TSTP Solution File: SEU320+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU320+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:10:13 EDT 2022
% Result : Theorem 0.17s 0.40s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 28
% Syntax : Number of formulae : 135 ( 84 unt; 14 typ; 0 def)
% Number of atoms : 607 ( 157 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 1219 ( 153 ~; 150 |; 8 &; 878 @)
% ( 10 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 163 ( 0 ^ 157 !; 6 ?; 163 :)
% Comments :
%------------------------------------------------------------------------------
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_SY17,type,
sK2_SY17: $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_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(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] :
( ( 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(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] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(5,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(6,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(7,axiom,
? [A: $i] : ( top_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(8,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(9,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(10,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(11,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(12,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(13,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(14,conjecture,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( open_subset @ B @ A )
<=> ( closed_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_tops_1) ).
thf(15,negated_conjecture,
( ( ! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( open_subset @ B @ A )
<=> ( closed_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[14]) ).
thf(16,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( open_subset @ B @ A )
<=> ( closed_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(18,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 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(21,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(22,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(23,plain,
( ( ? [A: $i] : ( top_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(24,plain,
$true = $true,
inference(unfold_def,[status(thm)],[8]) ).
thf(25,plain,
$true = $true,
inference(unfold_def,[status(thm)],[9]) ).
thf(26,plain,
$true = $true,
inference(unfold_def,[status(thm)],[10]) ).
thf(27,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(28,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(29,plain,
$true = $true,
inference(unfold_def,[status(thm)],[13]) ).
thf(30,plain,
( ( ( top_str @ sK1_A )
=> ! [SY17: $i] :
( ( element @ SY17 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
=> ( ( open_subset @ SY17 @ sK1_A )
<=> ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ SY17 ) @ sK1_A ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(31,plain,
( ( top_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[30]) ).
thf(32,plain,
( ( ! [SY17: $i] :
( ( element @ SY17 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
=> ( ( open_subset @ SY17 @ sK1_A )
<=> ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ SY17 ) @ sK1_A ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[30]) ).
thf(33,plain,
( ( ~ ! [SY17: $i] :
( ( element @ SY17 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
=> ( ( open_subset @ SY17 @ sK1_A )
<=> ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ SY17 ) @ sK1_A ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[32]) ).
thf(34,plain,
( ( ( element @ sK2_SY17 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
& ( ~ ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY17 ) @ sK1_A )
| ~ ( open_subset @ sK2_SY17 @ sK1_A ) )
& ( ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY17 ) @ sK1_A )
| ( open_subset @ sK2_SY17 @ sK1_A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(35,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)],[17]) ).
thf(36,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 ) )
& ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ~ ( open_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A )
| ( closed_subset @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(37,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(39,plain,
( ( ! [A: $i] : ( element @ ( sK3_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(40,plain,
( ( one_sorted_str @ sK4_A )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(41,plain,
( ( top_str @ sK5_A )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(42,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(43,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(44,plain,
$true = $true,
inference(copy,[status(thm)],[29]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(46,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(47,plain,
$true = $true,
inference(copy,[status(thm)],[26]) ).
thf(48,plain,
$true = $true,
inference(copy,[status(thm)],[25]) ).
thf(49,plain,
$true = $true,
inference(copy,[status(thm)],[24]) ).
thf(50,plain,
( ( top_str @ sK5_A )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(51,plain,
( ( one_sorted_str @ sK4_A )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(52,plain,
( ( ! [A: $i] : ( element @ ( sK3_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(53,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(54,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(55,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 ) )
& ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ~ ( open_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A )
| ( closed_subset @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(56,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)],[35]) ).
thf(57,plain,
( ( top_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(58,plain,
( ( ( element @ sK2_SY17 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
& ( ~ ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY17 ) @ sK1_A )
| ~ ( open_subset @ sK2_SY17 @ sK1_A ) )
& ( ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY17 ) @ sK1_A )
| ( open_subset @ sK2_SY17 @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(59,plain,
( ( ~ ( ~ ( element @ sK2_SY17 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ~ ( ~ ( ~ ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY17 ) @ sK1_A )
| ~ ( open_subset @ sK2_SY17 @ sK1_A ) )
| ~ ( ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY17 ) @ sK1_A )
| ( open_subset @ sK2_SY17 @ sK1_A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(60,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)],[56]) ).
thf(61,plain,
( ( ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ( closed_subset @ SX1 @ SX0 )
| ( open_subset @ ( subset_complement @ ( the_carrier @ SX0 ) @ SX1 ) @ SX0 ) )
| ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ( open_subset @ ( subset_complement @ ( the_carrier @ SX0 ) @ SX1 ) @ SX0 )
| ( closed_subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(62,plain,
! [SV1: $i] :
( ( ! [SY18: $i] :
( ~ ( element @ SY18 @ ( powerset @ SV1 ) )
| ( element @ ( subset_complement @ SV1 @ SY18 ) @ ( powerset @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(63,plain,
! [SV2: $i] :
( ( ~ ( top_str @ SV2 )
| ( one_sorted_str @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(64,plain,
! [SV3: $i] :
( ( element @ ( sK3_B @ SV3 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(65,plain,
! [SV4: $i] :
( ( ! [SY19: $i] :
( ~ ( element @ SY19 @ ( powerset @ SV4 ) )
| ( ( subset_complement @ SV4 @ ( subset_complement @ SV4 @ SY19 ) )
= SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(66,plain,
! [SV5: $i] :
( ( subset @ SV5 @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(67,plain,
( ( ~ ( element @ sK2_SY17 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ~ ( ~ ( ~ ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY17 ) @ sK1_A )
| ~ ( open_subset @ sK2_SY17 @ sK1_A ) )
| ~ ( ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY17 ) @ sK1_A )
| ( open_subset @ sK2_SY17 @ sK1_A ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(68,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)],[60]) ).
thf(69,plain,
! [SV6: $i] :
( ( ~ ( top_str @ SV6 )
| ~ ( ~ ! [SY20: $i] :
( ~ ( element @ SY20 @ ( powerset @ ( the_carrier @ SV6 ) ) )
| ~ ( closed_subset @ SY20 @ SV6 )
| ( open_subset @ ( subset_complement @ ( the_carrier @ SV6 ) @ SY20 ) @ SV6 ) )
| ~ ! [SY21: $i] :
( ~ ( element @ SY21 @ ( powerset @ ( the_carrier @ SV6 ) ) )
| ~ ( open_subset @ ( subset_complement @ ( the_carrier @ SV6 ) @ SY21 ) @ SV6 )
| ( closed_subset @ SY21 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(70,plain,
! [SV1: $i,SV7: $i] :
( ( ~ ( element @ SV7 @ ( powerset @ SV1 ) )
| ( element @ ( subset_complement @ SV1 @ SV7 ) @ ( powerset @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(71,plain,
! [SV2: $i] :
( ( ( ~ ( top_str @ SV2 ) )
= $true )
| ( ( one_sorted_str @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(72,plain,
! [SV4: $i,SV8: $i] :
( ( ~ ( element @ SV8 @ ( powerset @ SV4 ) )
| ( ( subset_complement @ SV4 @ ( subset_complement @ SV4 @ SV8 ) )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(73,plain,
( ( ~ ( element @ sK2_SY17 @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(74,plain,
( ( ~ ~ ( ~ ( ~ ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY17 ) @ sK1_A )
| ~ ( open_subset @ sK2_SY17 @ sK1_A ) )
| ~ ( ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY17 ) @ sK1_A )
| ( open_subset @ sK2_SY17 @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(75,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(76,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(77,plain,
! [SV6: $i] :
( ( ( ~ ( top_str @ SV6 ) )
= $true )
| ( ( ~ ( ~ ! [SY20: $i] :
( ~ ( element @ SY20 @ ( powerset @ ( the_carrier @ SV6 ) ) )
| ~ ( closed_subset @ SY20 @ SV6 )
| ( open_subset @ ( subset_complement @ ( the_carrier @ SV6 ) @ SY20 ) @ SV6 ) )
| ~ ! [SY21: $i] :
( ~ ( element @ SY21 @ ( powerset @ ( the_carrier @ SV6 ) ) )
| ~ ( open_subset @ ( subset_complement @ ( the_carrier @ SV6 ) @ SY21 ) @ SV6 )
| ( closed_subset @ SY21 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(78,plain,
! [SV1: $i,SV7: $i] :
( ( ( ~ ( element @ SV7 @ ( powerset @ SV1 ) ) )
= $true )
| ( ( element @ ( subset_complement @ SV1 @ SV7 ) @ ( powerset @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(79,plain,
! [SV2: $i] :
( ( ( top_str @ SV2 )
= $false )
| ( ( one_sorted_str @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(80,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( element @ SV8 @ ( powerset @ SV4 ) ) )
= $true )
| ( ( ( subset_complement @ SV4 @ ( subset_complement @ SV4 @ SV8 ) )
= SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(81,plain,
( ( element @ sK2_SY17 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(82,plain,
( ( ~ ( ~ ( ~ ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY17 ) @ sK1_A )
| ~ ( open_subset @ sK2_SY17 @ sK1_A ) )
| ~ ( ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY17 ) @ sK1_A )
| ( open_subset @ sK2_SY17 @ sK1_A ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(83,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(84,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(85,plain,
! [SV6: $i] :
( ( ( top_str @ SV6 )
= $false )
| ( ( ~ ( ~ ! [SY20: $i] :
( ~ ( element @ SY20 @ ( powerset @ ( the_carrier @ SV6 ) ) )
| ~ ( closed_subset @ SY20 @ SV6 )
| ( open_subset @ ( subset_complement @ ( the_carrier @ SV6 ) @ SY20 ) @ SV6 ) )
| ~ ! [SY21: $i] :
( ~ ( element @ SY21 @ ( powerset @ ( the_carrier @ SV6 ) ) )
| ~ ( open_subset @ ( subset_complement @ ( the_carrier @ SV6 ) @ SY21 ) @ SV6 )
| ( closed_subset @ SY21 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(86,plain,
! [SV1: $i,SV7: $i] :
( ( ( element @ SV7 @ ( powerset @ SV1 ) )
= $false )
| ( ( element @ ( subset_complement @ SV1 @ SV7 ) @ ( powerset @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(87,plain,
! [SV4: $i,SV8: $i] :
( ( ( element @ SV8 @ ( powerset @ SV4 ) )
= $false )
| ( ( ( subset_complement @ SV4 @ ( subset_complement @ SV4 @ SV8 ) )
= SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(88,plain,
( ( ~ ( ~ ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY17 ) @ sK1_A )
| ~ ( open_subset @ sK2_SY17 @ sK1_A ) )
| ~ ( ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY17 ) @ sK1_A )
| ( open_subset @ sK2_SY17 @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(89,plain,
! [SV9: $i] :
( ( ! [SY22: $i] :
( ~ ( element @ SV9 @ ( powerset @ SY22 ) )
| ( subset @ SV9 @ SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(90,plain,
! [SV10: $i] :
( ( ! [SY23: $i] :
( ~ ( subset @ SV10 @ SY23 )
| ( element @ SV10 @ ( powerset @ SY23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(91,plain,
! [SV6: $i] :
( ( ( ~ ! [SY20: $i] :
( ~ ( element @ SY20 @ ( powerset @ ( the_carrier @ SV6 ) ) )
| ~ ( closed_subset @ SY20 @ SV6 )
| ( open_subset @ ( subset_complement @ ( the_carrier @ SV6 ) @ SY20 ) @ SV6 ) )
| ~ ! [SY21: $i] :
( ~ ( element @ SY21 @ ( powerset @ ( the_carrier @ SV6 ) ) )
| ~ ( open_subset @ ( subset_complement @ ( the_carrier @ SV6 ) @ SY21 ) @ SV6 )
| ( closed_subset @ SY21 @ SV6 ) ) )
= $false )
| ( ( top_str @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(92,plain,
( ( ~ ( ~ ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY17 ) @ sK1_A )
| ~ ( open_subset @ sK2_SY17 @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(93,plain,
( ( ~ ( ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY17 ) @ sK1_A )
| ( open_subset @ sK2_SY17 @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(94,plain,
! [SV11: $i,SV9: $i] :
( ( ~ ( element @ SV9 @ ( powerset @ SV11 ) )
| ( subset @ SV9 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(95,plain,
! [SV12: $i,SV10: $i] :
( ( ~ ( subset @ SV10 @ SV12 )
| ( element @ SV10 @ ( powerset @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(96,plain,
! [SV6: $i] :
( ( ( ~ ! [SY20: $i] :
( ~ ( element @ SY20 @ ( powerset @ ( the_carrier @ SV6 ) ) )
| ~ ( closed_subset @ SY20 @ SV6 )
| ( open_subset @ ( subset_complement @ ( the_carrier @ SV6 ) @ SY20 ) @ SV6 ) ) )
= $false )
| ( ( top_str @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(97,plain,
! [SV6: $i] :
( ( ( ~ ! [SY21: $i] :
( ~ ( element @ SY21 @ ( powerset @ ( the_carrier @ SV6 ) ) )
| ~ ( open_subset @ ( subset_complement @ ( the_carrier @ SV6 ) @ SY21 ) @ SV6 )
| ( closed_subset @ SY21 @ SV6 ) ) )
= $false )
| ( ( top_str @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(98,plain,
( ( ~ ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY17 ) @ sK1_A )
| ~ ( open_subset @ sK2_SY17 @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(99,plain,
( ( ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY17 ) @ sK1_A )
| ( open_subset @ sK2_SY17 @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(100,plain,
! [SV11: $i,SV9: $i] :
( ( ( ~ ( element @ SV9 @ ( powerset @ SV11 ) ) )
= $true )
| ( ( subset @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(101,plain,
! [SV12: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV12 ) )
= $true )
| ( ( element @ SV10 @ ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(102,plain,
! [SV6: $i] :
( ( ( ! [SY20: $i] :
( ~ ( element @ SY20 @ ( powerset @ ( the_carrier @ SV6 ) ) )
| ~ ( closed_subset @ SY20 @ SV6 )
| ( open_subset @ ( subset_complement @ ( the_carrier @ SV6 ) @ SY20 ) @ SV6 ) ) )
= $true )
| ( ( top_str @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(103,plain,
! [SV6: $i] :
( ( ( ! [SY21: $i] :
( ~ ( element @ SY21 @ ( powerset @ ( the_carrier @ SV6 ) ) )
| ~ ( open_subset @ ( subset_complement @ ( the_carrier @ SV6 ) @ SY21 ) @ SV6 )
| ( closed_subset @ SY21 @ SV6 ) ) )
= $true )
| ( ( top_str @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(104,plain,
( ( ( ~ ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY17 ) @ sK1_A ) )
= $true )
| ( ( ~ ( open_subset @ sK2_SY17 @ sK1_A ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(105,plain,
( ( ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY17 ) @ sK1_A )
= $true )
| ( ( open_subset @ sK2_SY17 @ sK1_A )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(106,plain,
! [SV11: $i,SV9: $i] :
( ( ( element @ SV9 @ ( powerset @ SV11 ) )
= $false )
| ( ( subset @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(107,plain,
! [SV12: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV12 )
= $false )
| ( ( element @ SV10 @ ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(108,plain,
! [SV6: $i,SV13: $i] :
( ( ( ~ ( element @ SV13 @ ( powerset @ ( the_carrier @ SV6 ) ) )
| ~ ( closed_subset @ SV13 @ SV6 )
| ( open_subset @ ( subset_complement @ ( the_carrier @ SV6 ) @ SV13 ) @ SV6 ) )
= $true )
| ( ( top_str @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(109,plain,
! [SV6: $i,SV14: $i] :
( ( ( ~ ( element @ SV14 @ ( powerset @ ( the_carrier @ SV6 ) ) )
| ~ ( open_subset @ ( subset_complement @ ( the_carrier @ SV6 ) @ SV14 ) @ SV6 )
| ( closed_subset @ SV14 @ SV6 ) )
= $true )
| ( ( top_str @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(110,plain,
( ( ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY17 ) @ sK1_A )
= $false )
| ( ( ~ ( open_subset @ sK2_SY17 @ sK1_A ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(111,plain,
! [SV6: $i,SV13: $i] :
( ( ( ~ ( element @ SV13 @ ( powerset @ ( the_carrier @ SV6 ) ) ) )
= $true )
| ( ( ~ ( closed_subset @ SV13 @ SV6 )
| ( open_subset @ ( subset_complement @ ( the_carrier @ SV6 ) @ SV13 ) @ SV6 ) )
= $true )
| ( ( top_str @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(112,plain,
! [SV6: $i,SV14: $i] :
( ( ( ~ ( element @ SV14 @ ( powerset @ ( the_carrier @ SV6 ) ) ) )
= $true )
| ( ( ~ ( open_subset @ ( subset_complement @ ( the_carrier @ SV6 ) @ SV14 ) @ SV6 )
| ( closed_subset @ SV14 @ SV6 ) )
= $true )
| ( ( top_str @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(113,plain,
( ( ( open_subset @ sK2_SY17 @ sK1_A )
= $false )
| ( ( closed_subset @ ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY17 ) @ sK1_A )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(114,plain,
! [SV6: $i,SV13: $i] :
( ( ( element @ SV13 @ ( powerset @ ( the_carrier @ SV6 ) ) )
= $false )
| ( ( ~ ( closed_subset @ SV13 @ SV6 )
| ( open_subset @ ( subset_complement @ ( the_carrier @ SV6 ) @ SV13 ) @ SV6 ) )
= $true )
| ( ( top_str @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(115,plain,
! [SV6: $i,SV14: $i] :
( ( ( element @ SV14 @ ( powerset @ ( the_carrier @ SV6 ) ) )
= $false )
| ( ( ~ ( open_subset @ ( subset_complement @ ( the_carrier @ SV6 ) @ SV14 ) @ SV6 )
| ( closed_subset @ SV14 @ SV6 ) )
= $true )
| ( ( top_str @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(116,plain,
! [SV6: $i,SV13: $i] :
( ( ( ~ ( closed_subset @ SV13 @ SV6 ) )
= $true )
| ( ( open_subset @ ( subset_complement @ ( the_carrier @ SV6 ) @ SV13 ) @ SV6 )
= $true )
| ( ( element @ SV13 @ ( powerset @ ( the_carrier @ SV6 ) ) )
= $false )
| ( ( top_str @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(117,plain,
! [SV14: $i,SV6: $i] :
( ( ( ~ ( open_subset @ ( subset_complement @ ( the_carrier @ SV6 ) @ SV14 ) @ SV6 ) )
= $true )
| ( ( closed_subset @ SV14 @ SV6 )
= $true )
| ( ( element @ SV14 @ ( powerset @ ( the_carrier @ SV6 ) ) )
= $false )
| ( ( top_str @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(118,plain,
! [SV6: $i,SV13: $i] :
( ( ( closed_subset @ SV13 @ SV6 )
= $false )
| ( ( open_subset @ ( subset_complement @ ( the_carrier @ SV6 ) @ SV13 ) @ SV6 )
= $true )
| ( ( element @ SV13 @ ( powerset @ ( the_carrier @ SV6 ) ) )
= $false )
| ( ( top_str @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(119,plain,
! [SV14: $i,SV6: $i] :
( ( ( open_subset @ ( subset_complement @ ( the_carrier @ SV6 ) @ SV14 ) @ SV6 )
= $false )
| ( ( closed_subset @ SV14 @ SV6 )
= $true )
| ( ( element @ SV14 @ ( powerset @ ( the_carrier @ SV6 ) ) )
= $false )
| ( ( top_str @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(120,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[44,119,118,113,107,106,105,87,86,81,79,66,64,57,51,50,49,48,47]) ).
thf(121,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU320+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.31 % Computer : n022.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 600
% 0.12/0.32 % DateTime : Mon Jun 20 11:19:31 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33
% 0.12/0.33 No.of.Axioms: 13
% 0.12/0.33
% 0.12/0.33 Length.of.Defs: 0
% 0.12/0.33
% 0.12/0.33 Contains.Choice.Funs: false
% 0.12/0.34 (rf:0,axioms:13,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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:15,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.17/0.40
% 0.17/0.40 ********************************
% 0.17/0.40 * All subproblems solved! *
% 0.17/0.40 ********************************
% 0.17/0.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:14,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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:120,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.17/0.41
% 0.17/0.41 %**** Beginning of derivation protocol ****
% 0.17/0.41 % SZS output start CNFRefutation
% See solution above
% 0.17/0.41
% 0.17/0.41 %**** End of derivation protocol ****
% 0.17/0.41 %**** no. of clauses in derivation: 121 ****
% 0.17/0.41 %**** clause counter: 120 ****
% 0.17/0.41
% 0.17/0.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:14,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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:120,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------