TSTP Solution File: TOP001-2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : TOP001-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n024.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 : Thu Jul 21 21:31:40 EDT 2022

% Result   : Unsatisfiable 0.20s 0.41s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   26
% Syntax   : Number of formulae    :  117 (  64 unt;  12 typ;   0 def)
%            Number of atoms       :  495 ( 130 equ;   0 cnn)
%            Maximal formula atoms :    3 (   4 avg)
%            Number of connectives :  873 ( 105   ~; 130   |;   0   &; 638   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (  19   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  12 usr;   4 con; 0-3 aty)
%            Number of variables   :  220 (   0   ^ 220   !;   0   ?; 220   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_basis,type,
    basis: $i > $i > $o ).

thf(tp_cx,type,
    cx: $i ).

thf(tp_element_of_collection,type,
    element_of_collection: $i > $i > $o ).

thf(tp_element_of_set,type,
    element_of_set: $i > $i > $o ).

thf(tp_equal_sets,type,
    equal_sets: $i > $i > $o ).

thf(tp_f,type,
    f: $i ).

thf(tp_f1,type,
    f1: $i > $i > $i ).

thf(tp_f10,type,
    f10: $i > $i > $i > $i ).

thf(tp_in_1st_set,type,
    in_1st_set: $i > $i > $i ).

thf(tp_subset_sets,type,
    subset_sets: $i > $i > $o ).

thf(tp_top_of_basis,type,
    top_of_basis: $i > $i ).

thf(tp_union_of_members,type,
    union_of_members: $i > $i ).

thf(1,axiom,
    ! [X: $i,Y: $i] :
      ( ( subset_sets @ X @ Y )
      | ~ ( element_of_set @ ( in_1st_set @ X @ Y ) @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_5) ).

thf(2,axiom,
    ! [X: $i,Y: $i] :
      ( ( subset_sets @ X @ Y )
      | ( element_of_set @ ( in_1st_set @ X @ Y ) @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_4) ).

thf(3,axiom,
    ! [X: $i,Y: $i] :
      ( ~ ( equal_sets @ X @ Y )
      | ( subset_sets @ X @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_3) ).

thf(4,axiom,
    ! [X: $i,Y: $i,U: $i] :
      ( ~ ( subset_sets @ X @ Y )
      | ~ ( element_of_set @ U @ X )
      | ( element_of_set @ U @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_2) ).

thf(5,axiom,
    ! [X: $i] : ( subset_sets @ X @ X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_1) ).

thf(6,axiom,
    ! [U: $i,Vf: $i,X: $i] :
      ( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
      | ~ ( element_of_set @ X @ U )
      | ( element_of_collection @ ( f10 @ Vf @ U @ X ) @ Vf ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',topology_generated_38) ).

thf(7,axiom,
    ! [U: $i,Vf: $i,X: $i] :
      ( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
      | ~ ( element_of_set @ X @ U )
      | ( element_of_set @ X @ ( f10 @ Vf @ U @ X ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',topology_generated_37) ).

thf(8,axiom,
    ! [X: $i,Vf: $i] :
      ( ~ ( basis @ X @ Vf )
      | ( equal_sets @ ( union_of_members @ Vf ) @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_for_topology_28) ).

thf(9,axiom,
    ! [U: $i,Vf: $i,Uu1: $i] :
      ( ( element_of_set @ U @ ( union_of_members @ Vf ) )
      | ~ ( element_of_set @ U @ Uu1 )
      | ~ ( element_of_collection @ Uu1 @ Vf ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_of_members_3) ).

thf(10,axiom,
    ! [U: $i,Vf: $i] :
      ( ~ ( element_of_set @ U @ ( union_of_members @ Vf ) )
      | ( element_of_collection @ ( f1 @ Vf @ U ) @ Vf ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_of_members_2) ).

thf(11,axiom,
    ! [U: $i,Vf: $i] :
      ( ~ ( element_of_set @ U @ ( union_of_members @ Vf ) )
      | ( element_of_set @ U @ ( f1 @ Vf @ U ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_of_members_1) ).

thf(12,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(13,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[12]) ).

thf(14,negated_conjecture,
    ~ ( subset_sets @ ( union_of_members @ ( top_of_basis @ f ) ) @ cx ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1a_2) ).

thf(15,negated_conjecture,
    basis @ cx @ f,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1a_1) ).

thf(16,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[13]) ).

thf(17,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( subset_sets @ X @ Y )
          | ~ ( element_of_set @ ( in_1st_set @ X @ Y ) @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(18,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( subset_sets @ X @ Y )
          | ( element_of_set @ ( in_1st_set @ X @ Y ) @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(19,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equal_sets @ X @ Y )
          | ( subset_sets @ X @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(20,plain,
    ( ( ! [X: $i,Y: $i,U: $i] :
          ( ~ ( subset_sets @ X @ Y )
          | ~ ( element_of_set @ U @ X )
          | ( element_of_set @ U @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(21,plain,
    ( ( ! [X: $i] : ( subset_sets @ X @ X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(22,plain,
    ( ( ! [U: $i,Vf: $i,X: $i] :
          ( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
          | ~ ( element_of_set @ X @ U )
          | ( element_of_collection @ ( f10 @ Vf @ U @ X ) @ Vf ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(23,plain,
    ( ( ! [U: $i,Vf: $i,X: $i] :
          ( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
          | ~ ( element_of_set @ X @ U )
          | ( element_of_set @ X @ ( f10 @ Vf @ U @ X ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(24,plain,
    ( ( ! [X: $i,Vf: $i] :
          ( ~ ( basis @ X @ Vf )
          | ( equal_sets @ ( union_of_members @ Vf ) @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(25,plain,
    ( ( ! [U: $i,Vf: $i,Uu1: $i] :
          ( ( element_of_set @ U @ ( union_of_members @ Vf ) )
          | ~ ( element_of_set @ U @ Uu1 )
          | ~ ( element_of_collection @ Uu1 @ Vf ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(26,plain,
    ( ( ! [U: $i,Vf: $i] :
          ( ~ ( element_of_set @ U @ ( union_of_members @ Vf ) )
          | ( element_of_collection @ ( f1 @ Vf @ U ) @ Vf ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(27,plain,
    ( ( ! [U: $i,Vf: $i] :
          ( ~ ( element_of_set @ U @ ( union_of_members @ Vf ) )
          | ( element_of_set @ U @ ( f1 @ Vf @ U ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(28,plain,
    ( ( ~ ( subset_sets @ ( union_of_members @ ( top_of_basis @ f ) ) @ cx ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(29,plain,
    ( ( basis @ cx @ f )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(30,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[16]) ).

thf(31,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( element_of_set @ ( in_1st_set @ X @ Y ) @ X )
          | ( subset_sets @ X @ Y ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[18]) ).

thf(32,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( subset_sets @ X @ Y )
          | ! [U: $i] :
              ( ~ ( element_of_set @ U @ X )
              | ( element_of_set @ U @ Y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[20]) ).

thf(33,plain,
    ( ( ! [U: $i,Vf: $i] :
          ( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
          | ! [X: $i] :
              ( ~ ( element_of_set @ X @ U )
              | ( element_of_collection @ ( f10 @ Vf @ U @ X ) @ Vf ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[22]) ).

thf(34,plain,
    ( ( ! [U: $i,Vf: $i] :
          ( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
          | ! [X: $i] :
              ( ~ ( element_of_set @ X @ U )
              | ( element_of_set @ X @ ( f10 @ Vf @ U @ X ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[23]) ).

thf(35,plain,
    ( ( ! [U: $i,Vf: $i] :
          ( ( element_of_set @ U @ ( union_of_members @ Vf ) )
          | ! [Uu1: $i] :
              ( ~ ( element_of_set @ U @ Uu1 )
              | ~ ( element_of_collection @ Uu1 @ Vf ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[25]) ).

thf(36,plain,
    ( ( basis @ cx @ f )
    = $true ),
    inference(copy,[status(thm)],[29]) ).

thf(37,plain,
    ( ( ~ ( subset_sets @ ( union_of_members @ ( top_of_basis @ f ) ) @ cx ) )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(38,plain,
    ( ( ! [U: $i,Vf: $i] :
          ( ~ ( element_of_set @ U @ ( union_of_members @ Vf ) )
          | ( element_of_set @ U @ ( f1 @ Vf @ U ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(39,plain,
    ( ( ! [U: $i,Vf: $i] :
          ( ~ ( element_of_set @ U @ ( union_of_members @ Vf ) )
          | ( element_of_collection @ ( f1 @ Vf @ U ) @ Vf ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(40,plain,
    ( ( ! [U: $i,Vf: $i] :
          ( ( element_of_set @ U @ ( union_of_members @ Vf ) )
          | ! [Uu1: $i] :
              ( ~ ( element_of_set @ U @ Uu1 )
              | ~ ( element_of_collection @ Uu1 @ Vf ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(41,plain,
    ( ( ! [X: $i,Vf: $i] :
          ( ~ ( basis @ X @ Vf )
          | ( equal_sets @ ( union_of_members @ Vf ) @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(42,plain,
    ( ( ! [U: $i,Vf: $i] :
          ( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
          | ! [X: $i] :
              ( ~ ( element_of_set @ X @ U )
              | ( element_of_set @ X @ ( f10 @ Vf @ U @ X ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

thf(43,plain,
    ( ( ! [U: $i,Vf: $i] :
          ( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
          | ! [X: $i] :
              ( ~ ( element_of_set @ X @ U )
              | ( element_of_collection @ ( f10 @ Vf @ U @ X ) @ Vf ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(44,plain,
    ( ( ! [X: $i] : ( subset_sets @ X @ X ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(45,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( subset_sets @ X @ Y )
          | ! [U: $i] :
              ( ~ ( element_of_set @ U @ X )
              | ( element_of_set @ U @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(46,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equal_sets @ X @ Y )
          | ( subset_sets @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[19]) ).

thf(47,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( element_of_set @ ( in_1st_set @ X @ Y ) @ X )
          | ( subset_sets @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(48,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( subset_sets @ X @ Y )
          | ~ ( element_of_set @ ( in_1st_set @ X @ Y ) @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(49,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(50,plain,
    ( ( subset_sets @ ( union_of_members @ ( top_of_basis @ f ) ) @ cx )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[37]) ).

thf(51,plain,
    ! [SV1: $i] :
      ( ( ! [SY25: $i] :
            ( ~ ( element_of_set @ SV1 @ ( union_of_members @ SY25 ) )
            | ( element_of_set @ SV1 @ ( f1 @ SY25 @ SV1 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(52,plain,
    ! [SV2: $i] :
      ( ( ! [SY26: $i] :
            ( ~ ( element_of_set @ SV2 @ ( union_of_members @ SY26 ) )
            | ( element_of_collection @ ( f1 @ SY26 @ SV2 ) @ SY26 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[39]) ).

thf(53,plain,
    ! [SV3: $i] :
      ( ( ! [SY27: $i] :
            ( ( element_of_set @ SV3 @ ( union_of_members @ SY27 ) )
            | ! [SY28: $i] :
                ( ~ ( element_of_set @ SV3 @ SY28 )
                | ~ ( element_of_collection @ SY28 @ SY27 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[40]) ).

thf(54,plain,
    ! [SV4: $i] :
      ( ( ! [SY29: $i] :
            ( ~ ( basis @ SV4 @ SY29 )
            | ( equal_sets @ ( union_of_members @ SY29 ) @ SV4 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(55,plain,
    ! [SV5: $i] :
      ( ( ! [SY30: $i] :
            ( ~ ( element_of_collection @ SV5 @ ( top_of_basis @ SY30 ) )
            | ! [SY31: $i] :
                ( ~ ( element_of_set @ SY31 @ SV5 )
                | ( element_of_set @ SY31 @ ( f10 @ SY30 @ SV5 @ SY31 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(56,plain,
    ! [SV6: $i] :
      ( ( ! [SY32: $i] :
            ( ~ ( element_of_collection @ SV6 @ ( top_of_basis @ SY32 ) )
            | ! [SY33: $i] :
                ( ~ ( element_of_set @ SY33 @ SV6 )
                | ( element_of_collection @ ( f10 @ SY32 @ SV6 @ SY33 ) @ SY32 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(57,plain,
    ! [SV7: $i] :
      ( ( subset_sets @ SV7 @ SV7 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(58,plain,
    ! [SV8: $i] :
      ( ( ! [SY34: $i] :
            ( ~ ( subset_sets @ SV8 @ SY34 )
            | ! [SY35: $i] :
                ( ~ ( element_of_set @ SY35 @ SV8 )
                | ( element_of_set @ SY35 @ SY34 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[45]) ).

thf(59,plain,
    ! [SV9: $i] :
      ( ( ! [SY36: $i] :
            ( ~ ( equal_sets @ SV9 @ SY36 )
            | ( subset_sets @ SV9 @ SY36 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[46]) ).

thf(60,plain,
    ! [SV10: $i] :
      ( ( ! [SY37: $i] :
            ( ( element_of_set @ ( in_1st_set @ SV10 @ SY37 ) @ SV10 )
            | ( subset_sets @ SV10 @ SY37 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[47]) ).

thf(61,plain,
    ! [SV11: $i] :
      ( ( ! [SY38: $i] :
            ( ( subset_sets @ SV11 @ SY38 )
            | ~ ( element_of_set @ ( in_1st_set @ SV11 @ SY38 ) @ SY38 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(62,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[49]) ).

thf(63,plain,
    ! [SV12: $i,SV1: $i] :
      ( ( ~ ( element_of_set @ SV1 @ ( union_of_members @ SV12 ) )
        | ( element_of_set @ SV1 @ ( f1 @ SV12 @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(64,plain,
    ! [SV13: $i,SV2: $i] :
      ( ( ~ ( element_of_set @ SV2 @ ( union_of_members @ SV13 ) )
        | ( element_of_collection @ ( f1 @ SV13 @ SV2 ) @ SV13 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(65,plain,
    ! [SV14: $i,SV3: $i] :
      ( ( ( element_of_set @ SV3 @ ( union_of_members @ SV14 ) )
        | ! [SY39: $i] :
            ( ~ ( element_of_set @ SV3 @ SY39 )
            | ~ ( element_of_collection @ SY39 @ SV14 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(66,plain,
    ! [SV15: $i,SV4: $i] :
      ( ( ~ ( basis @ SV4 @ SV15 )
        | ( equal_sets @ ( union_of_members @ SV15 ) @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(67,plain,
    ! [SV16: $i,SV5: $i] :
      ( ( ~ ( element_of_collection @ SV5 @ ( top_of_basis @ SV16 ) )
        | ! [SY40: $i] :
            ( ~ ( element_of_set @ SY40 @ SV5 )
            | ( element_of_set @ SY40 @ ( f10 @ SV16 @ SV5 @ SY40 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[55]) ).

thf(68,plain,
    ! [SV17: $i,SV6: $i] :
      ( ( ~ ( element_of_collection @ SV6 @ ( top_of_basis @ SV17 ) )
        | ! [SY41: $i] :
            ( ~ ( element_of_set @ SY41 @ SV6 )
            | ( element_of_collection @ ( f10 @ SV17 @ SV6 @ SY41 ) @ SV17 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[56]) ).

thf(69,plain,
    ! [SV18: $i,SV8: $i] :
      ( ( ~ ( subset_sets @ SV8 @ SV18 )
        | ! [SY42: $i] :
            ( ~ ( element_of_set @ SY42 @ SV8 )
            | ( element_of_set @ SY42 @ SV18 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(70,plain,
    ! [SV19: $i,SV9: $i] :
      ( ( ~ ( equal_sets @ SV9 @ SV19 )
        | ( subset_sets @ SV9 @ SV19 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(71,plain,
    ! [SV20: $i,SV10: $i] :
      ( ( ( element_of_set @ ( in_1st_set @ SV10 @ SV20 ) @ SV10 )
        | ( subset_sets @ SV10 @ SV20 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(72,plain,
    ! [SV21: $i,SV11: $i] :
      ( ( ( subset_sets @ SV11 @ SV21 )
        | ~ ( element_of_set @ ( in_1st_set @ SV11 @ SV21 ) @ SV21 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(73,plain,
    ! [SV12: $i,SV1: $i] :
      ( ( ( ~ ( element_of_set @ SV1 @ ( union_of_members @ SV12 ) ) )
        = $true )
      | ( ( element_of_set @ SV1 @ ( f1 @ SV12 @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[63]) ).

thf(74,plain,
    ! [SV13: $i,SV2: $i] :
      ( ( ( ~ ( element_of_set @ SV2 @ ( union_of_members @ SV13 ) ) )
        = $true )
      | ( ( element_of_collection @ ( f1 @ SV13 @ SV2 ) @ SV13 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[64]) ).

thf(75,plain,
    ! [SV14: $i,SV3: $i] :
      ( ( ( element_of_set @ SV3 @ ( union_of_members @ SV14 ) )
        = $true )
      | ( ( ! [SY39: $i] :
              ( ~ ( element_of_set @ SV3 @ SY39 )
              | ~ ( element_of_collection @ SY39 @ SV14 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[65]) ).

thf(76,plain,
    ! [SV15: $i,SV4: $i] :
      ( ( ( ~ ( basis @ SV4 @ SV15 ) )
        = $true )
      | ( ( equal_sets @ ( union_of_members @ SV15 ) @ SV4 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[66]) ).

thf(77,plain,
    ! [SV16: $i,SV5: $i] :
      ( ( ( ~ ( element_of_collection @ SV5 @ ( top_of_basis @ SV16 ) ) )
        = $true )
      | ( ( ! [SY40: $i] :
              ( ~ ( element_of_set @ SY40 @ SV5 )
              | ( element_of_set @ SY40 @ ( f10 @ SV16 @ SV5 @ SY40 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[67]) ).

thf(78,plain,
    ! [SV17: $i,SV6: $i] :
      ( ( ( ~ ( element_of_collection @ SV6 @ ( top_of_basis @ SV17 ) ) )
        = $true )
      | ( ( ! [SY41: $i] :
              ( ~ ( element_of_set @ SY41 @ SV6 )
              | ( element_of_collection @ ( f10 @ SV17 @ SV6 @ SY41 ) @ SV17 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[68]) ).

thf(79,plain,
    ! [SV18: $i,SV8: $i] :
      ( ( ( ~ ( subset_sets @ SV8 @ SV18 ) )
        = $true )
      | ( ( ! [SY42: $i] :
              ( ~ ( element_of_set @ SY42 @ SV8 )
              | ( element_of_set @ SY42 @ SV18 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[69]) ).

thf(80,plain,
    ! [SV19: $i,SV9: $i] :
      ( ( ( ~ ( equal_sets @ SV9 @ SV19 ) )
        = $true )
      | ( ( subset_sets @ SV9 @ SV19 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[70]) ).

thf(81,plain,
    ! [SV20: $i,SV10: $i] :
      ( ( ( element_of_set @ ( in_1st_set @ SV10 @ SV20 ) @ SV10 )
        = $true )
      | ( ( subset_sets @ SV10 @ SV20 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[71]) ).

thf(82,plain,
    ! [SV21: $i,SV11: $i] :
      ( ( ( subset_sets @ SV11 @ SV21 )
        = $true )
      | ( ( ~ ( element_of_set @ ( in_1st_set @ SV11 @ SV21 ) @ SV21 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[72]) ).

thf(83,plain,
    ! [SV12: $i,SV1: $i] :
      ( ( ( element_of_set @ SV1 @ ( union_of_members @ SV12 ) )
        = $false )
      | ( ( element_of_set @ SV1 @ ( f1 @ SV12 @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[73]) ).

thf(84,plain,
    ! [SV13: $i,SV2: $i] :
      ( ( ( element_of_set @ SV2 @ ( union_of_members @ SV13 ) )
        = $false )
      | ( ( element_of_collection @ ( f1 @ SV13 @ SV2 ) @ SV13 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[74]) ).

thf(85,plain,
    ! [SV14: $i,SV22: $i,SV3: $i] :
      ( ( ( ~ ( element_of_set @ SV3 @ SV22 )
          | ~ ( element_of_collection @ SV22 @ SV14 ) )
        = $true )
      | ( ( element_of_set @ SV3 @ ( union_of_members @ SV14 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[75]) ).

thf(86,plain,
    ! [SV15: $i,SV4: $i] :
      ( ( ( basis @ SV4 @ SV15 )
        = $false )
      | ( ( equal_sets @ ( union_of_members @ SV15 ) @ SV4 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[76]) ).

thf(87,plain,
    ! [SV16: $i,SV5: $i] :
      ( ( ( element_of_collection @ SV5 @ ( top_of_basis @ SV16 ) )
        = $false )
      | ( ( ! [SY40: $i] :
              ( ~ ( element_of_set @ SY40 @ SV5 )
              | ( element_of_set @ SY40 @ ( f10 @ SV16 @ SV5 @ SY40 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[77]) ).

thf(88,plain,
    ! [SV17: $i,SV6: $i] :
      ( ( ( element_of_collection @ SV6 @ ( top_of_basis @ SV17 ) )
        = $false )
      | ( ( ! [SY41: $i] :
              ( ~ ( element_of_set @ SY41 @ SV6 )
              | ( element_of_collection @ ( f10 @ SV17 @ SV6 @ SY41 ) @ SV17 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[78]) ).

thf(89,plain,
    ! [SV18: $i,SV8: $i] :
      ( ( ( subset_sets @ SV8 @ SV18 )
        = $false )
      | ( ( ! [SY42: $i] :
              ( ~ ( element_of_set @ SY42 @ SV8 )
              | ( element_of_set @ SY42 @ SV18 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[79]) ).

thf(90,plain,
    ! [SV19: $i,SV9: $i] :
      ( ( ( equal_sets @ SV9 @ SV19 )
        = $false )
      | ( ( subset_sets @ SV9 @ SV19 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[80]) ).

thf(91,plain,
    ! [SV21: $i,SV11: $i] :
      ( ( ( element_of_set @ ( in_1st_set @ SV11 @ SV21 ) @ SV21 )
        = $false )
      | ( ( subset_sets @ SV11 @ SV21 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[82]) ).

thf(92,plain,
    ! [SV14: $i,SV22: $i,SV3: $i] :
      ( ( ( ~ ( element_of_set @ SV3 @ SV22 ) )
        = $true )
      | ( ( ~ ( element_of_collection @ SV22 @ SV14 ) )
        = $true )
      | ( ( element_of_set @ SV3 @ ( union_of_members @ SV14 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[85]) ).

thf(93,plain,
    ! [SV16: $i,SV5: $i,SV23: $i] :
      ( ( ( ~ ( element_of_set @ SV23 @ SV5 )
          | ( element_of_set @ SV23 @ ( f10 @ SV16 @ SV5 @ SV23 ) ) )
        = $true )
      | ( ( element_of_collection @ SV5 @ ( top_of_basis @ SV16 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[87]) ).

thf(94,plain,
    ! [SV17: $i,SV6: $i,SV24: $i] :
      ( ( ( ~ ( element_of_set @ SV24 @ SV6 )
          | ( element_of_collection @ ( f10 @ SV17 @ SV6 @ SV24 ) @ SV17 ) )
        = $true )
      | ( ( element_of_collection @ SV6 @ ( top_of_basis @ SV17 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[88]) ).

thf(95,plain,
    ! [SV18: $i,SV8: $i,SV25: $i] :
      ( ( ( ~ ( element_of_set @ SV25 @ SV8 )
          | ( element_of_set @ SV25 @ SV18 ) )
        = $true )
      | ( ( subset_sets @ SV8 @ SV18 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[89]) ).

thf(96,plain,
    ! [SV14: $i,SV22: $i,SV3: $i] :
      ( ( ( element_of_set @ SV3 @ SV22 )
        = $false )
      | ( ( ~ ( element_of_collection @ SV22 @ SV14 ) )
        = $true )
      | ( ( element_of_set @ SV3 @ ( union_of_members @ SV14 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[92]) ).

thf(97,plain,
    ! [SV16: $i,SV5: $i,SV23: $i] :
      ( ( ( ~ ( element_of_set @ SV23 @ SV5 ) )
        = $true )
      | ( ( element_of_set @ SV23 @ ( f10 @ SV16 @ SV5 @ SV23 ) )
        = $true )
      | ( ( element_of_collection @ SV5 @ ( top_of_basis @ SV16 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[93]) ).

thf(98,plain,
    ! [SV17: $i,SV6: $i,SV24: $i] :
      ( ( ( ~ ( element_of_set @ SV24 @ SV6 ) )
        = $true )
      | ( ( element_of_collection @ ( f10 @ SV17 @ SV6 @ SV24 ) @ SV17 )
        = $true )
      | ( ( element_of_collection @ SV6 @ ( top_of_basis @ SV17 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[94]) ).

thf(99,plain,
    ! [SV18: $i,SV8: $i,SV25: $i] :
      ( ( ( ~ ( element_of_set @ SV25 @ SV8 ) )
        = $true )
      | ( ( element_of_set @ SV25 @ SV18 )
        = $true )
      | ( ( subset_sets @ SV8 @ SV18 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[95]) ).

thf(100,plain,
    ! [SV3: $i,SV14: $i,SV22: $i] :
      ( ( ( element_of_collection @ SV22 @ SV14 )
        = $false )
      | ( ( element_of_set @ SV3 @ SV22 )
        = $false )
      | ( ( element_of_set @ SV3 @ ( union_of_members @ SV14 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[96]) ).

thf(101,plain,
    ! [SV16: $i,SV5: $i,SV23: $i] :
      ( ( ( element_of_set @ SV23 @ SV5 )
        = $false )
      | ( ( element_of_set @ SV23 @ ( f10 @ SV16 @ SV5 @ SV23 ) )
        = $true )
      | ( ( element_of_collection @ SV5 @ ( top_of_basis @ SV16 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[97]) ).

thf(102,plain,
    ! [SV17: $i,SV6: $i,SV24: $i] :
      ( ( ( element_of_set @ SV24 @ SV6 )
        = $false )
      | ( ( element_of_collection @ ( f10 @ SV17 @ SV6 @ SV24 ) @ SV17 )
        = $true )
      | ( ( element_of_collection @ SV6 @ ( top_of_basis @ SV17 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[98]) ).

thf(103,plain,
    ! [SV18: $i,SV8: $i,SV25: $i] :
      ( ( ( element_of_set @ SV25 @ SV8 )
        = $false )
      | ( ( element_of_set @ SV25 @ SV18 )
        = $true )
      | ( ( subset_sets @ SV8 @ SV18 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[99]) ).

thf(104,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[36,103,102,101,100,91,90,86,84,83,81,62,57,50]) ).

thf(105,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[104]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : TOP001-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33  % Computer : n024.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun May 29 14:13:36 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  
% 0.13/0.34   No.of.Axioms: 13
% 0.13/0.34  
% 0.13/0.34   Length.of.Defs: 0
% 0.13/0.34  
% 0.13/0.34   Contains.Choice.Funs: false
% 0.13/0.35  (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).....
% 0.20/0.41  
% 0.20/0.41  ********************************
% 0.20/0.41  *   All subproblems solved!    *
% 0.20/0.41  ********************************
% 0.20/0.41  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:104,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.42  
% 0.20/0.42  %**** Beginning of derivation protocol ****
% 0.20/0.42  % SZS output start CNFRefutation
% See solution above
% 0.20/0.42  
% 0.20/0.42  %**** End of derivation protocol ****
% 0.20/0.42  %**** no. of clauses in derivation: 105 ****
% 0.20/0.42  %**** clause counter: 104 ****
% 0.20/0.42  
% 0.20/0.42  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:104,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------