TSTP Solution File: SEU323-10 by LEO-II---1.7.0

View Problem - 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)
%------------------------------------------------------------------------------