TSTP Solution File: SEU323-10 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU323-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n017.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 12:10:29 EDT 2022
% Result : Unsatisfiable 0.68s 0.84s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 48
% Syntax : Number of formulae : 140 ( 118 unt; 22 typ; 0 def)
% Number of atoms : 300 ( 201 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 1296 ( 6 ~; 0 |; 0 &;1290 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 7 con; 0-4 aty)
% Number of variables : 164 ( 0 ^ 164 !; 0 ?; 164 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_closed_subset,type,
closed_subset: $i > $i > $i ).
thf(tp_element,type,
element: $i > $i > $i ).
thf(tp_ifeq,type,
ifeq: $i > $i > $i > $i > $i ).
thf(tp_ifeq2,type,
ifeq2: $i > $i > $i > $i > $i ).
thf(tp_interior,type,
interior: $i > $i > $i ).
thf(tp_one_sorted_str,type,
one_sorted_str: $i > $i ).
thf(tp_open_subset,type,
open_subset: $i > $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_sK1_t51_tops_1_B,type,
sK1_t51_tops_1_B: $i ).
thf(tp_sK2_t51_tops_1_A,type,
sK2_t51_tops_1_A: $i ).
thf(tp_sK3_rc1_tops_1_B,type,
sK3_rc1_tops_1_B: $i > $i ).
thf(tp_sK4_existence_m1_subset_1_B,type,
sK4_existence_m1_subset_1_B: $i > $i ).
thf(tp_sK5_existence_l1_pre_topc_A,type,
sK5_existence_l1_pre_topc_A: $i ).
thf(tp_sK6_existence_l1_struct_0_A,type,
sK6_existence_l1_struct_0_A: $i ).
thf(tp_sK7_rc6_pre_topc_B,type,
sK7_rc6_pre_topc_B: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $i ).
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 > $i ).
thf(tp_topological_space,type,
topological_space: $i > $i ).
thf(tp_topstr_closure,type,
topstr_closure: $i > $i > $i ).
thf(tp_true,type,
true: $i ).
thf(1,axiom,
! [B: $i,A: $i] :
( ( ifeq2 @ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) @ true @ ( ifeq2 @ ( top_str @ A ) @ true @ ( subset_complement @ ( the_carrier @ A ) @ ( topstr_closure @ A @ ( subset_complement @ ( the_carrier @ A ) @ B ) ) ) @ ( interior @ A @ B ) ) @ ( interior @ A @ B ) )
= ( interior @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tops_1) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( ifeq @ ( element @ A @ ( powerset @ B ) ) @ true @ ( subset @ A @ B ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ifeq @ ( subset @ A @ B ) @ true @ ( element @ A @ ( powerset @ B ) ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset_1) ).
thf(4,axiom,
! [A: $i] :
( ( ifeq @ ( topological_space @ A ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( element @ ( sK3_rc1_tops_1_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_tops_1) ).
thf(5,axiom,
! [A: $i] :
( ( ifeq @ ( topological_space @ A ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( open_subset @ ( sK3_rc1_tops_1_B @ A ) @ A ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_tops_1_1) ).
thf(6,axiom,
! [A: $i] :
( ( ifeq @ ( top_str @ A ) @ true @ ( one_sorted_str @ A ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( ifeq @ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( element @ ( interior @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tops_1) ).
thf(8,axiom,
! [A: $i] :
( ( element @ ( sK4_existence_m1_subset_1_B @ A ) @ A )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(9,axiom,
( ( top_str @ sK5_existence_l1_pre_topc_A )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( ifeq @ ( open_subset @ B @ A ) @ true @ ( ifeq @ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) @ true @ ( ifeq @ ( topological_space @ A ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( closed_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) @ true ) @ true ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_tops_1) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( ifeq @ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) @ true @ ( ifeq @ ( topological_space @ A ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( closed_subset @ ( topstr_closure @ A @ B ) @ A ) @ true ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_tops_1) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( ifeq @ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( element @ ( topstr_closure @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( ifeq @ ( element @ B @ ( powerset @ A ) ) @ true @ ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(14,axiom,
( ( one_sorted_str @ sK6_existence_l1_struct_0_A )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(15,axiom,
! [A: $i] :
( ( subset @ A @ A )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( ifeq2 @ ( element @ B @ ( powerset @ A ) ) @ true @ ( subset_complement @ A @ ( subset_complement @ A @ B ) ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(17,axiom,
! [A: $i] :
( ( ifeq @ ( topological_space @ A ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( closed_subset @ ( sK7_rc6_pre_topc_B @ A ) @ A ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_pre_topc) ).
thf(18,axiom,
! [A: $i] :
( ( ifeq @ ( topological_space @ A ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( element @ ( sK7_rc6_pre_topc_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_pre_topc_1) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( ifeq @ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) @ true @ ( ifeq @ ( closed_subset @ B @ A ) @ true @ ( ifeq @ ( topological_space @ A ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( open_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) @ true ) @ true ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_tops_1) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(22,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(23,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[22]) ).
thf(24,negated_conjecture,
( open_subset @ ( interior @ sK2_t51_tops_1_A @ sK1_t51_tops_1_B ) @ sK2_t51_tops_1_A )
!= true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1_3) ).
thf(25,negated_conjecture,
( ( element @ sK1_t51_tops_1_B @ ( powerset @ ( the_carrier @ sK2_t51_tops_1_A ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1_2) ).
thf(26,negated_conjecture,
( ( topological_space @ sK2_t51_tops_1_A )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1_1) ).
thf(27,negated_conjecture,
( ( top_str @ sK2_t51_tops_1_A )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1) ).
thf(28,plain,
$false = $false,
inference(unfold_def,[status(thm)],[23]) ).
thf(29,plain,
( ( ! [B: $i,A: $i] :
( ( ifeq2 @ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) @ true @ ( ifeq2 @ ( top_str @ A ) @ true @ ( subset_complement @ ( the_carrier @ A ) @ ( topstr_closure @ A @ ( subset_complement @ ( the_carrier @ A ) @ B ) ) ) @ ( interior @ A @ B ) ) @ ( interior @ A @ B ) )
= ( interior @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(30,plain,
( ( ! [A: $i,B: $i] :
( ( ifeq @ ( element @ A @ ( powerset @ B ) ) @ true @ ( subset @ A @ B ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(31,plain,
( ( ! [A: $i,B: $i] :
( ( ifeq @ ( subset @ A @ B ) @ true @ ( element @ A @ ( powerset @ B ) ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(32,plain,
( ( ! [A: $i] :
( ( ifeq @ ( topological_space @ A ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( element @ ( sK3_rc1_tops_1_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(33,plain,
( ( ! [A: $i] :
( ( ifeq @ ( topological_space @ A ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( open_subset @ ( sK3_rc1_tops_1_B @ A ) @ A ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(34,plain,
( ( ! [A: $i] :
( ( ifeq @ ( top_str @ A ) @ true @ ( one_sorted_str @ A ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(35,plain,
( ( ! [B: $i,A: $i] :
( ( ifeq @ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( element @ ( interior @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(36,plain,
( ( ! [A: $i] :
( ( element @ ( sK4_existence_m1_subset_1_B @ A ) @ A )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(37,plain,
( ( ( top_str @ sK5_existence_l1_pre_topc_A )
= true )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(38,plain,
( ( ! [B: $i,A: $i] :
( ( ifeq @ ( open_subset @ B @ A ) @ true @ ( ifeq @ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) @ true @ ( ifeq @ ( topological_space @ A ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( closed_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(39,plain,
( ( ! [B: $i,A: $i] :
( ( ifeq @ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) @ true @ ( ifeq @ ( topological_space @ A ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( closed_subset @ ( topstr_closure @ A @ B ) @ A ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(40,plain,
( ( ! [B: $i,A: $i] :
( ( ifeq @ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( element @ ( topstr_closure @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(41,plain,
( ( ! [B: $i,A: $i] :
( ( ifeq @ ( element @ B @ ( powerset @ A ) ) @ true @ ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(42,plain,
( ( ( one_sorted_str @ sK6_existence_l1_struct_0_A )
= true )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(43,plain,
( ( ! [A: $i] :
( ( subset @ A @ A )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(44,plain,
( ( ! [B: $i,A: $i] :
( ( ifeq2 @ ( element @ B @ ( powerset @ A ) ) @ true @ ( subset_complement @ A @ ( subset_complement @ A @ B ) ) @ B )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(45,plain,
( ( ! [A: $i] :
( ( ifeq @ ( topological_space @ A ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( closed_subset @ ( sK7_rc6_pre_topc_B @ A ) @ A ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(46,plain,
( ( ! [A: $i] :
( ( ifeq @ ( topological_space @ A ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( element @ ( sK7_rc6_pre_topc_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(47,plain,
( ( ! [B: $i,A: $i] :
( ( ifeq @ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) @ true @ ( ifeq @ ( closed_subset @ B @ A ) @ true @ ( ifeq @ ( topological_space @ A ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( open_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(48,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(49,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(50,plain,
( ( ( ( open_subset @ ( interior @ sK2_t51_tops_1_A @ sK1_t51_tops_1_B ) @ sK2_t51_tops_1_A )
!= true ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(51,plain,
( ( ( element @ sK1_t51_tops_1_B @ ( powerset @ ( the_carrier @ sK2_t51_tops_1_A ) ) )
= true )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(52,plain,
( ( ( topological_space @ sK2_t51_tops_1_A )
= true )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(53,plain,
( ( ( top_str @ sK2_t51_tops_1_A )
= true )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(54,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[28]) ).
thf(55,plain,
( ( ( ( open_subset @ ( interior @ sK2_t51_tops_1_A @ sK1_t51_tops_1_B ) @ sK2_t51_tops_1_A )
!= true ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(56,plain,
( ( ( top_str @ sK2_t51_tops_1_A )
= true )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(57,plain,
( ( ( topological_space @ sK2_t51_tops_1_A )
= true )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(58,plain,
( ( ( element @ sK1_t51_tops_1_B @ ( powerset @ ( the_carrier @ sK2_t51_tops_1_A ) ) )
= true )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(59,plain,
( ( ( ( open_subset @ ( interior @ sK2_t51_tops_1_A @ sK1_t51_tops_1_B ) @ sK2_t51_tops_1_A )
!= true ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(60,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(61,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(62,plain,
( ( ! [B: $i,A: $i] :
( ( ifeq @ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) @ true @ ( ifeq @ ( closed_subset @ B @ A ) @ true @ ( ifeq @ ( topological_space @ A ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( open_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(63,plain,
( ( ! [A: $i] :
( ( ifeq @ ( topological_space @ A ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( element @ ( sK7_rc6_pre_topc_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(64,plain,
( ( ! [A: $i] :
( ( ifeq @ ( topological_space @ A ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( closed_subset @ ( sK7_rc6_pre_topc_B @ A ) @ A ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(65,plain,
( ( ! [B: $i,A: $i] :
( ( ifeq2 @ ( element @ B @ ( powerset @ A ) ) @ true @ ( subset_complement @ A @ ( subset_complement @ A @ B ) ) @ B )
= B ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(66,plain,
( ( ! [A: $i] :
( ( subset @ A @ A )
= true ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(67,plain,
( ( ( one_sorted_str @ sK6_existence_l1_struct_0_A )
= true )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(68,plain,
( ( ! [B: $i,A: $i] :
( ( ifeq @ ( element @ B @ ( powerset @ A ) ) @ true @ ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(69,plain,
( ( ! [B: $i,A: $i] :
( ( ifeq @ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( element @ ( topstr_closure @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(70,plain,
( ( ! [B: $i,A: $i] :
( ( ifeq @ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) @ true @ ( ifeq @ ( topological_space @ A ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( closed_subset @ ( topstr_closure @ A @ B ) @ A ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(71,plain,
( ( ! [B: $i,A: $i] :
( ( ifeq @ ( open_subset @ B @ A ) @ true @ ( ifeq @ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) @ true @ ( ifeq @ ( topological_space @ A ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( closed_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(72,plain,
( ( ( top_str @ sK5_existence_l1_pre_topc_A )
= true )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(73,plain,
( ( ! [A: $i] :
( ( element @ ( sK4_existence_m1_subset_1_B @ A ) @ A )
= true ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(74,plain,
( ( ! [B: $i,A: $i] :
( ( ifeq @ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( element @ ( interior @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(75,plain,
( ( ! [A: $i] :
( ( ifeq @ ( top_str @ A ) @ true @ ( one_sorted_str @ A ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(76,plain,
( ( ! [A: $i] :
( ( ifeq @ ( topological_space @ A ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( open_subset @ ( sK3_rc1_tops_1_B @ A ) @ A ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(77,plain,
( ( ! [A: $i] :
( ( ifeq @ ( topological_space @ A ) @ true @ ( ifeq @ ( top_str @ A ) @ true @ ( element @ ( sK3_rc1_tops_1_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(78,plain,
( ( ! [A: $i,B: $i] :
( ( ifeq @ ( subset @ A @ B ) @ true @ ( element @ A @ ( powerset @ B ) ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
( ( ifeq @ ( element @ A @ ( powerset @ B ) ) @ true @ ( subset @ A @ B ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(80,plain,
( ( ! [B: $i,A: $i] :
( ( ifeq2 @ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) @ true @ ( ifeq2 @ ( top_str @ A ) @ true @ ( subset_complement @ ( the_carrier @ A ) @ ( topstr_closure @ A @ ( subset_complement @ ( the_carrier @ A ) @ B ) ) ) @ ( interior @ A @ B ) ) @ ( interior @ A @ B ) )
= ( interior @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(81,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(82,plain,
( ( ( open_subset @ ( interior @ sK2_t51_tops_1_A @ sK1_t51_tops_1_B ) @ sK2_t51_tops_1_A )
= true )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(83,plain,
! [SV1: $i] :
( ( ! [SY33: $i,SY34: $i] :
( ( ifeq2 @ SV1 @ SV1 @ SY33 @ SY34 )
= SY33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(84,plain,
! [SV2: $i] :
( ( ! [SY35: $i,SY36: $i] :
( ( ifeq @ SV2 @ SV2 @ SY35 @ SY36 )
= SY35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(85,plain,
! [SV3: $i] :
( ( ! [SY37: $i] :
( ( ifeq @ ( element @ SV3 @ ( powerset @ ( the_carrier @ SY37 ) ) ) @ true @ ( ifeq @ ( closed_subset @ SV3 @ SY37 ) @ true @ ( ifeq @ ( topological_space @ SY37 ) @ true @ ( ifeq @ ( top_str @ SY37 ) @ true @ ( open_subset @ ( subset_complement @ ( the_carrier @ SY37 ) @ SV3 ) @ SY37 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(86,plain,
! [SV4: $i] :
( ( ( ifeq @ ( topological_space @ SV4 ) @ true @ ( ifeq @ ( top_str @ SV4 ) @ true @ ( element @ ( sK7_rc6_pre_topc_B @ SV4 ) @ ( powerset @ ( the_carrier @ SV4 ) ) ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(87,plain,
! [SV5: $i] :
( ( ( ifeq @ ( topological_space @ SV5 ) @ true @ ( ifeq @ ( top_str @ SV5 ) @ true @ ( closed_subset @ ( sK7_rc6_pre_topc_B @ SV5 ) @ SV5 ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(88,plain,
! [SV6: $i] :
( ( ! [SY38: $i] :
( ( ifeq2 @ ( element @ SV6 @ ( powerset @ SY38 ) ) @ true @ ( subset_complement @ SY38 @ ( subset_complement @ SY38 @ SV6 ) ) @ SV6 )
= SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(89,plain,
! [SV7: $i] :
( ( ( subset @ SV7 @ SV7 )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(90,plain,
! [SV8: $i] :
( ( ! [SY39: $i] :
( ( ifeq @ ( element @ SV8 @ ( powerset @ SY39 ) ) @ true @ ( element @ ( subset_complement @ SY39 @ SV8 ) @ ( powerset @ SY39 ) ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(91,plain,
! [SV9: $i] :
( ( ! [SY40: $i] :
( ( ifeq @ ( element @ SV9 @ ( powerset @ ( the_carrier @ SY40 ) ) ) @ true @ ( ifeq @ ( top_str @ SY40 ) @ true @ ( element @ ( topstr_closure @ SY40 @ SV9 ) @ ( powerset @ ( the_carrier @ SY40 ) ) ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(92,plain,
! [SV10: $i] :
( ( ! [SY41: $i] :
( ( ifeq @ ( element @ SV10 @ ( powerset @ ( the_carrier @ SY41 ) ) ) @ true @ ( ifeq @ ( topological_space @ SY41 ) @ true @ ( ifeq @ ( top_str @ SY41 ) @ true @ ( closed_subset @ ( topstr_closure @ SY41 @ SV10 ) @ SY41 ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(93,plain,
! [SV11: $i] :
( ( ! [SY42: $i] :
( ( ifeq @ ( open_subset @ SV11 @ SY42 ) @ true @ ( ifeq @ ( element @ SV11 @ ( powerset @ ( the_carrier @ SY42 ) ) ) @ true @ ( ifeq @ ( topological_space @ SY42 ) @ true @ ( ifeq @ ( top_str @ SY42 ) @ true @ ( closed_subset @ ( subset_complement @ ( the_carrier @ SY42 ) @ SV11 ) @ SY42 ) @ true ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(94,plain,
! [SV12: $i] :
( ( ( element @ ( sK4_existence_m1_subset_1_B @ SV12 ) @ SV12 )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(95,plain,
! [SV13: $i] :
( ( ! [SY43: $i] :
( ( ifeq @ ( element @ SV13 @ ( powerset @ ( the_carrier @ SY43 ) ) ) @ true @ ( ifeq @ ( top_str @ SY43 ) @ true @ ( element @ ( interior @ SY43 @ SV13 ) @ ( powerset @ ( the_carrier @ SY43 ) ) ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(96,plain,
! [SV14: $i] :
( ( ( ifeq @ ( top_str @ SV14 ) @ true @ ( one_sorted_str @ SV14 ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(97,plain,
! [SV15: $i] :
( ( ( ifeq @ ( topological_space @ SV15 ) @ true @ ( ifeq @ ( top_str @ SV15 ) @ true @ ( open_subset @ ( sK3_rc1_tops_1_B @ SV15 ) @ SV15 ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(98,plain,
! [SV16: $i] :
( ( ( ifeq @ ( topological_space @ SV16 ) @ true @ ( ifeq @ ( top_str @ SV16 ) @ true @ ( element @ ( sK3_rc1_tops_1_B @ SV16 ) @ ( powerset @ ( the_carrier @ SV16 ) ) ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(99,plain,
! [SV17: $i] :
( ( ! [SY44: $i] :
( ( ifeq @ ( subset @ SV17 @ SY44 ) @ true @ ( element @ SV17 @ ( powerset @ SY44 ) ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(100,plain,
! [SV18: $i] :
( ( ! [SY45: $i] :
( ( ifeq @ ( element @ SV18 @ ( powerset @ SY45 ) ) @ true @ ( subset @ SV18 @ SY45 ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(101,plain,
! [SV19: $i] :
( ( ! [SY46: $i] :
( ( ifeq2 @ ( element @ SV19 @ ( powerset @ ( the_carrier @ SY46 ) ) ) @ true @ ( ifeq2 @ ( top_str @ SY46 ) @ true @ ( subset_complement @ ( the_carrier @ SY46 ) @ ( topstr_closure @ SY46 @ ( subset_complement @ ( the_carrier @ SY46 ) @ SV19 ) ) ) @ ( interior @ SY46 @ SV19 ) ) @ ( interior @ SY46 @ SV19 ) )
= ( interior @ SY46 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(102,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(103,plain,
! [SV20: $i,SV1: $i] :
( ( ! [SY47: $i] :
( ( ifeq2 @ SV1 @ SV1 @ SV20 @ SY47 )
= SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(104,plain,
! [SV21: $i,SV2: $i] :
( ( ! [SY48: $i] :
( ( ifeq @ SV2 @ SV2 @ SV21 @ SY48 )
= SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(105,plain,
! [SV22: $i,SV3: $i] :
( ( ( ifeq @ ( element @ SV3 @ ( powerset @ ( the_carrier @ SV22 ) ) ) @ true @ ( ifeq @ ( closed_subset @ SV3 @ SV22 ) @ true @ ( ifeq @ ( topological_space @ SV22 ) @ true @ ( ifeq @ ( top_str @ SV22 ) @ true @ ( open_subset @ ( subset_complement @ ( the_carrier @ SV22 ) @ SV3 ) @ SV22 ) @ true ) @ true ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(106,plain,
! [SV23: $i,SV6: $i] :
( ( ( ifeq2 @ ( element @ SV6 @ ( powerset @ SV23 ) ) @ true @ ( subset_complement @ SV23 @ ( subset_complement @ SV23 @ SV6 ) ) @ SV6 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(107,plain,
! [SV24: $i,SV8: $i] :
( ( ( ifeq @ ( element @ SV8 @ ( powerset @ SV24 ) ) @ true @ ( element @ ( subset_complement @ SV24 @ SV8 ) @ ( powerset @ SV24 ) ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(108,plain,
! [SV25: $i,SV9: $i] :
( ( ( ifeq @ ( element @ SV9 @ ( powerset @ ( the_carrier @ SV25 ) ) ) @ true @ ( ifeq @ ( top_str @ SV25 ) @ true @ ( element @ ( topstr_closure @ SV25 @ SV9 ) @ ( powerset @ ( the_carrier @ SV25 ) ) ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(109,plain,
! [SV26: $i,SV10: $i] :
( ( ( ifeq @ ( element @ SV10 @ ( powerset @ ( the_carrier @ SV26 ) ) ) @ true @ ( ifeq @ ( topological_space @ SV26 ) @ true @ ( ifeq @ ( top_str @ SV26 ) @ true @ ( closed_subset @ ( topstr_closure @ SV26 @ SV10 ) @ SV26 ) @ true ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(110,plain,
! [SV27: $i,SV11: $i] :
( ( ( ifeq @ ( open_subset @ SV11 @ SV27 ) @ true @ ( ifeq @ ( element @ SV11 @ ( powerset @ ( the_carrier @ SV27 ) ) ) @ true @ ( ifeq @ ( topological_space @ SV27 ) @ true @ ( ifeq @ ( top_str @ SV27 ) @ true @ ( closed_subset @ ( subset_complement @ ( the_carrier @ SV27 ) @ SV11 ) @ SV27 ) @ true ) @ true ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(111,plain,
! [SV28: $i,SV13: $i] :
( ( ( ifeq @ ( element @ SV13 @ ( powerset @ ( the_carrier @ SV28 ) ) ) @ true @ ( ifeq @ ( top_str @ SV28 ) @ true @ ( element @ ( interior @ SV28 @ SV13 ) @ ( powerset @ ( the_carrier @ SV28 ) ) ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(112,plain,
! [SV29: $i,SV17: $i] :
( ( ( ifeq @ ( subset @ SV17 @ SV29 ) @ true @ ( element @ SV17 @ ( powerset @ SV29 ) ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(113,plain,
! [SV30: $i,SV18: $i] :
( ( ( ifeq @ ( element @ SV18 @ ( powerset @ SV30 ) ) @ true @ ( subset @ SV18 @ SV30 ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(114,plain,
! [SV31: $i,SV19: $i] :
( ( ( ifeq2 @ ( element @ SV19 @ ( powerset @ ( the_carrier @ SV31 ) ) ) @ true @ ( ifeq2 @ ( top_str @ SV31 ) @ true @ ( subset_complement @ ( the_carrier @ SV31 ) @ ( topstr_closure @ SV31 @ ( subset_complement @ ( the_carrier @ SV31 ) @ SV19 ) ) ) @ ( interior @ SV31 @ SV19 ) ) @ ( interior @ SV31 @ SV19 ) )
= ( interior @ SV31 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(115,plain,
! [SV32: $i,SV20: $i,SV1: $i] :
( ( ( ifeq2 @ SV1 @ SV1 @ SV20 @ SV32 )
= SV20 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(116,plain,
! [SV33: $i,SV21: $i,SV2: $i] :
( ( ( ifeq @ SV2 @ SV2 @ SV21 @ SV33 )
= SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(117,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[56,116,115,114,113,112,111,110,109,108,107,106,105,102,98,97,96,94,89,87,86,82,72,67,58,57]) ).
thf(118,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU323-10 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jun 19 18:12:28 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.38
% 0.14/0.38 No.of.Axioms: 25
% 0.14/0.38
% 0.14/0.38 Length.of.Defs: 0
% 0.14/0.38
% 0.14/0.38 Contains.Choice.Funs: false
% 0.21/0.41 .
% 0.21/0.41 (rf:0,axioms:25,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:27,loop_count:0,foatp_calls:0,translation:fof_full)......
% 0.68/0.84
% 0.68/0.84 ********************************
% 0.68/0.84 * All subproblems solved! *
% 0.68/0.84 ********************************
% 0.68/0.84 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:25,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:117,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.68/0.84
% 0.68/0.84 %**** Beginning of derivation protocol ****
% 0.68/0.84 % SZS output start CNFRefutation
% See solution above
% 0.68/0.85
% 0.68/0.85 %**** End of derivation protocol ****
% 0.68/0.85 %**** no. of clauses in derivation: 118 ****
% 0.68/0.85 %**** clause counter: 117 ****
% 0.68/0.85
% 0.68/0.85 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:25,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:117,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------