%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU319+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:43:56 AM UTC 2026
% Result : Theorem 0.44s 0.31s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 19
% Syntax : Number of formulae : 163 ( 107 unt; 0 typ; 0 def)
% Number of atoms : 840 ( 238 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 1820 ( 198 ~; 207 |; 12 &;1363 @)
% ( 10 <=>; 30 =>; 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 : 20 ( 17 usr; 6 con; 0-3 aty)
% Number of variables : 256 ( 0 ^; 250 !; 6 ?; 256 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cast_as_carrier_subset,type,
cast_as_carrier_subset: $i > $i ).
thf(tp_closed_subset,type,
closed_subset: $i > $i > $o ).
thf(tp_element,type,
element: $i > $i > $o ).
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_SY26,type,
sK2_SY26: $i ).
thf(tp_sK3_B,type,
sK3_B: $i > $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_complement,type,
subset_complement: $i > $i > $i ).
thf(tp_subset_difference,type,
subset_difference: $i > $i > $i > $i ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(tp_top_str,type,
top_str: $i > $o ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(2,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( subset_complement @ ( the_carrier @ A ) @ B )
= ( subset_difference @ ( the_carrier @ A ) @ ( cast_as_carrier_subset @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_pre_topc) ).
thf(3,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(6,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(7,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(8,axiom,
? [A: $i] : ( top_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(9,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(10,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(11,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(12,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(14,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(16,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
thf(17,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(18,axiom,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( closed_subset @ B @ A )
<=> ( open_subset @ ( subset_difference @ ( the_carrier @ A ) @ ( cast_as_carrier_subset @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_pre_topc) ).
thf(19,conjecture,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( closed_subset @ B @ A )
<=> ( open_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_tops_1) ).
thf(20,negated_conjecture,
( ( ! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( closed_subset @ B @ A )
<=> ( open_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[19]) ).
thf(21,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( closed_subset @ B @ A )
<=> ( open_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[20]) ).
thf(22,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(23,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( subset_complement @ ( the_carrier @ A ) @ B )
= ( subset_difference @ ( the_carrier @ A ) @ ( cast_as_carrier_subset @ A ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(25,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(26,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(27,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(28,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(29,plain,
( ( ? [A: $i] : ( top_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(30,plain,
$true = $true,
inference(unfold_def,[status(thm)],[9]) ).
thf(31,plain,
$true = $true,
inference(unfold_def,[status(thm)],[10]) ).
thf(32,plain,
$true = $true,
inference(unfold_def,[status(thm)],[11]) ).
thf(33,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(34,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(35,plain,
$true = $true,
inference(unfold_def,[status(thm)],[14]) ).
thf(36,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(38,plain,
$true = $true,
inference(unfold_def,[status(thm)],[17]) ).
thf(39,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( closed_subset @ B @ A )
<=> ( open_subset @ ( subset_difference @ ( the_carrier @ A ) @ ( cast_as_carrier_subset @ A ) @ B ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(40,plain,
( ( ( top_str @ sK1_A )
=> ! [SY26: $i] :
( ( element @ SY26 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
=> ( ( closed_subset @ SY26 @ sK1_A )
<=> ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ SY26 ) @ sK1_A ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(41,plain,
( ( top_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[40]) ).
thf(42,plain,
( ( ! [SY26: $i] :
( ( element @ SY26 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
=> ( ( closed_subset @ SY26 @ sK1_A )
<=> ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ SY26 ) @ sK1_A ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[40]) ).
thf(43,plain,
( ( ~ ! [SY26: $i] :
( ( element @ SY26 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
=> ( ( closed_subset @ SY26 @ sK1_A )
<=> ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ SY26 ) @ sK1_A ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[42]) ).
thf(44,plain,
( ( ( element @ sK2_SY26 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
& ( ~ ( closed_subset @ sK2_SY26 @ sK1_A )
| ~ ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY26 ) @ sK1_A ) )
& ( ( closed_subset @ sK2_SY26 @ sK1_A )
| ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY26 ) @ sK1_A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(46,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ( ( subset_complement @ ( the_carrier @ A ) @ B )
= ( subset_difference @ ( the_carrier @ A ) @ ( cast_as_carrier_subset @ A ) @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(47,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(48,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(50,plain,
( ( ! [A: $i] : ( element @ ( sK3_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(51,plain,
( ( one_sorted_str @ sK4_A )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(52,plain,
( ( top_str @ sK5_A )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(53,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(54,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(55,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(56,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(57,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ( ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ~ ( closed_subset @ B @ A )
| ( open_subset @ ( subset_difference @ ( the_carrier @ A ) @ ( cast_as_carrier_subset @ A ) @ B ) @ A ) )
& ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ~ ( open_subset @ ( subset_difference @ ( the_carrier @ A ) @ ( cast_as_carrier_subset @ A ) @ B ) @ A )
| ( closed_subset @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(58,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ( ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ~ ( closed_subset @ B @ A )
| ( open_subset @ ( subset_difference @ ( the_carrier @ A ) @ ( cast_as_carrier_subset @ A ) @ B ) @ A ) )
& ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ~ ( open_subset @ ( subset_difference @ ( the_carrier @ A ) @ ( cast_as_carrier_subset @ A ) @ B ) @ A )
| ( closed_subset @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(59,plain,
$true = $true,
inference(copy,[status(thm)],[38]) ).
thf(60,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(61,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(62,plain,
$true = $true,
inference(copy,[status(thm)],[35]) ).
thf(63,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(64,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(65,plain,
$true = $true,
inference(copy,[status(thm)],[32]) ).
thf(66,plain,
$true = $true,
inference(copy,[status(thm)],[31]) ).
thf(67,plain,
$true = $true,
inference(copy,[status(thm)],[30]) ).
thf(68,plain,
( ( top_str @ sK5_A )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(69,plain,
( ( one_sorted_str @ sK4_A )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(70,plain,
( ( ! [A: $i] : ( element @ ( sK3_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(71,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(72,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(73,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(74,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ( ( subset_complement @ ( the_carrier @ A ) @ B )
= ( subset_difference @ ( the_carrier @ A ) @ ( cast_as_carrier_subset @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(75,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(76,plain,
( ( top_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(77,plain,
( ( ( element @ sK2_SY26 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
& ( ~ ( closed_subset @ sK2_SY26 @ sK1_A )
| ~ ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY26 ) @ sK1_A ) )
& ( ( closed_subset @ sK2_SY26 @ sK1_A )
| ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY26 ) @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(78,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(79,plain,
( ( ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ( closed_subset @ SX1 @ SX0 )
| ( open_subset @ ( subset_difference @ ( the_carrier @ SX0 ) @ ( cast_as_carrier_subset @ SX0 ) @ SX1 ) @ SX0 ) )
| ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ( open_subset @ ( subset_difference @ ( the_carrier @ SX0 ) @ ( cast_as_carrier_subset @ SX0 ) @ SX1 ) @ SX0 )
| ( closed_subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(80,plain,
( ( ~ ( ~ ( element @ sK2_SY26 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ~ ( ~ ( ~ ( closed_subset @ sK2_SY26 @ sK1_A )
| ~ ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY26 ) @ sK1_A ) )
| ~ ( ( closed_subset @ sK2_SY26 @ sK1_A )
| ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY26 ) @ sK1_A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(81,plain,
! [SV1: $i] :
( ( ~ ( one_sorted_str @ SV1 )
| ( element @ ( cast_as_carrier_subset @ SV1 ) @ ( powerset @ ( the_carrier @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(82,plain,
! [SV2: $i] :
( ( ! [SY27: $i] :
( ~ ( element @ SY27 @ ( powerset @ SV2 ) )
| ( element @ ( subset_complement @ SV2 @ SY27 ) @ ( powerset @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(83,plain,
! [SV3: $i] :
( ( ! [SY28: $i,SY29: $i] :
( ~ ( element @ SY28 @ ( powerset @ SV3 ) )
| ~ ( element @ SY29 @ ( powerset @ SV3 ) )
| ( element @ ( subset_difference @ SV3 @ SY28 @ SY29 ) @ ( powerset @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(84,plain,
! [SV4: $i] :
( ( ~ ( top_str @ SV4 )
| ( one_sorted_str @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(85,plain,
! [SV5: $i] :
( ( element @ ( sK3_B @ SV5 ) @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(86,plain,
! [SV6: $i] :
( ( ! [SY30: $i] :
( ~ ( element @ SY30 @ ( powerset @ SV6 ) )
| ( ( subset_complement @ SV6 @ ( subset_complement @ SV6 @ SY30 ) )
= SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(87,plain,
! [SV7: $i] :
( ( ! [SY31: $i,SY32: $i] :
( ~ ( element @ SY31 @ ( powerset @ SV7 ) )
| ~ ( element @ SY32 @ ( powerset @ SV7 ) )
| ( ( subset_difference @ SV7 @ SY31 @ SY32 )
= ( set_difference @ SY31 @ SY32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(88,plain,
! [SV8: $i] :
( ( subset @ SV8 @ SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(89,plain,
! [SV9: $i] :
( ( ~ ( one_sorted_str @ SV9 )
| ! [SY33: $i] :
( ~ ( element @ SY33 @ ( powerset @ ( the_carrier @ SV9 ) ) )
| ( ( subset_complement @ ( the_carrier @ SV9 ) @ SY33 )
= ( subset_difference @ ( the_carrier @ SV9 ) @ ( cast_as_carrier_subset @ SV9 ) @ SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(90,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(91,plain,
! [SV10: $i] :
( ( ~ ( top_str @ SV10 )
| ~ ( ~ ! [SY34: $i] :
( ~ ( element @ SY34 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ~ ( closed_subset @ SY34 @ SV10 )
| ( open_subset @ ( subset_difference @ ( the_carrier @ SV10 ) @ ( cast_as_carrier_subset @ SV10 ) @ SY34 ) @ SV10 ) )
| ~ ! [SY35: $i] :
( ~ ( element @ SY35 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ~ ( open_subset @ ( subset_difference @ ( the_carrier @ SV10 ) @ ( cast_as_carrier_subset @ SV10 ) @ SY35 ) @ SV10 )
| ( closed_subset @ SY35 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(92,plain,
( ( ~ ( element @ sK2_SY26 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ~ ( ~ ( ~ ( closed_subset @ sK2_SY26 @ sK1_A )
| ~ ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY26 ) @ sK1_A ) )
| ~ ( ( closed_subset @ sK2_SY26 @ sK1_A )
| ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY26 ) @ sK1_A ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(93,plain,
! [SV1: $i] :
( ( ( ~ ( one_sorted_str @ SV1 ) )
= $true )
| ( ( element @ ( cast_as_carrier_subset @ SV1 ) @ ( powerset @ ( the_carrier @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(94,plain,
! [SV2: $i,SV11: $i] :
( ( ~ ( element @ SV11 @ ( powerset @ SV2 ) )
| ( element @ ( subset_complement @ SV2 @ SV11 ) @ ( powerset @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(95,plain,
! [SV3: $i,SV12: $i] :
( ( ! [SY36: $i] :
( ~ ( element @ SV12 @ ( powerset @ SV3 ) )
| ~ ( element @ SY36 @ ( powerset @ SV3 ) )
| ( element @ ( subset_difference @ SV3 @ SV12 @ SY36 ) @ ( powerset @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(96,plain,
! [SV4: $i] :
( ( ( ~ ( top_str @ SV4 ) )
= $true )
| ( ( one_sorted_str @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(97,plain,
! [SV6: $i,SV13: $i] :
( ( ~ ( element @ SV13 @ ( powerset @ SV6 ) )
| ( ( subset_complement @ SV6 @ ( subset_complement @ SV6 @ SV13 ) )
= SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(98,plain,
! [SV7: $i,SV14: $i] :
( ( ! [SY37: $i] :
( ~ ( element @ SV14 @ ( powerset @ SV7 ) )
| ~ ( element @ SY37 @ ( powerset @ SV7 ) )
| ( ( subset_difference @ SV7 @ SV14 @ SY37 )
= ( set_difference @ SV14 @ SY37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(99,plain,
! [SV9: $i] :
( ( ( ~ ( one_sorted_str @ SV9 ) )
= $true )
| ( ( ! [SY33: $i] :
( ~ ( element @ SY33 @ ( powerset @ ( the_carrier @ SV9 ) ) )
| ( ( subset_complement @ ( the_carrier @ SV9 ) @ SY33 )
= ( subset_difference @ ( the_carrier @ SV9 ) @ ( cast_as_carrier_subset @ SV9 ) @ SY33 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(100,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(101,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(102,plain,
! [SV10: $i] :
( ( ( ~ ( top_str @ SV10 ) )
= $true )
| ( ( ~ ( ~ ! [SY34: $i] :
( ~ ( element @ SY34 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ~ ( closed_subset @ SY34 @ SV10 )
| ( open_subset @ ( subset_difference @ ( the_carrier @ SV10 ) @ ( cast_as_carrier_subset @ SV10 ) @ SY34 ) @ SV10 ) )
| ~ ! [SY35: $i] :
( ~ ( element @ SY35 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ~ ( open_subset @ ( subset_difference @ ( the_carrier @ SV10 ) @ ( cast_as_carrier_subset @ SV10 ) @ SY35 ) @ SV10 )
| ( closed_subset @ SY35 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(103,plain,
( ( ~ ( element @ sK2_SY26 @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(104,plain,
( ( ~ ~ ( ~ ( ~ ( closed_subset @ sK2_SY26 @ sK1_A )
| ~ ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY26 ) @ sK1_A ) )
| ~ ( ( closed_subset @ sK2_SY26 @ sK1_A )
| ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY26 ) @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(105,plain,
! [SV1: $i] :
( ( ( one_sorted_str @ SV1 )
= $false )
| ( ( element @ ( cast_as_carrier_subset @ SV1 ) @ ( powerset @ ( the_carrier @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(106,plain,
! [SV2: $i,SV11: $i] :
( ( ( ~ ( element @ SV11 @ ( powerset @ SV2 ) ) )
= $true )
| ( ( element @ ( subset_complement @ SV2 @ SV11 ) @ ( powerset @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(107,plain,
! [SV15: $i,SV3: $i,SV12: $i] :
( ( ~ ( element @ SV12 @ ( powerset @ SV3 ) )
| ~ ( element @ SV15 @ ( powerset @ SV3 ) )
| ( element @ ( subset_difference @ SV3 @ SV12 @ SV15 ) @ ( powerset @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(108,plain,
! [SV4: $i] :
( ( ( top_str @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(109,plain,
! [SV6: $i,SV13: $i] :
( ( ( ~ ( element @ SV13 @ ( powerset @ SV6 ) ) )
= $true )
| ( ( ( subset_complement @ SV6 @ ( subset_complement @ SV6 @ SV13 ) )
= SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(110,plain,
! [SV16: $i,SV7: $i,SV14: $i] :
( ( ~ ( element @ SV14 @ ( powerset @ SV7 ) )
| ~ ( element @ SV16 @ ( powerset @ SV7 ) )
| ( ( subset_difference @ SV7 @ SV14 @ SV16 )
= ( set_difference @ SV14 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(111,plain,
! [SV9: $i] :
( ( ( one_sorted_str @ SV9 )
= $false )
| ( ( ! [SY33: $i] :
( ~ ( element @ SY33 @ ( powerset @ ( the_carrier @ SV9 ) ) )
| ( ( subset_complement @ ( the_carrier @ SV9 ) @ SY33 )
= ( subset_difference @ ( the_carrier @ SV9 ) @ ( cast_as_carrier_subset @ SV9 ) @ SY33 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(112,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(113,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(114,plain,
! [SV10: $i] :
( ( ( top_str @ SV10 )
= $false )
| ( ( ~ ( ~ ! [SY34: $i] :
( ~ ( element @ SY34 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ~ ( closed_subset @ SY34 @ SV10 )
| ( open_subset @ ( subset_difference @ ( the_carrier @ SV10 ) @ ( cast_as_carrier_subset @ SV10 ) @ SY34 ) @ SV10 ) )
| ~ ! [SY35: $i] :
( ~ ( element @ SY35 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ~ ( open_subset @ ( subset_difference @ ( the_carrier @ SV10 ) @ ( cast_as_carrier_subset @ SV10 ) @ SY35 ) @ SV10 )
| ( closed_subset @ SY35 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(115,plain,
( ( element @ sK2_SY26 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(116,plain,
( ( ~ ( ~ ( ~ ( closed_subset @ sK2_SY26 @ sK1_A )
| ~ ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY26 ) @ sK1_A ) )
| ~ ( ( closed_subset @ sK2_SY26 @ sK1_A )
| ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY26 ) @ sK1_A ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(117,plain,
! [SV2: $i,SV11: $i] :
( ( ( element @ SV11 @ ( powerset @ SV2 ) )
= $false )
| ( ( element @ ( subset_complement @ SV2 @ SV11 ) @ ( powerset @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(118,plain,
! [SV15: $i,SV3: $i,SV12: $i] :
( ( ( ~ ( element @ SV12 @ ( powerset @ SV3 ) )
| ~ ( element @ SV15 @ ( powerset @ SV3 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV3 @ SV12 @ SV15 ) @ ( powerset @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(119,plain,
! [SV6: $i,SV13: $i] :
( ( ( element @ SV13 @ ( powerset @ SV6 ) )
= $false )
| ( ( ( subset_complement @ SV6 @ ( subset_complement @ SV6 @ SV13 ) )
= SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(120,plain,
! [SV16: $i,SV7: $i,SV14: $i] :
( ( ( ~ ( element @ SV14 @ ( powerset @ SV7 ) )
| ~ ( element @ SV16 @ ( powerset @ SV7 ) ) )
= $true )
| ( ( ( subset_difference @ SV7 @ SV14 @ SV16 )
= ( set_difference @ SV14 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(121,plain,
! [SV9: $i,SV17: $i] :
( ( ( ~ ( element @ SV17 @ ( powerset @ ( the_carrier @ SV9 ) ) )
| ( ( subset_complement @ ( the_carrier @ SV9 ) @ SV17 )
= ( subset_difference @ ( the_carrier @ SV9 ) @ ( cast_as_carrier_subset @ SV9 ) @ SV17 ) ) )
= $true )
| ( ( one_sorted_str @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(122,plain,
! [SV18: $i] :
( ( ! [SY38: $i] :
( ~ ( element @ SV18 @ ( powerset @ SY38 ) )
| ( subset @ SV18 @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(123,plain,
! [SV19: $i] :
( ( ! [SY39: $i] :
( ~ ( subset @ SV19 @ SY39 )
| ( element @ SV19 @ ( powerset @ SY39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(124,plain,
! [SV10: $i] :
( ( ( ~ ! [SY34: $i] :
( ~ ( element @ SY34 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ~ ( closed_subset @ SY34 @ SV10 )
| ( open_subset @ ( subset_difference @ ( the_carrier @ SV10 ) @ ( cast_as_carrier_subset @ SV10 ) @ SY34 ) @ SV10 ) )
| ~ ! [SY35: $i] :
( ~ ( element @ SY35 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ~ ( open_subset @ ( subset_difference @ ( the_carrier @ SV10 ) @ ( cast_as_carrier_subset @ SV10 ) @ SY35 ) @ SV10 )
| ( closed_subset @ SY35 @ SV10 ) ) )
= $false )
| ( ( top_str @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(125,plain,
( ( ~ ( ~ ( closed_subset @ sK2_SY26 @ sK1_A )
| ~ ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY26 ) @ sK1_A ) )
| ~ ( ( closed_subset @ sK2_SY26 @ sK1_A )
| ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY26 ) @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(126,plain,
! [SV15: $i,SV3: $i,SV12: $i] :
( ( ( ~ ( element @ SV12 @ ( powerset @ SV3 ) ) )
= $true )
| ( ( ~ ( element @ SV15 @ ( powerset @ SV3 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV3 @ SV12 @ SV15 ) @ ( powerset @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(127,plain,
! [SV16: $i,SV7: $i,SV14: $i] :
( ( ( ~ ( element @ SV14 @ ( powerset @ SV7 ) ) )
= $true )
| ( ( ~ ( element @ SV16 @ ( powerset @ SV7 ) ) )
= $true )
| ( ( ( subset_difference @ SV7 @ SV14 @ SV16 )
= ( set_difference @ SV14 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(128,plain,
! [SV9: $i,SV17: $i] :
( ( ( ~ ( element @ SV17 @ ( powerset @ ( the_carrier @ SV9 ) ) ) )
= $true )
| ( ( ( subset_complement @ ( the_carrier @ SV9 ) @ SV17 )
= ( subset_difference @ ( the_carrier @ SV9 ) @ ( cast_as_carrier_subset @ SV9 ) @ SV17 ) )
= $true )
| ( ( one_sorted_str @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(129,plain,
! [SV20: $i,SV18: $i] :
( ( ~ ( element @ SV18 @ ( powerset @ SV20 ) )
| ( subset @ SV18 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(130,plain,
! [SV21: $i,SV19: $i] :
( ( ~ ( subset @ SV19 @ SV21 )
| ( element @ SV19 @ ( powerset @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(131,plain,
! [SV10: $i] :
( ( ( ~ ! [SY34: $i] :
( ~ ( element @ SY34 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ~ ( closed_subset @ SY34 @ SV10 )
| ( open_subset @ ( subset_difference @ ( the_carrier @ SV10 ) @ ( cast_as_carrier_subset @ SV10 ) @ SY34 ) @ SV10 ) ) )
= $false )
| ( ( top_str @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(132,plain,
! [SV10: $i] :
( ( ( ~ ! [SY35: $i] :
( ~ ( element @ SY35 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ~ ( open_subset @ ( subset_difference @ ( the_carrier @ SV10 ) @ ( cast_as_carrier_subset @ SV10 ) @ SY35 ) @ SV10 )
| ( closed_subset @ SY35 @ SV10 ) ) )
= $false )
| ( ( top_str @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(133,plain,
( ( ~ ( ~ ( closed_subset @ sK2_SY26 @ sK1_A )
| ~ ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY26 ) @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(134,plain,
( ( ~ ( ( closed_subset @ sK2_SY26 @ sK1_A )
| ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY26 ) @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(135,plain,
! [SV15: $i,SV3: $i,SV12: $i] :
( ( ( element @ SV12 @ ( powerset @ SV3 ) )
= $false )
| ( ( ~ ( element @ SV15 @ ( powerset @ SV3 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV3 @ SV12 @ SV15 ) @ ( powerset @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(136,plain,
! [SV16: $i,SV7: $i,SV14: $i] :
( ( ( element @ SV14 @ ( powerset @ SV7 ) )
= $false )
| ( ( ~ ( element @ SV16 @ ( powerset @ SV7 ) ) )
= $true )
| ( ( ( subset_difference @ SV7 @ SV14 @ SV16 )
= ( set_difference @ SV14 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(137,plain,
! [SV9: $i,SV17: $i] :
( ( ( element @ SV17 @ ( powerset @ ( the_carrier @ SV9 ) ) )
= $false )
| ( ( ( subset_complement @ ( the_carrier @ SV9 ) @ SV17 )
= ( subset_difference @ ( the_carrier @ SV9 ) @ ( cast_as_carrier_subset @ SV9 ) @ SV17 ) )
= $true )
| ( ( one_sorted_str @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(138,plain,
! [SV20: $i,SV18: $i] :
( ( ( ~ ( element @ SV18 @ ( powerset @ SV20 ) ) )
= $true )
| ( ( subset @ SV18 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(139,plain,
! [SV21: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV21 ) )
= $true )
| ( ( element @ SV19 @ ( powerset @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(140,plain,
! [SV10: $i] :
( ( ( ! [SY34: $i] :
( ~ ( element @ SY34 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ~ ( closed_subset @ SY34 @ SV10 )
| ( open_subset @ ( subset_difference @ ( the_carrier @ SV10 ) @ ( cast_as_carrier_subset @ SV10 ) @ SY34 ) @ SV10 ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(141,plain,
! [SV10: $i] :
( ( ( ! [SY35: $i] :
( ~ ( element @ SY35 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ~ ( open_subset @ ( subset_difference @ ( the_carrier @ SV10 ) @ ( cast_as_carrier_subset @ SV10 ) @ SY35 ) @ SV10 )
| ( closed_subset @ SY35 @ SV10 ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(142,plain,
( ( ~ ( closed_subset @ sK2_SY26 @ sK1_A )
| ~ ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY26 ) @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(143,plain,
( ( ( closed_subset @ sK2_SY26 @ sK1_A )
| ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY26 ) @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(144,plain,
! [SV12: $i,SV3: $i,SV15: $i] :
( ( ( element @ SV15 @ ( powerset @ SV3 ) )
= $false )
| ( ( element @ SV12 @ ( powerset @ SV3 ) )
= $false )
| ( ( element @ ( subset_difference @ SV3 @ SV12 @ SV15 ) @ ( powerset @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(145,plain,
! [SV14: $i,SV7: $i,SV16: $i] :
( ( ( element @ SV16 @ ( powerset @ SV7 ) )
= $false )
| ( ( element @ SV14 @ ( powerset @ SV7 ) )
= $false )
| ( ( ( subset_difference @ SV7 @ SV14 @ SV16 )
= ( set_difference @ SV14 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(146,plain,
! [SV20: $i,SV18: $i] :
( ( ( element @ SV18 @ ( powerset @ SV20 ) )
= $false )
| ( ( subset @ SV18 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(147,plain,
! [SV21: $i,SV19: $i] :
( ( ( subset @ SV19 @ SV21 )
= $false )
| ( ( element @ SV19 @ ( powerset @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(148,plain,
! [SV10: $i,SV22: $i] :
( ( ( ~ ( element @ SV22 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ~ ( closed_subset @ SV22 @ SV10 )
| ( open_subset @ ( subset_difference @ ( the_carrier @ SV10 ) @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV10 ) )
= $true )
| ( ( top_str @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(149,plain,
! [SV10: $i,SV23: $i] :
( ( ( ~ ( element @ SV23 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ~ ( open_subset @ ( subset_difference @ ( the_carrier @ SV10 ) @ ( cast_as_carrier_subset @ SV10 ) @ SV23 ) @ SV10 )
| ( closed_subset @ SV23 @ SV10 ) )
= $true )
| ( ( top_str @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(150,plain,
( ( ( ~ ( closed_subset @ sK2_SY26 @ sK1_A ) )
= $true )
| ( ( ~ ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY26 ) @ sK1_A ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(151,plain,
( ( ( closed_subset @ sK2_SY26 @ sK1_A )
= $true )
| ( ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY26 ) @ sK1_A )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(152,plain,
! [SV10: $i,SV22: $i] :
( ( ( ~ ( element @ SV22 @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $true )
| ( ( ~ ( closed_subset @ SV22 @ SV10 )
| ( open_subset @ ( subset_difference @ ( the_carrier @ SV10 ) @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV10 ) )
= $true )
| ( ( top_str @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(153,plain,
! [SV10: $i,SV23: $i] :
( ( ( ~ ( element @ SV23 @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $true )
| ( ( ~ ( open_subset @ ( subset_difference @ ( the_carrier @ SV10 ) @ ( cast_as_carrier_subset @ SV10 ) @ SV23 ) @ SV10 )
| ( closed_subset @ SV23 @ SV10 ) )
= $true )
| ( ( top_str @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(154,plain,
( ( ( closed_subset @ sK2_SY26 @ sK1_A )
= $false )
| ( ( ~ ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY26 ) @ sK1_A ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(155,plain,
! [SV10: $i,SV22: $i] :
( ( ( element @ SV22 @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( ~ ( closed_subset @ SV22 @ SV10 )
| ( open_subset @ ( subset_difference @ ( the_carrier @ SV10 ) @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV10 ) )
= $true )
| ( ( top_str @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(156,plain,
! [SV10: $i,SV23: $i] :
( ( ( element @ SV23 @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( ~ ( open_subset @ ( subset_difference @ ( the_carrier @ SV10 ) @ ( cast_as_carrier_subset @ SV10 ) @ SV23 ) @ SV10 )
| ( closed_subset @ SV23 @ SV10 ) )
= $true )
| ( ( top_str @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(157,plain,
( ( ( open_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY26 ) @ sK1_A )
= $false )
| ( ( closed_subset @ sK2_SY26 @ sK1_A )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(158,plain,
! [SV10: $i,SV22: $i] :
( ( ( ~ ( closed_subset @ SV22 @ SV10 ) )
= $true )
| ( ( open_subset @ ( subset_difference @ ( the_carrier @ SV10 ) @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV10 )
= $true )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( top_str @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(159,plain,
! [SV23: $i,SV10: $i] :
( ( ( ~ ( open_subset @ ( subset_difference @ ( the_carrier @ SV10 ) @ ( cast_as_carrier_subset @ SV10 ) @ SV23 ) @ SV10 ) )
= $true )
| ( ( closed_subset @ SV23 @ SV10 )
= $true )
| ( ( element @ SV23 @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( top_str @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(160,plain,
! [SV10: $i,SV22: $i] :
( ( ( closed_subset @ SV22 @ SV10 )
= $false )
| ( ( open_subset @ ( subset_difference @ ( the_carrier @ SV10 ) @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV10 )
= $true )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( top_str @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(161,plain,
! [SV23: $i,SV10: $i] :
( ( ( open_subset @ ( subset_difference @ ( the_carrier @ SV10 ) @ ( cast_as_carrier_subset @ SV10 ) @ SV23 ) @ SV10 )
= $false )
| ( ( closed_subset @ SV23 @ SV10 )
= $true )
| ( ( element @ SV23 @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( top_str @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(162,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[59,161,160,157,151,147,146,145,144,137,119,117,115,108,105,88,85,76,69,68,67,66,65,62]) ).
thf(163,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU319+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n017.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 15:09:16 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.44/0.31
% 0.44/0.31 No.of.Axioms: 18
% 0.44/0.31
% 0.44/0.31 Length.of.Defs: 0
% 0.44/0.31
% 0.44/0.31 Contains.Choice.Funs: false
% 0.44/0.31 ....
% 0.44/0.31
% 0.44/0.31 ********************************
% 0.44/0.31 * All subproblems solved! *
% 0.44/0.31 ********************************
% 0.44/0.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:19,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:162,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.44/0.31
% 0.44/0.31 %**** Beginning of derivation protocol ****
% 0.44/0.31 % SZS output start CNFRefutation
% See solution above
% 0.44/0.31
% 0.44/0.31 %**** End of derivation protocol ****
% 0.44/0.31 %**** no. of clauses in derivation: 163 ****
% 0.44/0.31 %**** clause counter: 162 ****
% 0.44/0.31
% 0.44/0.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:19,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:162,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------