%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU323+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:43:58 AM UTC 2026
% Result : Theorem 0.45s 0.30s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 21
% Syntax : Number of formulae : 224 ( 118 unt; 0 typ; 0 def)
% Number of atoms : 1438 ( 402 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 2744 ( 529 ~; 350 |; 46 &;1769 @)
% ( 3 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 6 con; 0-2 aty)
% Number of variables : 356 ( 0 ^; 341 !; 15 ?; 356 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_closed_subset,type,
closed_subset: $i > $i > $o ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_interior,type,
interior: $i > $i > $i ).
thf(tp_one_sorted_str,type,
one_sorted_str: $i > $o ).
thf(tp_open_subset,type,
open_subset: $i > $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SY36,type,
sK5_SY36: $i > $i ).
thf(tp_sK6_SY33,type,
sK6_SY33: $i > $i ).
thf(tp_sK7_SY44,type,
sK7_SY44: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_complement,type,
subset_complement: $i > $i > $i ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(tp_top_str,type,
top_str: $i > $o ).
thf(tp_topological_space,type,
topological_space: $i > $o ).
thf(tp_topstr_closure,type,
topstr_closure: $i > $i > $i ).
thf(1,axiom,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( interior @ A @ B )
= ( subset_complement @ ( the_carrier @ A ) @ ( topstr_closure @ A @ ( subset_complement @ ( the_carrier @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tops_1) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(3,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( open_subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_tops_1) ).
thf(4,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(5,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(6,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(7,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( interior @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tops_1) ).
thf(9,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(10,axiom,
? [A: $i] : ( top_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( open_subset @ B @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( closed_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_tops_1) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( closed_subset @ ( topstr_closure @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_tops_1) ).
thf(13,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( topstr_closure @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(16,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(17,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(19,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( closed_subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_pre_topc) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( closed_subset @ B @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( open_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_tops_1) ).
thf(21,conjecture,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( open_subset @ ( interior @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_tops_1) ).
thf(22,negated_conjecture,
( ( ! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( open_subset @ ( interior @ A @ B ) @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[21]) ).
thf(23,plain,
( ( ! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( open_subset @ ( interior @ A @ B ) @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[22]) ).
thf(24,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( interior @ A @ B )
= ( subset_complement @ ( the_carrier @ A ) @ ( topstr_closure @ A @ ( subset_complement @ ( the_carrier @ A ) @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(26,plain,
( ( ! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( open_subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(27,plain,
$true = $true,
inference(unfold_def,[status(thm)],[4]) ).
thf(28,plain,
$true = $true,
inference(unfold_def,[status(thm)],[5]) ).
thf(29,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(30,plain,
$true = $true,
inference(unfold_def,[status(thm)],[7]) ).
thf(31,plain,
( ( ! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( interior @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(32,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(33,plain,
( ( ? [A: $i] : ( top_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(34,plain,
( ( ! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( open_subset @ B @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( closed_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(35,plain,
( ( ! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( closed_subset @ ( topstr_closure @ A @ B ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(36,plain,
$true = $true,
inference(unfold_def,[status(thm)],[13]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( topstr_closure @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(39,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(40,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(42,plain,
( ( ! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( closed_subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(43,plain,
( ( ! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( closed_subset @ B @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( open_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(44,plain,
( ( ( ( topological_space @ sK1_A )
& ( top_str @ sK1_A ) )
=> ! [SY31: $i] :
( ( element @ SY31 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
=> ( open_subset @ ( interior @ sK1_A @ SY31 ) @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).
thf(45,plain,
( ( topological_space @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[44]) ).
thf(46,plain,
( ( top_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[44]) ).
thf(47,plain,
( ( ! [SY31: $i] :
( ( element @ SY31 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
=> ( open_subset @ ( interior @ sK1_A @ SY31 ) @ sK1_A ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[44]) ).
thf(48,plain,
( ( ~ ! [SY31: $i] :
( ( element @ SY31 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
=> ( open_subset @ ( interior @ sK1_A @ SY31 ) @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[47]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( closed_subset @ B @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( open_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(50,plain,
( ( ! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( closed_subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(51,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(52,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(53,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(54,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(55,plain,
( ( ! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( topstr_closure @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(56,plain,
$true = $true,
inference(copy,[status(thm)],[36]) ).
thf(57,plain,
( ( ! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( closed_subset @ ( topstr_closure @ A @ B ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( open_subset @ B @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( closed_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(59,plain,
( ( ? [A: $i] : ( top_str @ A ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(60,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(61,plain,
( ( ! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( interior @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(62,plain,
$true = $true,
inference(copy,[status(thm)],[30]) ).
thf(63,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(64,plain,
$true = $true,
inference(copy,[status(thm)],[28]) ).
thf(65,plain,
$true = $true,
inference(copy,[status(thm)],[27]) ).
thf(66,plain,
( ( ! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( open_subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(68,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( interior @ A @ B )
= ( subset_complement @ ( the_carrier @ A ) @ ( topstr_closure @ A @ ( subset_complement @ ( the_carrier @ A ) @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(69,plain,
( ( top_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(70,plain,
( ( topological_space @ sK1_A )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(71,plain,
( ( ~ ! [SY31: $i] :
( ( element @ SY31 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
=> ( open_subset @ ( interior @ sK1_A @ SY31 ) @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(72,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( topological_space @ SX0 )
| ~ ( top_str @ SX0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ( open_subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(73,plain,
( ( ~ ! [SX0: $i] :
~ ( one_sorted_str @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(74,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( open_subset @ ( interior @ sK1_A @ SX0 ) @ sK1_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(75,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( topological_space @ SX0 )
| ~ ( top_str @ SX0 ) )
| ~ ( open_subset @ SX1 @ SX0 ) )
| ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) ) )
| ( closed_subset @ ( subset_complement @ ( the_carrier @ SX0 ) @ SX1 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(76,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( top_str @ SX0 )
| ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) ) )
| ( element @ ( interior @ SX0 @ SX1 ) @ ( powerset @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(77,plain,
( ( ~ ! [SX0: $i] :
~ ( top_str @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(78,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( element @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(79,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( top_str @ SX0 )
| ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) ) )
| ( element @ ( topstr_closure @ SX0 @ SX1 ) @ ( powerset @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(80,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)],[67]) ).
thf(81,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( ( subset_complement @ SX0 @ ( subset_complement @ SX0 @ SX1 ) )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(82,plain,
( ( ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ( one_sorted_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(83,plain,
( ( ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ( ( interior @ SX0 @ SX1 )
= ( subset_complement @ ( the_carrier @ SX0 ) @ ( topstr_closure @ SX0 @ ( subset_complement @ ( the_carrier @ SX0 ) @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(84,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ( topological_space @ SX0 )
| ~ ( top_str @ SX0 ) )
| ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) ) )
| ( closed_subset @ ( topstr_closure @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(85,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( element @ ( subset_complement @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(86,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( topological_space @ SX0 )
| ~ ( top_str @ SX0 ) )
| ~ ( closed_subset @ SX1 @ SX0 ) )
| ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) ) )
| ( open_subset @ ( subset_complement @ ( the_carrier @ SX0 ) @ SX1 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(87,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( topological_space @ SX0 )
| ~ ( top_str @ SX0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ( closed_subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(88,plain,
! [SV1: $i] :
( ( ! [SY32: $i] : ( subset @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(89,plain,
! [SV2: $i] :
( ( ~ ~ ( ~ ( topological_space @ SV2 )
| ~ ( top_str @ SV2 ) )
| ~ ! [SY33: $i] :
~ ~ ( ~ ( element @ SY33 @ ( powerset @ ( the_carrier @ SV2 ) ) )
| ~ ( open_subset @ SY33 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(90,plain,
( ( ! [SX0: $i] :
~ ( one_sorted_str @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(91,plain,
( ( ! [SX0: $i] :
( ~ ( element @ SX0 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( open_subset @ ( interior @ sK1_A @ SX0 ) @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(92,plain,
! [SV3: $i] :
( ( ! [SY34: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( topological_space @ SV3 )
| ~ ( top_str @ SV3 ) )
| ~ ( open_subset @ SY34 @ SV3 ) )
| ~ ( element @ SY34 @ ( powerset @ ( the_carrier @ SV3 ) ) ) )
| ( closed_subset @ ( subset_complement @ ( the_carrier @ SV3 ) @ SY34 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(93,plain,
! [SV4: $i] :
( ( ! [SY35: $i] :
( ~ ~ ( ~ ( top_str @ SV4 )
| ~ ( element @ SY35 @ ( powerset @ ( the_carrier @ SV4 ) ) ) )
| ( element @ ( interior @ SV4 @ SY35 ) @ ( powerset @ ( the_carrier @ SV4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(94,plain,
( ( ! [SX0: $i] :
~ ( top_str @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(95,plain,
! [SV5: $i] :
( ( ~ ! [SY36: $i] :
~ ( element @ SY36 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(96,plain,
! [SV6: $i] :
( ( ! [SY37: $i] :
( ~ ~ ( ~ ( top_str @ SV6 )
| ~ ( element @ SY37 @ ( powerset @ ( the_carrier @ SV6 ) ) ) )
| ( element @ ( topstr_closure @ SV6 @ SY37 ) @ ( powerset @ ( the_carrier @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(97,plain,
! [SV7: $i] :
( ( ! [SY38: $i] :
~ ( ~ ( ~ ( element @ SV7 @ ( powerset @ SY38 ) )
| ( subset @ SV7 @ SY38 ) )
| ~ ( ~ ( subset @ SV7 @ SY38 )
| ( element @ SV7 @ ( powerset @ SY38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(98,plain,
! [SV8: $i] :
( ( ! [SY39: $i] :
( ~ ( element @ SY39 @ ( powerset @ SV8 ) )
| ( ( subset_complement @ SV8 @ ( subset_complement @ SV8 @ SY39 ) )
= SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(99,plain,
! [SV9: $i] :
( ( ~ ( top_str @ SV9 )
| ( one_sorted_str @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(100,plain,
! [SV10: $i] :
( ( ~ ( top_str @ SV10 )
| ! [SY40: $i] :
( ~ ( element @ SY40 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( interior @ SV10 @ SY40 )
= ( subset_complement @ ( the_carrier @ SV10 ) @ ( topstr_closure @ SV10 @ ( subset_complement @ ( the_carrier @ SV10 ) @ SY40 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(101,plain,
! [SV11: $i] :
( ( ! [SY41: $i] :
( ~ ~ ( ~ ~ ( ~ ( topological_space @ SV11 )
| ~ ( top_str @ SV11 ) )
| ~ ( element @ SY41 @ ( powerset @ ( the_carrier @ SV11 ) ) ) )
| ( closed_subset @ ( topstr_closure @ SV11 @ SY41 ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(102,plain,
! [SV12: $i] :
( ( ! [SY42: $i] :
( ~ ( element @ SY42 @ ( powerset @ SV12 ) )
| ( element @ ( subset_complement @ SV12 @ SY42 ) @ ( powerset @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(103,plain,
! [SV13: $i] :
( ( ! [SY43: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( topological_space @ SV13 )
| ~ ( top_str @ SV13 ) )
| ~ ( closed_subset @ SY43 @ SV13 ) )
| ~ ( element @ SY43 @ ( powerset @ ( the_carrier @ SV13 ) ) ) )
| ( open_subset @ ( subset_complement @ ( the_carrier @ SV13 ) @ SY43 ) @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(104,plain,
! [SV14: $i] :
( ( ~ ~ ( ~ ( topological_space @ SV14 )
| ~ ( top_str @ SV14 ) )
| ~ ! [SY44: $i] :
~ ~ ( ~ ( element @ SY44 @ ( powerset @ ( the_carrier @ SV14 ) ) )
| ~ ( closed_subset @ SY44 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(105,plain,
! [SV1: $i] :
( ( subset @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(106,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ( topological_space @ SV2 )
| ~ ( top_str @ SV2 ) ) )
= $true )
| ( ( ~ ! [SY33: $i] :
~ ~ ( ~ ( element @ SY33 @ ( powerset @ ( the_carrier @ SV2 ) ) )
| ~ ( open_subset @ SY33 @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(107,plain,
( ( ~ ( one_sorted_str @ sK2_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[90]) ).
thf(108,plain,
( ( ~ ( element @ sK3_SX0 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( open_subset @ ( interior @ sK1_A @ sK3_SX0 ) @ sK1_A ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[91]) ).
thf(109,plain,
! [SV16: $i,SV3: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( topological_space @ SV3 )
| ~ ( top_str @ SV3 ) )
| ~ ( open_subset @ SV16 @ SV3 ) )
| ~ ( element @ SV16 @ ( powerset @ ( the_carrier @ SV3 ) ) ) )
| ( closed_subset @ ( subset_complement @ ( the_carrier @ SV3 ) @ SV16 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(110,plain,
! [SV17: $i,SV4: $i] :
( ( ~ ~ ( ~ ( top_str @ SV4 )
| ~ ( element @ SV17 @ ( powerset @ ( the_carrier @ SV4 ) ) ) )
| ( element @ ( interior @ SV4 @ SV17 ) @ ( powerset @ ( the_carrier @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(111,plain,
( ( ~ ( top_str @ sK4_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[94]) ).
thf(112,plain,
! [SV5: $i] :
( ( ! [SY36: $i] :
~ ( element @ SY36 @ SV5 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(113,plain,
! [SV18: $i,SV6: $i] :
( ( ~ ~ ( ~ ( top_str @ SV6 )
| ~ ( element @ SV18 @ ( powerset @ ( the_carrier @ SV6 ) ) ) )
| ( element @ ( topstr_closure @ SV6 @ SV18 ) @ ( powerset @ ( the_carrier @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(114,plain,
! [SV19: $i,SV7: $i] :
( ( ~ ( ~ ( ~ ( element @ SV7 @ ( powerset @ SV19 ) )
| ( subset @ SV7 @ SV19 ) )
| ~ ( ~ ( subset @ SV7 @ SV19 )
| ( element @ SV7 @ ( powerset @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(115,plain,
! [SV8: $i,SV20: $i] :
( ( ~ ( element @ SV20 @ ( powerset @ SV8 ) )
| ( ( subset_complement @ SV8 @ ( subset_complement @ SV8 @ SV20 ) )
= SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(116,plain,
! [SV9: $i] :
( ( ( ~ ( top_str @ SV9 ) )
= $true )
| ( ( one_sorted_str @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(117,plain,
! [SV10: $i] :
( ( ( ~ ( top_str @ SV10 ) )
= $true )
| ( ( ! [SY40: $i] :
( ~ ( element @ SY40 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( interior @ SV10 @ SY40 )
= ( subset_complement @ ( the_carrier @ SV10 ) @ ( topstr_closure @ SV10 @ ( subset_complement @ ( the_carrier @ SV10 ) @ SY40 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(118,plain,
! [SV21: $i,SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( topological_space @ SV11 )
| ~ ( top_str @ SV11 ) )
| ~ ( element @ SV21 @ ( powerset @ ( the_carrier @ SV11 ) ) ) )
| ( closed_subset @ ( topstr_closure @ SV11 @ SV21 ) @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(119,plain,
! [SV12: $i,SV22: $i] :
( ( ~ ( element @ SV22 @ ( powerset @ SV12 ) )
| ( element @ ( subset_complement @ SV12 @ SV22 ) @ ( powerset @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(120,plain,
! [SV23: $i,SV13: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( topological_space @ SV13 )
| ~ ( top_str @ SV13 ) )
| ~ ( closed_subset @ SV23 @ SV13 ) )
| ~ ( element @ SV23 @ ( powerset @ ( the_carrier @ SV13 ) ) ) )
| ( open_subset @ ( subset_complement @ ( the_carrier @ SV13 ) @ SV23 ) @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(121,plain,
! [SV14: $i] :
( ( ( ~ ~ ( ~ ( topological_space @ SV14 )
| ~ ( top_str @ SV14 ) ) )
= $true )
| ( ( ~ ! [SY44: $i] :
~ ~ ( ~ ( element @ SY44 @ ( powerset @ ( the_carrier @ SV14 ) ) )
| ~ ( closed_subset @ SY44 @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(122,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ( topological_space @ SV2 )
| ~ ( top_str @ SV2 ) ) )
= $false )
| ( ( ~ ! [SY33: $i] :
~ ~ ( ~ ( element @ SY33 @ ( powerset @ ( the_carrier @ SV2 ) ) )
| ~ ( open_subset @ SY33 @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(123,plain,
( ( one_sorted_str @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(124,plain,
( ( ~ ( element @ sK3_SX0 @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(125,plain,
( ( open_subset @ ( interior @ sK1_A @ sK3_SX0 ) @ sK1_A )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(126,plain,
! [SV16: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( topological_space @ SV3 )
| ~ ( top_str @ SV3 ) )
| ~ ( open_subset @ SV16 @ SV3 ) )
| ~ ( element @ SV16 @ ( powerset @ ( the_carrier @ SV3 ) ) ) ) )
= $true )
| ( ( closed_subset @ ( subset_complement @ ( the_carrier @ SV3 ) @ SV16 ) @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(127,plain,
! [SV17: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( top_str @ SV4 )
| ~ ( element @ SV17 @ ( powerset @ ( the_carrier @ SV4 ) ) ) ) )
= $true )
| ( ( element @ ( interior @ SV4 @ SV17 ) @ ( powerset @ ( the_carrier @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(128,plain,
( ( top_str @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(129,plain,
! [SV5: $i] :
( ( ~ ( element @ ( sK5_SY36 @ SV5 ) @ SV5 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[112]) ).
thf(130,plain,
! [SV18: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( top_str @ SV6 )
| ~ ( element @ SV18 @ ( powerset @ ( the_carrier @ SV6 ) ) ) ) )
= $true )
| ( ( element @ ( topstr_closure @ SV6 @ SV18 ) @ ( powerset @ ( the_carrier @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(131,plain,
! [SV19: $i,SV7: $i] :
( ( ~ ( ~ ( element @ SV7 @ ( powerset @ SV19 ) )
| ( subset @ SV7 @ SV19 ) )
| ~ ( ~ ( subset @ SV7 @ SV19 )
| ( element @ SV7 @ ( powerset @ SV19 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(132,plain,
! [SV8: $i,SV20: $i] :
( ( ( ~ ( element @ SV20 @ ( powerset @ SV8 ) ) )
= $true )
| ( ( ( subset_complement @ SV8 @ ( subset_complement @ SV8 @ SV20 ) )
= SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(133,plain,
! [SV9: $i] :
( ( ( top_str @ SV9 )
= $false )
| ( ( one_sorted_str @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(134,plain,
! [SV10: $i] :
( ( ( top_str @ SV10 )
= $false )
| ( ( ! [SY40: $i] :
( ~ ( element @ SY40 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( interior @ SV10 @ SY40 )
= ( subset_complement @ ( the_carrier @ SV10 ) @ ( topstr_closure @ SV10 @ ( subset_complement @ ( the_carrier @ SV10 ) @ SY40 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(135,plain,
! [SV21: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( topological_space @ SV11 )
| ~ ( top_str @ SV11 ) )
| ~ ( element @ SV21 @ ( powerset @ ( the_carrier @ SV11 ) ) ) ) )
= $true )
| ( ( closed_subset @ ( topstr_closure @ SV11 @ SV21 ) @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(136,plain,
! [SV12: $i,SV22: $i] :
( ( ( ~ ( element @ SV22 @ ( powerset @ SV12 ) ) )
= $true )
| ( ( element @ ( subset_complement @ SV12 @ SV22 ) @ ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(137,plain,
! [SV23: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( topological_space @ SV13 )
| ~ ( top_str @ SV13 ) )
| ~ ( closed_subset @ SV23 @ SV13 ) )
| ~ ( element @ SV23 @ ( powerset @ ( the_carrier @ SV13 ) ) ) ) )
= $true )
| ( ( open_subset @ ( subset_complement @ ( the_carrier @ SV13 ) @ SV23 ) @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(138,plain,
! [SV14: $i] :
( ( ( ~ ( ~ ( topological_space @ SV14 )
| ~ ( top_str @ SV14 ) ) )
= $false )
| ( ( ~ ! [SY44: $i] :
~ ~ ( ~ ( element @ SY44 @ ( powerset @ ( the_carrier @ SV14 ) ) )
| ~ ( closed_subset @ SY44 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(139,plain,
! [SV2: $i] :
( ( ( ~ ( topological_space @ SV2 )
| ~ ( top_str @ SV2 ) )
= $true )
| ( ( ~ ! [SY33: $i] :
~ ~ ( ~ ( element @ SY33 @ ( powerset @ ( the_carrier @ SV2 ) ) )
| ~ ( open_subset @ SY33 @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(140,plain,
( ( element @ sK3_SX0 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(141,plain,
! [SV16: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( topological_space @ SV3 )
| ~ ( top_str @ SV3 ) )
| ~ ( open_subset @ SV16 @ SV3 ) )
| ~ ( element @ SV16 @ ( powerset @ ( the_carrier @ SV3 ) ) ) ) )
= $false )
| ( ( closed_subset @ ( subset_complement @ ( the_carrier @ SV3 ) @ SV16 ) @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(142,plain,
! [SV17: $i,SV4: $i] :
( ( ( ~ ( ~ ( top_str @ SV4 )
| ~ ( element @ SV17 @ ( powerset @ ( the_carrier @ SV4 ) ) ) ) )
= $false )
| ( ( element @ ( interior @ SV4 @ SV17 ) @ ( powerset @ ( the_carrier @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(143,plain,
! [SV5: $i] :
( ( element @ ( sK5_SY36 @ SV5 ) @ SV5 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(144,plain,
! [SV18: $i,SV6: $i] :
( ( ( ~ ( ~ ( top_str @ SV6 )
| ~ ( element @ SV18 @ ( powerset @ ( the_carrier @ SV6 ) ) ) ) )
= $false )
| ( ( element @ ( topstr_closure @ SV6 @ SV18 ) @ ( powerset @ ( the_carrier @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(145,plain,
! [SV19: $i,SV7: $i] :
( ( ~ ( ~ ( element @ SV7 @ ( powerset @ SV19 ) )
| ( subset @ SV7 @ SV19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(146,plain,
! [SV19: $i,SV7: $i] :
( ( ~ ( ~ ( subset @ SV7 @ SV19 )
| ( element @ SV7 @ ( powerset @ SV19 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(147,plain,
! [SV8: $i,SV20: $i] :
( ( ( element @ SV20 @ ( powerset @ SV8 ) )
= $false )
| ( ( ( subset_complement @ SV8 @ ( subset_complement @ SV8 @ SV20 ) )
= SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(148,plain,
! [SV10: $i,SV24: $i] :
( ( ( ~ ( element @ SV24 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( interior @ SV10 @ SV24 )
= ( subset_complement @ ( the_carrier @ SV10 ) @ ( topstr_closure @ SV10 @ ( subset_complement @ ( the_carrier @ SV10 ) @ SV24 ) ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(149,plain,
! [SV21: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( ~ ( topological_space @ SV11 )
| ~ ( top_str @ SV11 ) )
| ~ ( element @ SV21 @ ( powerset @ ( the_carrier @ SV11 ) ) ) ) )
= $false )
| ( ( closed_subset @ ( topstr_closure @ SV11 @ SV21 ) @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(150,plain,
! [SV12: $i,SV22: $i] :
( ( ( element @ SV22 @ ( powerset @ SV12 ) )
= $false )
| ( ( element @ ( subset_complement @ SV12 @ SV22 ) @ ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(151,plain,
! [SV23: $i,SV13: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( topological_space @ SV13 )
| ~ ( top_str @ SV13 ) )
| ~ ( closed_subset @ SV23 @ SV13 ) )
| ~ ( element @ SV23 @ ( powerset @ ( the_carrier @ SV13 ) ) ) ) )
= $false )
| ( ( open_subset @ ( subset_complement @ ( the_carrier @ SV13 ) @ SV23 ) @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(152,plain,
! [SV14: $i] :
( ( ( ~ ( topological_space @ SV14 )
| ~ ( top_str @ SV14 ) )
= $true )
| ( ( ~ ! [SY44: $i] :
~ ~ ( ~ ( element @ SY44 @ ( powerset @ ( the_carrier @ SV14 ) ) )
| ~ ( closed_subset @ SY44 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(153,plain,
! [SV2: $i] :
( ( ( ~ ( topological_space @ SV2 ) )
= $true )
| ( ( ~ ( top_str @ SV2 ) )
= $true )
| ( ( ~ ! [SY33: $i] :
~ ~ ( ~ ( element @ SY33 @ ( powerset @ ( the_carrier @ SV2 ) ) )
| ~ ( open_subset @ SY33 @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(154,plain,
! [SV16: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( topological_space @ SV3 )
| ~ ( top_str @ SV3 ) )
| ~ ( open_subset @ SV16 @ SV3 ) )
| ~ ( element @ SV16 @ ( powerset @ ( the_carrier @ SV3 ) ) ) )
= $true )
| ( ( closed_subset @ ( subset_complement @ ( the_carrier @ SV3 ) @ SV16 ) @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(155,plain,
! [SV17: $i,SV4: $i] :
( ( ( ~ ( top_str @ SV4 )
| ~ ( element @ SV17 @ ( powerset @ ( the_carrier @ SV4 ) ) ) )
= $true )
| ( ( element @ ( interior @ SV4 @ SV17 ) @ ( powerset @ ( the_carrier @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(156,plain,
! [SV18: $i,SV6: $i] :
( ( ( ~ ( top_str @ SV6 )
| ~ ( element @ SV18 @ ( powerset @ ( the_carrier @ SV6 ) ) ) )
= $true )
| ( ( element @ ( topstr_closure @ SV6 @ SV18 ) @ ( powerset @ ( the_carrier @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(157,plain,
! [SV19: $i,SV7: $i] :
( ( ~ ( element @ SV7 @ ( powerset @ SV19 ) )
| ( subset @ SV7 @ SV19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(158,plain,
! [SV19: $i,SV7: $i] :
( ( ~ ( subset @ SV7 @ SV19 )
| ( element @ SV7 @ ( powerset @ SV19 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(159,plain,
! [SV10: $i,SV24: $i] :
( ( ( ~ ( element @ SV24 @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $true )
| ( ( ( interior @ SV10 @ SV24 )
= ( subset_complement @ ( the_carrier @ SV10 ) @ ( topstr_closure @ SV10 @ ( subset_complement @ ( the_carrier @ SV10 ) @ SV24 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(160,plain,
! [SV21: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( topological_space @ SV11 )
| ~ ( top_str @ SV11 ) )
| ~ ( element @ SV21 @ ( powerset @ ( the_carrier @ SV11 ) ) ) )
= $true )
| ( ( closed_subset @ ( topstr_closure @ SV11 @ SV21 ) @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(161,plain,
! [SV23: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( topological_space @ SV13 )
| ~ ( top_str @ SV13 ) )
| ~ ( closed_subset @ SV23 @ SV13 ) )
| ~ ( element @ SV23 @ ( powerset @ ( the_carrier @ SV13 ) ) ) )
= $true )
| ( ( open_subset @ ( subset_complement @ ( the_carrier @ SV13 ) @ SV23 ) @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(162,plain,
! [SV14: $i] :
( ( ( ~ ( topological_space @ SV14 ) )
= $true )
| ( ( ~ ( top_str @ SV14 ) )
= $true )
| ( ( ~ ! [SY44: $i] :
~ ~ ( ~ ( element @ SY44 @ ( powerset @ ( the_carrier @ SV14 ) ) )
| ~ ( closed_subset @ SY44 @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(163,plain,
! [SV2: $i] :
( ( ( topological_space @ SV2 )
= $false )
| ( ( ~ ( top_str @ SV2 ) )
= $true )
| ( ( ~ ! [SY33: $i] :
~ ~ ( ~ ( element @ SY33 @ ( powerset @ ( the_carrier @ SV2 ) ) )
| ~ ( open_subset @ SY33 @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(164,plain,
! [SV16: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( topological_space @ SV3 )
| ~ ( top_str @ SV3 ) )
| ~ ( open_subset @ SV16 @ SV3 ) ) )
= $true )
| ( ( ~ ( element @ SV16 @ ( powerset @ ( the_carrier @ SV3 ) ) ) )
= $true )
| ( ( closed_subset @ ( subset_complement @ ( the_carrier @ SV3 ) @ SV16 ) @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(165,plain,
! [SV17: $i,SV4: $i] :
( ( ( ~ ( top_str @ SV4 ) )
= $true )
| ( ( ~ ( element @ SV17 @ ( powerset @ ( the_carrier @ SV4 ) ) ) )
= $true )
| ( ( element @ ( interior @ SV4 @ SV17 ) @ ( powerset @ ( the_carrier @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(166,plain,
! [SV18: $i,SV6: $i] :
( ( ( ~ ( top_str @ SV6 ) )
= $true )
| ( ( ~ ( element @ SV18 @ ( powerset @ ( the_carrier @ SV6 ) ) ) )
= $true )
| ( ( element @ ( topstr_closure @ SV6 @ SV18 ) @ ( powerset @ ( the_carrier @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(167,plain,
! [SV19: $i,SV7: $i] :
( ( ( ~ ( element @ SV7 @ ( powerset @ SV19 ) ) )
= $true )
| ( ( subset @ SV7 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(168,plain,
! [SV19: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV19 ) )
= $true )
| ( ( element @ SV7 @ ( powerset @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(169,plain,
! [SV10: $i,SV24: $i] :
( ( ( element @ SV24 @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( ( interior @ SV10 @ SV24 )
= ( subset_complement @ ( the_carrier @ SV10 ) @ ( topstr_closure @ SV10 @ ( subset_complement @ ( the_carrier @ SV10 ) @ SV24 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(170,plain,
! [SV21: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( topological_space @ SV11 )
| ~ ( top_str @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV21 @ ( powerset @ ( the_carrier @ SV11 ) ) ) )
= $true )
| ( ( closed_subset @ ( topstr_closure @ SV11 @ SV21 ) @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(171,plain,
! [SV23: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( topological_space @ SV13 )
| ~ ( top_str @ SV13 ) )
| ~ ( closed_subset @ SV23 @ SV13 ) ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( powerset @ ( the_carrier @ SV13 ) ) ) )
= $true )
| ( ( open_subset @ ( subset_complement @ ( the_carrier @ SV13 ) @ SV23 ) @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(172,plain,
! [SV14: $i] :
( ( ( topological_space @ SV14 )
= $false )
| ( ( ~ ( top_str @ SV14 ) )
= $true )
| ( ( ~ ! [SY44: $i] :
~ ~ ( ~ ( element @ SY44 @ ( powerset @ ( the_carrier @ SV14 ) ) )
| ~ ( closed_subset @ SY44 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(173,plain,
! [SV2: $i] :
( ( ( top_str @ SV2 )
= $false )
| ( ( topological_space @ SV2 )
= $false )
| ( ( ~ ! [SY33: $i] :
~ ~ ( ~ ( element @ SY33 @ ( powerset @ ( the_carrier @ SV2 ) ) )
| ~ ( open_subset @ SY33 @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(174,plain,
! [SV16: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ( topological_space @ SV3 )
| ~ ( top_str @ SV3 ) )
| ~ ( open_subset @ SV16 @ SV3 ) ) )
= $false )
| ( ( ~ ( element @ SV16 @ ( powerset @ ( the_carrier @ SV3 ) ) ) )
= $true )
| ( ( closed_subset @ ( subset_complement @ ( the_carrier @ SV3 ) @ SV16 ) @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(175,plain,
! [SV17: $i,SV4: $i] :
( ( ( top_str @ SV4 )
= $false )
| ( ( ~ ( element @ SV17 @ ( powerset @ ( the_carrier @ SV4 ) ) ) )
= $true )
| ( ( element @ ( interior @ SV4 @ SV17 ) @ ( powerset @ ( the_carrier @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(176,plain,
! [SV18: $i,SV6: $i] :
( ( ( top_str @ SV6 )
= $false )
| ( ( ~ ( element @ SV18 @ ( powerset @ ( the_carrier @ SV6 ) ) ) )
= $true )
| ( ( element @ ( topstr_closure @ SV6 @ SV18 ) @ ( powerset @ ( the_carrier @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(177,plain,
! [SV19: $i,SV7: $i] :
( ( ( element @ SV7 @ ( powerset @ SV19 ) )
= $false )
| ( ( subset @ SV7 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(178,plain,
! [SV19: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV19 )
= $false )
| ( ( element @ SV7 @ ( powerset @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(179,plain,
! [SV21: $i,SV11: $i] :
( ( ( ~ ( ~ ( topological_space @ SV11 )
| ~ ( top_str @ SV11 ) ) )
= $false )
| ( ( ~ ( element @ SV21 @ ( powerset @ ( the_carrier @ SV11 ) ) ) )
= $true )
| ( ( closed_subset @ ( topstr_closure @ SV11 @ SV21 ) @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(180,plain,
! [SV23: $i,SV13: $i] :
( ( ( ~ ( ~ ~ ( ~ ( topological_space @ SV13 )
| ~ ( top_str @ SV13 ) )
| ~ ( closed_subset @ SV23 @ SV13 ) ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( powerset @ ( the_carrier @ SV13 ) ) ) )
= $true )
| ( ( open_subset @ ( subset_complement @ ( the_carrier @ SV13 ) @ SV23 ) @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(181,plain,
! [SV14: $i] :
( ( ( top_str @ SV14 )
= $false )
| ( ( topological_space @ SV14 )
= $false )
| ( ( ~ ! [SY44: $i] :
~ ~ ( ~ ( element @ SY44 @ ( powerset @ ( the_carrier @ SV14 ) ) )
| ~ ( closed_subset @ SY44 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(182,plain,
! [SV2: $i] :
( ( ( ! [SY33: $i] :
~ ~ ( ~ ( element @ SY33 @ ( powerset @ ( the_carrier @ SV2 ) ) )
| ~ ( open_subset @ SY33 @ SV2 ) ) )
= $false )
| ( ( topological_space @ SV2 )
= $false )
| ( ( top_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(183,plain,
! [SV16: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( topological_space @ SV3 )
| ~ ( top_str @ SV3 ) )
| ~ ( open_subset @ SV16 @ SV3 ) )
= $true )
| ( ( ~ ( element @ SV16 @ ( powerset @ ( the_carrier @ SV3 ) ) ) )
= $true )
| ( ( closed_subset @ ( subset_complement @ ( the_carrier @ SV3 ) @ SV16 ) @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(184,plain,
! [SV4: $i,SV17: $i] :
( ( ( element @ SV17 @ ( powerset @ ( the_carrier @ SV4 ) ) )
= $false )
| ( ( top_str @ SV4 )
= $false )
| ( ( element @ ( interior @ SV4 @ SV17 ) @ ( powerset @ ( the_carrier @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(185,plain,
! [SV6: $i,SV18: $i] :
( ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV6 ) ) )
= $false )
| ( ( top_str @ SV6 )
= $false )
| ( ( element @ ( topstr_closure @ SV6 @ SV18 ) @ ( powerset @ ( the_carrier @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(186,plain,
! [SV21: $i,SV11: $i] :
( ( ( ~ ( topological_space @ SV11 )
| ~ ( top_str @ SV11 ) )
= $true )
| ( ( ~ ( element @ SV21 @ ( powerset @ ( the_carrier @ SV11 ) ) ) )
= $true )
| ( ( closed_subset @ ( topstr_closure @ SV11 @ SV21 ) @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(187,plain,
! [SV23: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( topological_space @ SV13 )
| ~ ( top_str @ SV13 ) )
| ~ ( closed_subset @ SV23 @ SV13 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( powerset @ ( the_carrier @ SV13 ) ) ) )
= $true )
| ( ( open_subset @ ( subset_complement @ ( the_carrier @ SV13 ) @ SV23 ) @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(188,plain,
! [SV14: $i] :
( ( ( ! [SY44: $i] :
~ ~ ( ~ ( element @ SY44 @ ( powerset @ ( the_carrier @ SV14 ) ) )
| ~ ( closed_subset @ SY44 @ SV14 ) ) )
= $false )
| ( ( topological_space @ SV14 )
= $false )
| ( ( top_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(189,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK6_SY33 @ SV2 ) @ ( powerset @ ( the_carrier @ SV2 ) ) )
| ~ ( open_subset @ ( sK6_SY33 @ SV2 ) @ SV2 ) ) )
= $false )
| ( ( topological_space @ SV2 )
= $false )
| ( ( top_str @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[182]) ).
thf(190,plain,
! [SV16: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( topological_space @ SV3 )
| ~ ( top_str @ SV3 ) ) )
= $true )
| ( ( ~ ( open_subset @ SV16 @ SV3 ) )
= $true )
| ( ( ~ ( element @ SV16 @ ( powerset @ ( the_carrier @ SV3 ) ) ) )
= $true )
| ( ( closed_subset @ ( subset_complement @ ( the_carrier @ SV3 ) @ SV16 ) @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(191,plain,
! [SV21: $i,SV11: $i] :
( ( ( ~ ( topological_space @ SV11 ) )
= $true )
| ( ( ~ ( top_str @ SV11 ) )
= $true )
| ( ( ~ ( element @ SV21 @ ( powerset @ ( the_carrier @ SV11 ) ) ) )
= $true )
| ( ( closed_subset @ ( topstr_closure @ SV11 @ SV21 ) @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(192,plain,
! [SV23: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( topological_space @ SV13 )
| ~ ( top_str @ SV13 ) ) )
= $true )
| ( ( ~ ( closed_subset @ SV23 @ SV13 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( powerset @ ( the_carrier @ SV13 ) ) ) )
= $true )
| ( ( open_subset @ ( subset_complement @ ( the_carrier @ SV13 ) @ SV23 ) @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(193,plain,
! [SV14: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK7_SY44 @ SV14 ) @ ( powerset @ ( the_carrier @ SV14 ) ) )
| ~ ( closed_subset @ ( sK7_SY44 @ SV14 ) @ SV14 ) ) )
= $false )
| ( ( topological_space @ SV14 )
= $false )
| ( ( top_str @ SV14 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[188]) ).
thf(194,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ( element @ ( sK6_SY33 @ SV2 ) @ ( powerset @ ( the_carrier @ SV2 ) ) )
| ~ ( open_subset @ ( sK6_SY33 @ SV2 ) @ SV2 ) ) )
= $true )
| ( ( topological_space @ SV2 )
= $false )
| ( ( top_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(195,plain,
! [SV16: $i,SV3: $i] :
( ( ( ~ ( ~ ( topological_space @ SV3 )
| ~ ( top_str @ SV3 ) ) )
= $false )
| ( ( ~ ( open_subset @ SV16 @ SV3 ) )
= $true )
| ( ( ~ ( element @ SV16 @ ( powerset @ ( the_carrier @ SV3 ) ) ) )
= $true )
| ( ( closed_subset @ ( subset_complement @ ( the_carrier @ SV3 ) @ SV16 ) @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(196,plain,
! [SV21: $i,SV11: $i] :
( ( ( topological_space @ SV11 )
= $false )
| ( ( ~ ( top_str @ SV11 ) )
= $true )
| ( ( ~ ( element @ SV21 @ ( powerset @ ( the_carrier @ SV11 ) ) ) )
= $true )
| ( ( closed_subset @ ( topstr_closure @ SV11 @ SV21 ) @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(197,plain,
! [SV23: $i,SV13: $i] :
( ( ( ~ ( ~ ( topological_space @ SV13 )
| ~ ( top_str @ SV13 ) ) )
= $false )
| ( ( ~ ( closed_subset @ SV23 @ SV13 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( powerset @ ( the_carrier @ SV13 ) ) ) )
= $true )
| ( ( open_subset @ ( subset_complement @ ( the_carrier @ SV13 ) @ SV23 ) @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(198,plain,
! [SV14: $i] :
( ( ( ~ ( ~ ( element @ ( sK7_SY44 @ SV14 ) @ ( powerset @ ( the_carrier @ SV14 ) ) )
| ~ ( closed_subset @ ( sK7_SY44 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( top_str @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(199,plain,
! [SV2: $i] :
( ( ( ~ ( element @ ( sK6_SY33 @ SV2 ) @ ( powerset @ ( the_carrier @ SV2 ) ) )
| ~ ( open_subset @ ( sK6_SY33 @ SV2 ) @ SV2 ) )
= $false )
| ( ( topological_space @ SV2 )
= $false )
| ( ( top_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(200,plain,
! [SV16: $i,SV3: $i] :
( ( ( ~ ( topological_space @ SV3 )
| ~ ( top_str @ SV3 ) )
= $true )
| ( ( ~ ( open_subset @ SV16 @ SV3 ) )
= $true )
| ( ( ~ ( element @ SV16 @ ( powerset @ ( the_carrier @ SV3 ) ) ) )
= $true )
| ( ( closed_subset @ ( subset_complement @ ( the_carrier @ SV3 ) @ SV16 ) @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(201,plain,
! [SV21: $i,SV11: $i] :
( ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( ~ ( element @ SV21 @ ( powerset @ ( the_carrier @ SV11 ) ) ) )
= $true )
| ( ( closed_subset @ ( topstr_closure @ SV11 @ SV21 ) @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(202,plain,
! [SV23: $i,SV13: $i] :
( ( ( ~ ( topological_space @ SV13 )
| ~ ( top_str @ SV13 ) )
= $true )
| ( ( ~ ( closed_subset @ SV23 @ SV13 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( powerset @ ( the_carrier @ SV13 ) ) ) )
= $true )
| ( ( open_subset @ ( subset_complement @ ( the_carrier @ SV13 ) @ SV23 ) @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(203,plain,
! [SV14: $i] :
( ( ( ~ ( element @ ( sK7_SY44 @ SV14 ) @ ( powerset @ ( the_carrier @ SV14 ) ) )
| ~ ( closed_subset @ ( sK7_SY44 @ SV14 ) @ SV14 ) )
= $false )
| ( ( topological_space @ SV14 )
= $false )
| ( ( top_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(204,plain,
! [SV2: $i] :
( ( ( ~ ( element @ ( sK6_SY33 @ SV2 ) @ ( powerset @ ( the_carrier @ SV2 ) ) ) )
= $false )
| ( ( topological_space @ SV2 )
= $false )
| ( ( top_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(205,plain,
! [SV2: $i] :
( ( ( ~ ( open_subset @ ( sK6_SY33 @ SV2 ) @ SV2 ) )
= $false )
| ( ( topological_space @ SV2 )
= $false )
| ( ( top_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(206,plain,
! [SV16: $i,SV3: $i] :
( ( ( ~ ( topological_space @ SV3 ) )
= $true )
| ( ( ~ ( top_str @ SV3 ) )
= $true )
| ( ( ~ ( open_subset @ SV16 @ SV3 ) )
= $true )
| ( ( ~ ( element @ SV16 @ ( powerset @ ( the_carrier @ SV3 ) ) ) )
= $true )
| ( ( closed_subset @ ( subset_complement @ ( the_carrier @ SV3 ) @ SV16 ) @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(207,plain,
! [SV11: $i,SV21: $i] :
( ( ( element @ SV21 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( closed_subset @ ( topstr_closure @ SV11 @ SV21 ) @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(208,plain,
! [SV23: $i,SV13: $i] :
( ( ( ~ ( topological_space @ SV13 ) )
= $true )
| ( ( ~ ( top_str @ SV13 ) )
= $true )
| ( ( ~ ( closed_subset @ SV23 @ SV13 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( powerset @ ( the_carrier @ SV13 ) ) ) )
= $true )
| ( ( open_subset @ ( subset_complement @ ( the_carrier @ SV13 ) @ SV23 ) @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(209,plain,
! [SV14: $i] :
( ( ( ~ ( element @ ( sK7_SY44 @ SV14 ) @ ( powerset @ ( the_carrier @ SV14 ) ) ) )
= $false )
| ( ( topological_space @ SV14 )
= $false )
| ( ( top_str @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(210,plain,
! [SV14: $i] :
( ( ( ~ ( closed_subset @ ( sK7_SY44 @ SV14 ) @ SV14 ) )
= $false )
| ( ( topological_space @ SV14 )
= $false )
| ( ( top_str @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(211,plain,
! [SV2: $i] :
( ( ( element @ ( sK6_SY33 @ SV2 ) @ ( powerset @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( topological_space @ SV2 )
= $false )
| ( ( top_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(212,plain,
! [SV2: $i] :
( ( ( open_subset @ ( sK6_SY33 @ SV2 ) @ SV2 )
= $true )
| ( ( topological_space @ SV2 )
= $false )
| ( ( top_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(213,plain,
! [SV16: $i,SV3: $i] :
( ( ( topological_space @ SV3 )
= $false )
| ( ( ~ ( top_str @ SV3 ) )
= $true )
| ( ( ~ ( open_subset @ SV16 @ SV3 ) )
= $true )
| ( ( ~ ( element @ SV16 @ ( powerset @ ( the_carrier @ SV3 ) ) ) )
= $true )
| ( ( closed_subset @ ( subset_complement @ ( the_carrier @ SV3 ) @ SV16 ) @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(214,plain,
! [SV23: $i,SV13: $i] :
( ( ( topological_space @ SV13 )
= $false )
| ( ( ~ ( top_str @ SV13 ) )
= $true )
| ( ( ~ ( closed_subset @ SV23 @ SV13 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( powerset @ ( the_carrier @ SV13 ) ) ) )
= $true )
| ( ( open_subset @ ( subset_complement @ ( the_carrier @ SV13 ) @ SV23 ) @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(215,plain,
! [SV14: $i] :
( ( ( element @ ( sK7_SY44 @ SV14 ) @ ( powerset @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( top_str @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(216,plain,
! [SV14: $i] :
( ( ( closed_subset @ ( sK7_SY44 @ SV14 ) @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( top_str @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(217,plain,
! [SV16: $i,SV3: $i] :
( ( ( top_str @ SV3 )
= $false )
| ( ( topological_space @ SV3 )
= $false )
| ( ( ~ ( open_subset @ SV16 @ SV3 ) )
= $true )
| ( ( ~ ( element @ SV16 @ ( powerset @ ( the_carrier @ SV3 ) ) ) )
= $true )
| ( ( closed_subset @ ( subset_complement @ ( the_carrier @ SV3 ) @ SV16 ) @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(218,plain,
! [SV23: $i,SV13: $i] :
( ( ( top_str @ SV13 )
= $false )
| ( ( topological_space @ SV13 )
= $false )
| ( ( ~ ( closed_subset @ SV23 @ SV13 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( powerset @ ( the_carrier @ SV13 ) ) ) )
= $true )
| ( ( open_subset @ ( subset_complement @ ( the_carrier @ SV13 ) @ SV23 ) @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(219,plain,
! [SV3: $i,SV16: $i] :
( ( ( open_subset @ SV16 @ SV3 )
= $false )
| ( ( topological_space @ SV3 )
= $false )
| ( ( top_str @ SV3 )
= $false )
| ( ( ~ ( element @ SV16 @ ( powerset @ ( the_carrier @ SV3 ) ) ) )
= $true )
| ( ( closed_subset @ ( subset_complement @ ( the_carrier @ SV3 ) @ SV16 ) @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(220,plain,
! [SV13: $i,SV23: $i] :
( ( ( closed_subset @ SV23 @ SV13 )
= $false )
| ( ( topological_space @ SV13 )
= $false )
| ( ( top_str @ SV13 )
= $false )
| ( ( ~ ( element @ SV23 @ ( powerset @ ( the_carrier @ SV13 ) ) ) )
= $true )
| ( ( open_subset @ ( subset_complement @ ( the_carrier @ SV13 ) @ SV23 ) @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(221,plain,
! [SV3: $i,SV16: $i] :
( ( ( element @ SV16 @ ( powerset @ ( the_carrier @ SV3 ) ) )
= $false )
| ( ( top_str @ SV3 )
= $false )
| ( ( topological_space @ SV3 )
= $false )
| ( ( open_subset @ SV16 @ SV3 )
= $false )
| ( ( closed_subset @ ( subset_complement @ ( the_carrier @ SV3 ) @ SV16 ) @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(222,plain,
! [SV13: $i,SV23: $i] :
( ( ( element @ SV23 @ ( powerset @ ( the_carrier @ SV13 ) ) )
= $false )
| ( ( top_str @ SV13 )
= $false )
| ( ( topological_space @ SV13 )
= $false )
| ( ( closed_subset @ SV23 @ SV13 )
= $false )
| ( ( open_subset @ ( subset_complement @ ( the_carrier @ SV13 ) @ SV23 ) @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(223,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[56,222,221,216,215,212,211,207,185,184,178,177,169,150,147,143,140,133,128,125,123,105,70,69,65,64,62]) ).
thf(224,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU323+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n008.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 15:14:39 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/0.30
% 0.45/0.30 No.of.Axioms: 20
% 0.45/0.30
% 0.45/0.30 Length.of.Defs: 0
% 0.45/0.30
% 0.45/0.30 Contains.Choice.Funs: false
% 0.45/0.30 .....
% 0.45/0.30
% 0.45/0.30 ********************************
% 0.45/0.30 * All subproblems solved! *
% 0.45/0.30 ********************************
% 0.45/0.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:22,ps:3,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:223,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.45/0.30
% 0.45/0.30 %**** Beginning of derivation protocol ****
% 0.45/0.30 % SZS output start CNFRefutation
% See solution above
% 0.45/0.30
% 0.45/0.30 %**** End of derivation protocol ****
% 0.45/0.30 %**** no. of clauses in derivation: 224 ****
% 0.45/0.30 %**** clause counter: 223 ****
% 0.45/0.30
% 0.45/0.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:22,ps:3,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:223,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------