
! [SV30: $i,SV9: $i,SV29: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV29 @ SV9 )
| ~ ( in @ SV30 @ SV9 ) )
| ~ ~ ( in @ SV29 @ SV30 ) )
| ~ ( ( SV29 != SV30 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV30 @ SV29 ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(309,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK5_SY43 @ SV9 ) @ SV9 )
| ~ ( in @ ( sK6_SY59 @ SV9 ) @ SV9 ) )
| ~ ~ ( in @ ( sK5_SY43 @ SV9 ) @ ( sK6_SY59 @ SV9 ) ) )
| ~ ( ( ( sK5_SY43 @ SV9 )
!= ( sK6_SY59 @ SV9 ) ) ) )
= $false )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(310,plain,
! [SV9: $i] :
( ( ( in @ ( sK6_SY59 @ SV9 ) @ ( sK5_SY43 @ SV9 ) )
= $false )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(311,plain,
! [SV27: $i,SV5: $i] :
( ( ( in @ SV5 @ SV27 )
= $true )
| ( ( ~ ( ( SV5 != SV27 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV27 @ SV5 ) )
= $true )
| ( ( ordinal @ SV27 )
= $false )
| ( ( ordinal @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(312,plain,
! [SV30: $i,SV9: $i,SV29: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV29 @ SV9 )
| ~ ( in @ SV30 @ SV9 ) )
| ~ ~ ( in @ SV29 @ SV30 ) ) )
= $true )
| ( ( ~ ( ( SV29 != SV30 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV30 @ SV29 ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(313,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK5_SY43 @ SV9 ) @ SV9 )
| ~ ( in @ ( sK6_SY59 @ SV9 ) @ SV9 ) )
| ~ ~ ( in @ ( sK5_SY43 @ SV9 ) @ ( sK6_SY59 @ SV9 ) ) ) )
= $false )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(314,plain,
! [SV9: $i] :
( ( ( ~ ( ( ( sK5_SY43 @ SV9 )
!= ( sK6_SY59 @ SV9 ) ) ) )
= $false )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(315,plain,
! [SV27: $i,SV5: $i] :
( ( ( SV5 != SV27 )
= $false )
| ( ( in @ SV5 @ SV27 )
= $true )
| ( ( ~ ~ ( in @ SV27 @ SV5 ) )
= $true )
| ( ( ordinal @ SV27 )
= $false )
| ( ( ordinal @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(316,plain,
! [SV30: $i,SV9: $i,SV29: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV29 @ SV9 )
| ~ ( in @ SV30 @ SV9 ) )
| ~ ~ ( in @ SV29 @ SV30 ) ) )
= $false )
| ( ( ~ ( ( SV29 != SV30 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV30 @ SV29 ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(317,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY43 @ SV9 ) @ SV9 )
| ~ ( in @ ( sK6_SY59 @ SV9 ) @ SV9 ) )
| ~ ~ ( in @ ( sK5_SY43 @ SV9 ) @ ( sK6_SY59 @ SV9 ) ) ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(318,plain,
! [SV9: $i] :
( ( ( ( sK5_SY43 @ SV9 )
!= ( sK6_SY59 @ SV9 ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[314]) ).
thf(319,plain,
! [SV27: $i,SV5: $i] :
( ( ( SV5 = SV27 )
= $true )
| ( ( in @ SV5 @ SV27 )
= $true )
| ( ( ~ ~ ( in @ SV27 @ SV5 ) )
= $true )
| ( ( ordinal @ SV27 )
= $false )
| ( ( ordinal @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(320,plain,
! [SV30: $i,SV9: $i,SV29: $i] :
( ( ( ~ ~ ( ~ ( in @ SV29 @ SV9 )
| ~ ( in @ SV30 @ SV9 ) )
| ~ ~ ( in @ SV29 @ SV30 ) )
= $true )
| ( ( ~ ( ( SV29 != SV30 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV30 @ SV29 ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(321,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY43 @ SV9 ) @ SV9 )
| ~ ( in @ ( sK6_SY59 @ SV9 ) @ SV9 ) )
| ~ ~ ( in @ ( sK5_SY43 @ SV9 ) @ ( sK6_SY59 @ SV9 ) ) )
= $false )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(322,plain,
! [SV9: $i] :
( ( ( ( sK5_SY43 @ SV9 )
= ( sK6_SY59 @ SV9 ) )
= $false )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(323,plain,
! [SV5: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV5 ) )
= $false )
| ( ( in @ SV5 @ SV27 )
= $true )
| ( ( SV5 = SV27 )
= $true )
| ( ( ordinal @ SV27 )
= $false )
| ( ( ordinal @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(324,plain,
! [SV30: $i,SV9: $i,SV29: $i] :
( ( ( ~ ~ ( ~ ( in @ SV29 @ SV9 )
| ~ ( in @ SV30 @ SV9 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV29 @ SV30 ) )
= $true )
| ( ( ~ ( ( SV29 != SV30 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV30 @ SV29 ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(325,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY43 @ SV9 ) @ SV9 )
| ~ ( in @ ( sK6_SY59 @ SV9 ) @ SV9 ) ) )
= $false )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[321]) ).
thf(326,plain,
! [SV9: $i] :
( ( ( ~ ~ ( in @ ( sK5_SY43 @ SV9 ) @ ( sK6_SY59 @ SV9 ) ) )
= $false )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[321]) ).
thf(327,plain,
! [SV5: $i,SV27: $i] :
( ( ( in @ SV27 @ SV5 )
= $true )
| ( ( in @ SV5 @ SV27 )
= $true )
| ( ( SV5 = SV27 )
= $true )
| ( ( ordinal @ SV27 )
= $false )
| ( ( ordinal @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(328,plain,
! [SV30: $i,SV9: $i,SV29: $i] :
( ( ( ~ ( ~ ( in @ SV29 @ SV9 )
| ~ ( in @ SV30 @ SV9 ) ) )
= $false )
| ( ( ~ ~ ( in @ SV29 @ SV30 ) )
= $true )
| ( ( ~ ( ( SV29 != SV30 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV30 @ SV29 ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(329,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY43 @ SV9 ) @ SV9 )
| ~ ( in @ ( sK6_SY59 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[325]) ).
thf(330,plain,
! [SV9: $i] :
( ( ( ~ ( in @ ( sK5_SY43 @ SV9 ) @ ( sK6_SY59 @ SV9 ) ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(331,plain,
! [SV30: $i,SV9: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ SV9 )
| ~ ( in @ SV30 @ SV9 ) )
= $true )
| ( ( ~ ~ ( in @ SV29 @ SV30 ) )
= $true )
| ( ( ~ ( ( SV29 != SV30 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV30 @ SV29 ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(332,plain,
! [SV9: $i] :
( ( ( ~ ( in @ ( sK5_SY43 @ SV9 ) @ SV9 )
| ~ ( in @ ( sK6_SY59 @ SV9 ) @ SV9 ) )
= $false )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(333,plain,
! [SV9: $i] :
( ( ( in @ ( sK5_SY43 @ SV9 ) @ ( sK6_SY59 @ SV9 ) )
= $false )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(334,plain,
! [SV30: $i,SV9: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ SV9 ) )
= $true )
| ( ( ~ ( in @ SV30 @ SV9 ) )
= $true )
| ( ( ~ ~ ( in @ SV29 @ SV30 ) )
= $true )
| ( ( ~ ( ( SV29 != SV30 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV30 @ SV29 ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(335,plain,
! [SV9: $i] :
( ( ( ~ ( in @ ( sK5_SY43 @ SV9 ) @ SV9 ) )
= $false )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[332]) ).
thf(336,plain,
! [SV9: $i] :
( ( ( ~ ( in @ ( sK6_SY59 @ SV9 ) @ SV9 ) )
= $false )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[332]) ).
thf(337,plain,
! [SV30: $i,SV9: $i,SV29: $i] :
( ( ( in @ SV29 @ SV9 )
= $false )
| ( ( ~ ( in @ SV30 @ SV9 ) )
= $true )
| ( ( ~ ~ ( in @ SV29 @ SV30 ) )
= $true )
| ( ( ~ ( ( SV29 != SV30 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV30 @ SV29 ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(338,plain,
! [SV9: $i] :
( ( ( in @ ( sK5_SY43 @ SV9 ) @ SV9 )
= $true )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(339,plain,
! [SV9: $i] :
( ( ( in @ ( sK6_SY59 @ SV9 ) @ SV9 )
= $true )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[336]) ).
thf(340,plain,
! [SV29: $i,SV9: $i,SV30: $i] :
( ( ( in @ SV30 @ SV9 )
= $false )
| ( ( in @ SV29 @ SV9 )
= $false )
| ( ( ~ ~ ( in @ SV29 @ SV30 ) )
= $true )
| ( ( ~ ( ( SV29 != SV30 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV30 @ SV29 ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(341,plain,
! [SV9: $i,SV30: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ SV30 ) )
= $false )
| ( ( in @ SV29 @ SV9 )
= $false )
| ( ( in @ SV30 @ SV9 )
= $false )
| ( ( ~ ( ( SV29 != SV30 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV30 @ SV29 ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(342,plain,
! [SV9: $i,SV30: $i,SV29: $i] :
( ( ( in @ SV29 @ SV30 )
= $true )
| ( ( in @ SV29 @ SV9 )
= $false )
| ( ( in @ SV30 @ SV9 )
= $false )
| ( ( ~ ( ( SV29 != SV30 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV30 @ SV29 ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(343,plain,
! [SV9: $i,SV30: $i,SV29: $i] :
( ( ( SV29 != SV30 )
= $false )
| ( ( in @ SV30 @ SV9 )
= $false )
| ( ( in @ SV29 @ SV9 )
= $false )
| ( ( in @ SV29 @ SV30 )
= $true )
| ( ( ~ ~ ( in @ SV30 @ SV29 ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(344,plain,
! [SV9: $i,SV30: $i,SV29: $i] :
( ( ( SV29 = SV30 )
= $true )
| ( ( in @ SV30 @ SV9 )
= $false )
| ( ( in @ SV29 @ SV9 )
= $false )
| ( ( in @ SV29 @ SV30 )
= $true )
| ( ( ~ ~ ( in @ SV30 @ SV29 ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(345,plain,
! [SV9: $i,SV29: $i,SV30: $i] :
( ( ( ~ ( in @ SV30 @ SV29 ) )
= $false )
| ( ( in @ SV29 @ SV30 )
= $true )
| ( ( in @ SV29 @ SV9 )
= $false )
| ( ( in @ SV30 @ SV9 )
= $false )
| ( ( SV29 = SV30 )
= $true )
| ( ( epsilon_connected @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(346,plain,
! [SV9: $i,SV29: $i,SV30: $i] :
( ( ( in @ SV30 @ SV29 )
= $true )
| ( ( in @ SV29 @ SV30 )
= $true )
| ( ( in @ SV29 @ SV9 )
= $false )
| ( ( in @ SV30 @ SV9 )
= $false )
| ( ( SV29 = SV30 )
= $true )
| ( ( epsilon_connected @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[345]) ).
thf(347,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[160,346,339,338,333,327,322,310,306,305,300,291,290,288,283,279,277,276,273,272,270,269,268,266,265,255,245,232,229,228,216,214,211,209,208,207,196,193]) ).
thf(348,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[347]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM404+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
% 0.09/0.20 % Computer : n018.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Oct 6 13:14:06 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.12/0.47
% 1.12/0.47 No.of.Axioms: 17
% 1.12/0.47
% 1.12/0.47 Length.of.Defs: 0
% 1.12/0.47
% 1.12/0.47 Contains.Choice.Funs: false
% 1.12/0.47 ........
% 1.12/0.47
% 1.12/0.47 ********************************
% 1.12/0.47 * All subproblems solved! *
% 1.12/0.47 ********************************
% 1.12/0.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:17,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:347,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.12/0.47
% 1.12/0.47 %**** Beginning of derivation protocol ****
% 1.12/0.47 % SZS output start CNFRefutation
% See solution above
% 1.12/0.47
% 1.12/0.47 %**** End of derivation protocol ****
% 1.12/0.47 %**** no. of clauses in derivation: 325 ****
% 1.12/0.47 %**** clause counter: 347 ****
% 1.12/0.47
% 1.12/0.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:17,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:347,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------