TSTP Solution File: SET007-1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SET007-1 : 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 : n007.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 02:57:41 EDT 2022

% Result   : Unsatisfiable 0.83s 1.05s
% Output   : CNFRefutation 0.90s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   39
% Syntax   : Number of formulae    :  219 ( 116 unt;  15 typ;   0 def)
%            Number of atoms       : 1156 ( 286 equ;   0 cnn)
%            Maximal formula atoms :    4 (   5 avg)
%            Number of connectives : 2353 ( 240   ~; 380   |;   0   &;1733   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  20   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  15 usr;   9 con; 0-3 aty)
%            Number of variables   :  578 (   0   ^ 578   !;   0   ?; 578   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_a,type,
    a: $i ).

thf(tp_aI_bUc,type,
    aI_bUc: $i ).

thf(tp_aIb,type,
    aIb: $i ).

thf(tp_aIc,type,
    aIc: $i ).

thf(tp_b,type,
    b: $i ).

thf(tp_bUc,type,
    bUc: $i ).

thf(tp_c,type,
    c: $i ).

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

thf(tp_g,type,
    g: $i > $i > $i > $i ).

thf(tp_h,type,
    h: $i > $i > $i > $i ).

thf(tp_intersection,type,
    intersection: $i > $i > $i > $o ).

thf(tp_member,type,
    member: $i > $i > $o ).

thf(tp_member_of_1_not_of_2,type,
    member_of_1_not_of_2: $i > $i > $i ).

thf(tp_subset,type,
    subset: $i > $i > $o ).

thf(tp_union,type,
    union: $i > $i > $i > $o ).

thf(1,axiom,
    intersection @ a @ bUc @ aI_bUc,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_bUc) ).

thf(2,axiom,
    intersection @ a @ c @ aIc,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_c) ).

thf(3,axiom,
    intersection @ a @ b @ aIb,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_b) ).

thf(4,axiom,
    union @ b @ c @ bUc,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_union_c) ).

thf(5,axiom,
    ! [Set1: $i,Set2: $i,Intersection: $i] :
      ( ~ ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Intersection )
      | ~ ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set2 )
      | ~ ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set1 )
      | ( intersection @ Set1 @ Set2 @ Intersection ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_axiom3) ).

thf(6,axiom,
    ! [Set1: $i,Set2: $i,Intersection: $i] :
      ( ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Intersection )
      | ( intersection @ Set1 @ Set2 @ Intersection )
      | ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_axiom2) ).

thf(7,axiom,
    ! [Set1: $i,Set2: $i,Intersection: $i] :
      ( ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Intersection )
      | ( intersection @ Set1 @ Set2 @ Intersection )
      | ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_axiom1) ).

thf(8,axiom,
    ! [Set1: $i,Set2: $i,Intersection: $i,Element: $i] :
      ( ~ ( intersection @ Set1 @ Set2 @ Intersection )
      | ~ ( member @ Element @ Set2 )
      | ~ ( member @ Element @ Set1 )
      | ( member @ Element @ Intersection ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_both_is_member_of_intersection) ).

thf(9,axiom,
    ! [Set1: $i,Set2: $i,Intersection: $i,Element: $i] :
      ( ~ ( intersection @ Set1 @ Set2 @ Intersection )
      | ~ ( member @ Element @ Intersection )
      | ( member @ Element @ Set2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set2) ).

thf(10,axiom,
    ! [Set1: $i,Set2: $i,Intersection: $i,Element: $i] :
      ( ~ ( intersection @ Set1 @ Set2 @ Intersection )
      | ~ ( member @ Element @ Intersection )
      | ( member @ Element @ Set1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set1) ).

thf(11,axiom,
    ! [Set1: $i,Set2: $i,Union: $i] :
      ( ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set2 )
      | ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Union )
      | ( union @ Set1 @ Set2 @ Union ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_axiom3) ).

thf(12,axiom,
    ! [Set1: $i,Set2: $i,Union: $i] :
      ( ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set1 )
      | ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Union )
      | ( union @ Set1 @ Set2 @ Union ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_axiom2) ).

thf(13,axiom,
    ! [Set1: $i,Set2: $i,Union: $i] :
      ( ( union @ Set1 @ Set2 @ Union )
      | ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set1 )
      | ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set2 )
      | ( member @ ( g @ Set1 @ Set2 @ Union ) @ Union ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_axiom1) ).

thf(14,axiom,
    ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
      ( ~ ( union @ Set1 @ Set2 @ Union )
      | ~ ( member @ Element @ Set2 )
      | ( member @ Element @ Union ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set2_is_member_of_union) ).

thf(15,axiom,
    ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
      ( ~ ( union @ Set1 @ Set2 @ Union )
      | ~ ( member @ Element @ Set1 )
      | ( member @ Element @ Union ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set1_is_member_of_union) ).

thf(16,axiom,
    ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
      ( ~ ( union @ Set1 @ Set2 @ Union )
      | ~ ( member @ Element @ Union )
      | ( member @ Element @ Set1 )
      | ( member @ Element @ Set2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_union_is_member_of_one_set) ).

thf(17,axiom,
    ! [Set1: $i,Set2: $i] :
      ( ~ ( subset @ Set1 @ Set2 )
      | ~ ( subset @ Set2 @ Set1 )
      | ( equal_sets @ Set2 @ Set1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_are_set_equal_sets) ).

thf(18,axiom,
    ! [Superset: $i,Subset: $i] :
      ( ~ ( equal_sets @ Superset @ Subset )
      | ( subset @ Subset @ Superset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_equal_sets_are_subsets2) ).

thf(19,axiom,
    ! [Subset: $i,Superset: $i] :
      ( ~ ( equal_sets @ Subset @ Superset )
      | ( subset @ Subset @ Superset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_equal_sets_are_subsets1) ).

thf(20,axiom,
    ! [Subset: $i,Superset: $i] :
      ( ~ ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Superset )
      | ( subset @ Subset @ Superset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom2) ).

thf(21,axiom,
    ! [Subset: $i,Superset: $i] :
      ( ( subset @ Subset @ Superset )
      | ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Subset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom1) ).

thf(22,axiom,
    ! [Element: $i,Subset: $i,Superset: $i] :
      ( ~ ( member @ Element @ Subset )
      | ~ ( subset @ Subset @ Superset )
      | ( member @ Element @ Superset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',membership_in_subsets) ).

thf(23,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(24,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[23]) ).

thf(25,negated_conjecture,
    ~ ( union @ aIb @ aIc @ aI_bUc ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_aIb_union_aIc_is_aI_bUc) ).

thf(26,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[24]) ).

thf(27,plain,
    ( ( intersection @ a @ bUc @ aI_bUc )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(28,plain,
    ( ( intersection @ a @ c @ aIc )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(29,plain,
    ( ( intersection @ a @ b @ aIb )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(30,plain,
    ( ( union @ b @ c @ bUc )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(31,plain,
    ( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
          ( ~ ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Intersection )
          | ~ ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set2 )
          | ~ ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set1 )
          | ( intersection @ Set1 @ Set2 @ Intersection ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(32,plain,
    ( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
          ( ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Intersection )
          | ( intersection @ Set1 @ Set2 @ Intersection )
          | ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(33,plain,
    ( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
          ( ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Intersection )
          | ( intersection @ Set1 @ Set2 @ Intersection )
          | ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(34,plain,
    ( ( ! [Set1: $i,Set2: $i,Intersection: $i,Element: $i] :
          ( ~ ( intersection @ Set1 @ Set2 @ Intersection )
          | ~ ( member @ Element @ Set2 )
          | ~ ( member @ Element @ Set1 )
          | ( member @ Element @ Intersection ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(35,plain,
    ( ( ! [Set1: $i,Set2: $i,Intersection: $i,Element: $i] :
          ( ~ ( intersection @ Set1 @ Set2 @ Intersection )
          | ~ ( member @ Element @ Intersection )
          | ( member @ Element @ Set2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(36,plain,
    ( ( ! [Set1: $i,Set2: $i,Intersection: $i,Element: $i] :
          ( ~ ( intersection @ Set1 @ Set2 @ Intersection )
          | ~ ( member @ Element @ Intersection )
          | ( member @ Element @ Set1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(37,plain,
    ( ( ! [Set1: $i,Set2: $i,Union: $i] :
          ( ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set2 )
          | ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Union )
          | ( union @ Set1 @ Set2 @ Union ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(38,plain,
    ( ( ! [Set1: $i,Set2: $i,Union: $i] :
          ( ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set1 )
          | ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Union )
          | ( union @ Set1 @ Set2 @ Union ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(39,plain,
    ( ( ! [Set1: $i,Set2: $i,Union: $i] :
          ( ( union @ Set1 @ Set2 @ Union )
          | ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set1 )
          | ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set2 )
          | ( member @ ( g @ Set1 @ Set2 @ Union ) @ Union ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(40,plain,
    ( ( ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
          ( ~ ( union @ Set1 @ Set2 @ Union )
          | ~ ( member @ Element @ Set2 )
          | ( member @ Element @ Union ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(41,plain,
    ( ( ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
          ( ~ ( union @ Set1 @ Set2 @ Union )
          | ~ ( member @ Element @ Set1 )
          | ( member @ Element @ Union ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(42,plain,
    ( ( ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
          ( ~ ( union @ Set1 @ Set2 @ Union )
          | ~ ( member @ Element @ Union )
          | ( member @ Element @ Set1 )
          | ( member @ Element @ Set2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(43,plain,
    ( ( ! [Set1: $i,Set2: $i] :
          ( ~ ( subset @ Set1 @ Set2 )
          | ~ ( subset @ Set2 @ Set1 )
          | ( equal_sets @ Set2 @ Set1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(44,plain,
    ( ( ! [Superset: $i,Subset: $i] :
          ( ~ ( equal_sets @ Superset @ Subset )
          | ( subset @ Subset @ Superset ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(45,plain,
    ( ( ! [Subset: $i,Superset: $i] :
          ( ~ ( equal_sets @ Subset @ Superset )
          | ( subset @ Subset @ Superset ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(46,plain,
    ( ( ! [Subset: $i,Superset: $i] :
          ( ~ ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Superset )
          | ( subset @ Subset @ Superset ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(47,plain,
    ( ( ! [Subset: $i,Superset: $i] :
          ( ( subset @ Subset @ Superset )
          | ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Subset ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[21]) ).

thf(48,plain,
    ( ( ! [Element: $i,Subset: $i,Superset: $i] :
          ( ~ ( member @ Element @ Subset )
          | ~ ( subset @ Subset @ Superset )
          | ( member @ Element @ Superset ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[22]) ).

thf(49,plain,
    ( ( ~ ( union @ aIb @ aIc @ aI_bUc ) )
    = $true ),
    inference(unfold_def,[status(thm)],[25]) ).

thf(50,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[26]) ).

thf(51,plain,
    ( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
          ( ~ ( intersection @ Set1 @ Set2 @ Intersection )
          | ! [Element: $i] :
              ( ~ ( member @ Element @ Set2 )
              | ~ ( member @ Element @ Set1 )
              | ( member @ Element @ Intersection ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[34]) ).

thf(52,plain,
    ( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
          ( ~ ( intersection @ Set1 @ Set2 @ Intersection )
          | ! [Element: $i] :
              ( ~ ( member @ Element @ Intersection )
              | ( member @ Element @ Set2 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[35]) ).

thf(53,plain,
    ( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
          ( ~ ( intersection @ Set1 @ Set2 @ Intersection )
          | ! [Element: $i] :
              ( ~ ( member @ Element @ Intersection )
              | ( member @ Element @ Set1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[36]) ).

thf(54,plain,
    ( ( ! [Set1: $i,Set2: $i,Union: $i] :
          ( ~ ( union @ Set1 @ Set2 @ Union )
          | ! [Element: $i] :
              ( ~ ( member @ Element @ Set2 )
              | ( member @ Element @ Union ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[40]) ).

thf(55,plain,
    ( ( ! [Set1: $i,Set2: $i,Union: $i] :
          ( ~ ( union @ Set1 @ Set2 @ Union )
          | ! [Element: $i] :
              ( ~ ( member @ Element @ Set1 )
              | ( member @ Element @ Union ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[41]) ).

thf(56,plain,
    ( ( ! [Set1: $i,Set2: $i,Union: $i] :
          ( ~ ( union @ Set1 @ Set2 @ Union )
          | ! [Element: $i] :
              ( ~ ( member @ Element @ Union )
              | ( member @ Element @ Set1 )
              | ( member @ Element @ Set2 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[42]) ).

thf(57,plain,
    ( ( ! [Subset: $i,Superset: $i] :
          ( ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Subset )
          | ( subset @ Subset @ Superset ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[47]) ).

thf(58,plain,
    ( ( ! [Element: $i,Subset: $i] :
          ( ~ ( member @ Element @ Subset )
          | ! [Superset: $i] :
              ( ~ ( subset @ Subset @ Superset )
              | ( member @ Element @ Superset ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[48]) ).

thf(59,plain,
    ( ( ~ ( union @ aIb @ aIc @ aI_bUc ) )
    = $true ),
    inference(copy,[status(thm)],[49]) ).

thf(60,plain,
    ( ( ! [Element: $i,Subset: $i] :
          ( ~ ( member @ Element @ Subset )
          | ! [Superset: $i] :
              ( ~ ( subset @ Subset @ Superset )
              | ( member @ Element @ Superset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[58]) ).

thf(61,plain,
    ( ( ! [Subset: $i,Superset: $i] :
          ( ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Subset )
          | ( subset @ Subset @ Superset ) ) )
    = $true ),
    inference(copy,[status(thm)],[57]) ).

thf(62,plain,
    ( ( ! [Subset: $i,Superset: $i] :
          ( ~ ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Superset )
          | ( subset @ Subset @ Superset ) ) )
    = $true ),
    inference(copy,[status(thm)],[46]) ).

thf(63,plain,
    ( ( ! [Subset: $i,Superset: $i] :
          ( ~ ( equal_sets @ Subset @ Superset )
          | ( subset @ Subset @ Superset ) ) )
    = $true ),
    inference(copy,[status(thm)],[45]) ).

thf(64,plain,
    ( ( ! [Superset: $i,Subset: $i] :
          ( ~ ( equal_sets @ Superset @ Subset )
          | ( subset @ Subset @ Superset ) ) )
    = $true ),
    inference(copy,[status(thm)],[44]) ).

thf(65,plain,
    ( ( ! [Set1: $i,Set2: $i] :
          ( ~ ( subset @ Set1 @ Set2 )
          | ~ ( subset @ Set2 @ Set1 )
          | ( equal_sets @ Set2 @ Set1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[43]) ).

thf(66,plain,
    ( ( ! [Set1: $i,Set2: $i,Union: $i] :
          ( ~ ( union @ Set1 @ Set2 @ Union )
          | ! [Element: $i] :
              ( ~ ( member @ Element @ Union )
              | ( member @ Element @ Set1 )
              | ( member @ Element @ Set2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[56]) ).

thf(67,plain,
    ( ( ! [Set1: $i,Set2: $i,Union: $i] :
          ( ~ ( union @ Set1 @ Set2 @ Union )
          | ! [Element: $i] :
              ( ~ ( member @ Element @ Set1 )
              | ( member @ Element @ Union ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[55]) ).

thf(68,plain,
    ( ( ! [Set1: $i,Set2: $i,Union: $i] :
          ( ~ ( union @ Set1 @ Set2 @ Union )
          | ! [Element: $i] :
              ( ~ ( member @ Element @ Set2 )
              | ( member @ Element @ Union ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[54]) ).

thf(69,plain,
    ( ( ! [Set1: $i,Set2: $i,Union: $i] :
          ( ( union @ Set1 @ Set2 @ Union )
          | ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set1 )
          | ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set2 )
          | ( member @ ( g @ Set1 @ Set2 @ Union ) @ Union ) ) )
    = $true ),
    inference(copy,[status(thm)],[39]) ).

thf(70,plain,
    ( ( ! [Set1: $i,Set2: $i,Union: $i] :
          ( ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set1 )
          | ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Union )
          | ( union @ Set1 @ Set2 @ Union ) ) )
    = $true ),
    inference(copy,[status(thm)],[38]) ).

thf(71,plain,
    ( ( ! [Set1: $i,Set2: $i,Union: $i] :
          ( ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set2 )
          | ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Union )
          | ( union @ Set1 @ Set2 @ Union ) ) )
    = $true ),
    inference(copy,[status(thm)],[37]) ).

thf(72,plain,
    ( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
          ( ~ ( intersection @ Set1 @ Set2 @ Intersection )
          | ! [Element: $i] :
              ( ~ ( member @ Element @ Intersection )
              | ( member @ Element @ Set1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[53]) ).

thf(73,plain,
    ( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
          ( ~ ( intersection @ Set1 @ Set2 @ Intersection )
          | ! [Element: $i] :
              ( ~ ( member @ Element @ Intersection )
              | ( member @ Element @ Set2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[52]) ).

thf(74,plain,
    ( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
          ( ~ ( intersection @ Set1 @ Set2 @ Intersection )
          | ! [Element: $i] :
              ( ~ ( member @ Element @ Set2 )
              | ~ ( member @ Element @ Set1 )
              | ( member @ Element @ Intersection ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[51]) ).

thf(75,plain,
    ( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
          ( ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Intersection )
          | ( intersection @ Set1 @ Set2 @ Intersection )
          | ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(76,plain,
    ( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
          ( ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Intersection )
          | ( intersection @ Set1 @ Set2 @ Intersection )
          | ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(77,plain,
    ( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
          ( ~ ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Intersection )
          | ~ ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set2 )
          | ~ ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set1 )
          | ( intersection @ Set1 @ Set2 @ Intersection ) ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(78,plain,
    ( ( union @ b @ c @ bUc )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(79,plain,
    ( ( intersection @ a @ b @ aIb )
    = $true ),
    inference(copy,[status(thm)],[29]) ).

thf(80,plain,
    ( ( intersection @ a @ c @ aIc )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(81,plain,
    ( ( intersection @ a @ bUc @ aI_bUc )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(82,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[50]) ).

thf(83,plain,
    ( ( union @ aIb @ aIc @ aI_bUc )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[59]) ).

thf(84,plain,
    ! [SV1: $i] :
      ( ( ! [SY55: $i] :
            ( ~ ( member @ SV1 @ SY55 )
            | ! [SY56: $i] :
                ( ~ ( subset @ SY55 @ SY56 )
                | ( member @ SV1 @ SY56 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(85,plain,
    ! [SV2: $i] :
      ( ( ! [SY57: $i] :
            ( ( member @ ( member_of_1_not_of_2 @ SV2 @ SY57 ) @ SV2 )
            | ( subset @ SV2 @ SY57 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(86,plain,
    ! [SV3: $i] :
      ( ( ! [SY58: $i] :
            ( ~ ( member @ ( member_of_1_not_of_2 @ SV3 @ SY58 ) @ SY58 )
            | ( subset @ SV3 @ SY58 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(87,plain,
    ! [SV4: $i] :
      ( ( ! [SY59: $i] :
            ( ~ ( equal_sets @ SV4 @ SY59 )
            | ( subset @ SV4 @ SY59 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[63]) ).

thf(88,plain,
    ! [SV5: $i] :
      ( ( ! [SY60: $i] :
            ( ~ ( equal_sets @ SV5 @ SY60 )
            | ( subset @ SY60 @ SV5 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[64]) ).

thf(89,plain,
    ! [SV6: $i] :
      ( ( ! [SY61: $i] :
            ( ~ ( subset @ SV6 @ SY61 )
            | ~ ( subset @ SY61 @ SV6 )
            | ( equal_sets @ SY61 @ SV6 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[65]) ).

thf(90,plain,
    ! [SV7: $i] :
      ( ( ! [SY62: $i,SY63: $i] :
            ( ~ ( union @ SV7 @ SY62 @ SY63 )
            | ! [SY64: $i] :
                ( ~ ( member @ SY64 @ SY63 )
                | ( member @ SY64 @ SV7 )
                | ( member @ SY64 @ SY62 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(91,plain,
    ! [SV8: $i] :
      ( ( ! [SY65: $i,SY66: $i] :
            ( ~ ( union @ SV8 @ SY65 @ SY66 )
            | ! [SY67: $i] :
                ( ~ ( member @ SY67 @ SV8 )
                | ( member @ SY67 @ SY66 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(92,plain,
    ! [SV9: $i] :
      ( ( ! [SY68: $i,SY69: $i] :
            ( ~ ( union @ SV9 @ SY68 @ SY69 )
            | ! [Element: $i] :
                ( ~ ( member @ Element @ SY68 )
                | ( member @ Element @ SY69 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[68]) ).

thf(93,plain,
    ! [SV10: $i] :
      ( ( ! [SY71: $i,SY72: $i] :
            ( ( union @ SV10 @ SY71 @ SY72 )
            | ( member @ ( g @ SV10 @ SY71 @ SY72 ) @ SV10 )
            | ( member @ ( g @ SV10 @ SY71 @ SY72 ) @ SY71 )
            | ( member @ ( g @ SV10 @ SY71 @ SY72 ) @ SY72 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[69]) ).

thf(94,plain,
    ! [SV11: $i] :
      ( ( ! [SY73: $i,SY74: $i] :
            ( ~ ( member @ ( g @ SV11 @ SY73 @ SY74 ) @ SV11 )
            | ~ ( member @ ( g @ SV11 @ SY73 @ SY74 ) @ SY74 )
            | ( union @ SV11 @ SY73 @ SY74 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[70]) ).

thf(95,plain,
    ! [SV12: $i] :
      ( ( ! [SY75: $i,SY76: $i] :
            ( ~ ( member @ ( g @ SV12 @ SY75 @ SY76 ) @ SY75 )
            | ~ ( member @ ( g @ SV12 @ SY75 @ SY76 ) @ SY76 )
            | ( union @ SV12 @ SY75 @ SY76 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[71]) ).

thf(96,plain,
    ! [SV13: $i] :
      ( ( ! [SY77: $i,SY78: $i] :
            ( ~ ( intersection @ SV13 @ SY77 @ SY78 )
            | ! [SY79: $i] :
                ( ~ ( member @ SY79 @ SY78 )
                | ( member @ SY79 @ SV13 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[72]) ).

thf(97,plain,
    ! [SV14: $i] :
      ( ( ! [SY80: $i,SY81: $i] :
            ( ~ ( intersection @ SV14 @ SY80 @ SY81 )
            | ! [Element: $i] :
                ( ~ ( member @ Element @ SY81 )
                | ( member @ Element @ SY80 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(98,plain,
    ! [SV15: $i] :
      ( ( ! [SY83: $i,SY84: $i] :
            ( ~ ( intersection @ SV15 @ SY83 @ SY84 )
            | ! [SY85: $i] :
                ( ~ ( member @ SY85 @ SY83 )
                | ~ ( member @ SY85 @ SV15 )
                | ( member @ SY85 @ SY84 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[74]) ).

thf(99,plain,
    ! [SV16: $i] :
      ( ( ! [SY86: $i,SY87: $i] :
            ( ( member @ ( h @ SV16 @ SY86 @ SY87 ) @ SY87 )
            | ( intersection @ SV16 @ SY86 @ SY87 )
            | ( member @ ( h @ SV16 @ SY86 @ SY87 ) @ SV16 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[75]) ).

thf(100,plain,
    ! [SV17: $i] :
      ( ( ! [SY88: $i,SY89: $i] :
            ( ( member @ ( h @ SV17 @ SY88 @ SY89 ) @ SY89 )
            | ( intersection @ SV17 @ SY88 @ SY89 )
            | ( member @ ( h @ SV17 @ SY88 @ SY89 ) @ SY88 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[76]) ).

thf(101,plain,
    ! [SV18: $i] :
      ( ( ! [SY90: $i,SY91: $i] :
            ( ~ ( member @ ( h @ SV18 @ SY90 @ SY91 ) @ SY91 )
            | ~ ( member @ ( h @ SV18 @ SY90 @ SY91 ) @ SY90 )
            | ~ ( member @ ( h @ SV18 @ SY90 @ SY91 ) @ SV18 )
            | ( intersection @ SV18 @ SY90 @ SY91 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(102,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[82]) ).

thf(103,plain,
    ! [SV19: $i,SV1: $i] :
      ( ( ~ ( member @ SV1 @ SV19 )
        | ! [SY92: $i] :
            ( ~ ( subset @ SV19 @ SY92 )
            | ( member @ SV1 @ SY92 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[84]) ).

thf(104,plain,
    ! [SV20: $i,SV2: $i] :
      ( ( ( member @ ( member_of_1_not_of_2 @ SV2 @ SV20 ) @ SV2 )
        | ( subset @ SV2 @ SV20 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[85]) ).

thf(105,plain,
    ! [SV21: $i,SV3: $i] :
      ( ( ~ ( member @ ( member_of_1_not_of_2 @ SV3 @ SV21 ) @ SV21 )
        | ( subset @ SV3 @ SV21 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[86]) ).

thf(106,plain,
    ! [SV22: $i,SV4: $i] :
      ( ( ~ ( equal_sets @ SV4 @ SV22 )
        | ( subset @ SV4 @ SV22 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[87]) ).

thf(107,plain,
    ! [SV23: $i,SV5: $i] :
      ( ( ~ ( equal_sets @ SV5 @ SV23 )
        | ( subset @ SV23 @ SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[88]) ).

thf(108,plain,
    ! [SV24: $i,SV6: $i] :
      ( ( ~ ( subset @ SV6 @ SV24 )
        | ~ ( subset @ SV24 @ SV6 )
        | ( equal_sets @ SV24 @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[89]) ).

thf(109,plain,
    ! [SV25: $i,SV7: $i] :
      ( ( ! [SY93: $i] :
            ( ~ ( union @ SV7 @ SV25 @ SY93 )
            | ! [SY94: $i] :
                ( ~ ( member @ SY94 @ SY93 )
                | ( member @ SY94 @ SV7 )
                | ( member @ SY94 @ SV25 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[90]) ).

thf(110,plain,
    ! [SV26: $i,SV8: $i] :
      ( ( ! [SY95: $i] :
            ( ~ ( union @ SV8 @ SV26 @ SY95 )
            | ! [SY67: $i] :
                ( ~ ( member @ SY67 @ SV8 )
                | ( member @ SY67 @ SY95 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[91]) ).

thf(111,plain,
    ! [SV27: $i,SV9: $i] :
      ( ( ! [SY97: $i] :
            ( ~ ( union @ SV9 @ SV27 @ SY97 )
            | ! [SY98: $i] :
                ( ~ ( member @ SY98 @ SV27 )
                | ( member @ SY98 @ SY97 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[92]) ).

thf(112,plain,
    ! [SV28: $i,SV10: $i] :
      ( ( ! [SY99: $i] :
            ( ( union @ SV10 @ SV28 @ SY99 )
            | ( member @ ( g @ SV10 @ SV28 @ SY99 ) @ SV10 )
            | ( member @ ( g @ SV10 @ SV28 @ SY99 ) @ SV28 )
            | ( member @ ( g @ SV10 @ SV28 @ SY99 ) @ SY99 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[93]) ).

thf(113,plain,
    ! [SV29: $i,SV11: $i] :
      ( ( ! [SY100: $i] :
            ( ~ ( member @ ( g @ SV11 @ SV29 @ SY100 ) @ SV11 )
            | ~ ( member @ ( g @ SV11 @ SV29 @ SY100 ) @ SY100 )
            | ( union @ SV11 @ SV29 @ SY100 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[94]) ).

thf(114,plain,
    ! [SV30: $i,SV12: $i] :
      ( ( ! [SY101: $i] :
            ( ~ ( member @ ( g @ SV12 @ SV30 @ SY101 ) @ SV30 )
            | ~ ( member @ ( g @ SV12 @ SV30 @ SY101 ) @ SY101 )
            | ( union @ SV12 @ SV30 @ SY101 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[95]) ).

thf(115,plain,
    ! [SV31: $i,SV13: $i] :
      ( ( ! [SY102: $i] :
            ( ~ ( intersection @ SV13 @ SV31 @ SY102 )
            | ! [SY79: $i] :
                ( ~ ( member @ SY79 @ SY102 )
                | ( member @ SY79 @ SV13 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[96]) ).

thf(116,plain,
    ! [SV32: $i,SV14: $i] :
      ( ( ! [SY104: $i] :
            ( ~ ( intersection @ SV14 @ SV32 @ SY104 )
            | ! [SY105: $i] :
                ( ~ ( member @ SY105 @ SY104 )
                | ( member @ SY105 @ SV32 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[97]) ).

thf(117,plain,
    ! [SV33: $i,SV15: $i] :
      ( ( ! [SY106: $i] :
            ( ~ ( intersection @ SV15 @ SV33 @ SY106 )
            | ! [SY107: $i] :
                ( ~ ( member @ SY107 @ SV33 )
                | ~ ( member @ SY107 @ SV15 )
                | ( member @ SY107 @ SY106 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[98]) ).

thf(118,plain,
    ! [SV34: $i,SV16: $i] :
      ( ( ! [SY108: $i] :
            ( ( member @ ( h @ SV16 @ SV34 @ SY108 ) @ SY108 )
            | ( intersection @ SV16 @ SV34 @ SY108 )
            | ( member @ ( h @ SV16 @ SV34 @ SY108 ) @ SV16 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[99]) ).

thf(119,plain,
    ! [SV35: $i,SV17: $i] :
      ( ( ! [SY109: $i] :
            ( ( member @ ( h @ SV17 @ SV35 @ SY109 ) @ SY109 )
            | ( intersection @ SV17 @ SV35 @ SY109 )
            | ( member @ ( h @ SV17 @ SV35 @ SY109 ) @ SV35 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[100]) ).

thf(120,plain,
    ! [SV36: $i,SV18: $i] :
      ( ( ! [SY110: $i] :
            ( ~ ( member @ ( h @ SV18 @ SV36 @ SY110 ) @ SY110 )
            | ~ ( member @ ( h @ SV18 @ SV36 @ SY110 ) @ SV36 )
            | ~ ( member @ ( h @ SV18 @ SV36 @ SY110 ) @ SV18 )
            | ( intersection @ SV18 @ SV36 @ SY110 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[101]) ).

thf(121,plain,
    ! [SV19: $i,SV1: $i] :
      ( ( ( ~ ( member @ SV1 @ SV19 ) )
        = $true )
      | ( ( ! [SY92: $i] :
              ( ~ ( subset @ SV19 @ SY92 )
              | ( member @ SV1 @ SY92 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[103]) ).

thf(122,plain,
    ! [SV20: $i,SV2: $i] :
      ( ( ( member @ ( member_of_1_not_of_2 @ SV2 @ SV20 ) @ SV2 )
        = $true )
      | ( ( subset @ SV2 @ SV20 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[104]) ).

thf(123,plain,
    ! [SV21: $i,SV3: $i] :
      ( ( ( ~ ( member @ ( member_of_1_not_of_2 @ SV3 @ SV21 ) @ SV21 ) )
        = $true )
      | ( ( subset @ SV3 @ SV21 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[105]) ).

thf(124,plain,
    ! [SV22: $i,SV4: $i] :
      ( ( ( ~ ( equal_sets @ SV4 @ SV22 ) )
        = $true )
      | ( ( subset @ SV4 @ SV22 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[106]) ).

thf(125,plain,
    ! [SV23: $i,SV5: $i] :
      ( ( ( ~ ( equal_sets @ SV5 @ SV23 ) )
        = $true )
      | ( ( subset @ SV23 @ SV5 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[107]) ).

thf(126,plain,
    ! [SV24: $i,SV6: $i] :
      ( ( ( ~ ( subset @ SV6 @ SV24 ) )
        = $true )
      | ( ( ~ ( subset @ SV24 @ SV6 )
          | ( equal_sets @ SV24 @ SV6 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[108]) ).

thf(127,plain,
    ! [SV37: $i,SV25: $i,SV7: $i] :
      ( ( ~ ( union @ SV7 @ SV25 @ SV37 )
        | ! [SY111: $i] :
            ( ~ ( member @ SY111 @ SV37 )
            | ( member @ SY111 @ SV7 )
            | ( member @ SY111 @ SV25 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[109]) ).

thf(128,plain,
    ! [SV38: $i,SV26: $i,SV8: $i] :
      ( ( ~ ( union @ SV8 @ SV26 @ SV38 )
        | ! [SY112: $i] :
            ( ~ ( member @ SY112 @ SV8 )
            | ( member @ SY112 @ SV38 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[110]) ).

thf(129,plain,
    ! [SV39: $i,SV27: $i,SV9: $i] :
      ( ( ~ ( union @ SV9 @ SV27 @ SV39 )
        | ! [SY113: $i] :
            ( ~ ( member @ SY113 @ SV27 )
            | ( member @ SY113 @ SV39 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[111]) ).

thf(130,plain,
    ! [SV40: $i,SV28: $i,SV10: $i] :
      ( ( ( union @ SV10 @ SV28 @ SV40 )
        | ( member @ ( g @ SV10 @ SV28 @ SV40 ) @ SV10 )
        | ( member @ ( g @ SV10 @ SV28 @ SV40 ) @ SV28 )
        | ( member @ ( g @ SV10 @ SV28 @ SV40 ) @ SV40 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[112]) ).

thf(131,plain,
    ! [SV41: $i,SV29: $i,SV11: $i] :
      ( ( ~ ( member @ ( g @ SV11 @ SV29 @ SV41 ) @ SV11 )
        | ~ ( member @ ( g @ SV11 @ SV29 @ SV41 ) @ SV41 )
        | ( union @ SV11 @ SV29 @ SV41 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[113]) ).

thf(132,plain,
    ! [SV42: $i,SV30: $i,SV12: $i] :
      ( ( ~ ( member @ ( g @ SV12 @ SV30 @ SV42 ) @ SV30 )
        | ~ ( member @ ( g @ SV12 @ SV30 @ SV42 ) @ SV42 )
        | ( union @ SV12 @ SV30 @ SV42 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[114]) ).

thf(133,plain,
    ! [SV43: $i,SV31: $i,SV13: $i] :
      ( ( ~ ( intersection @ SV13 @ SV31 @ SV43 )
        | ! [SY114: $i] :
            ( ~ ( member @ SY114 @ SV43 )
            | ( member @ SY114 @ SV13 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[115]) ).

thf(134,plain,
    ! [SV44: $i,SV32: $i,SV14: $i] :
      ( ( ~ ( intersection @ SV14 @ SV32 @ SV44 )
        | ! [SY115: $i] :
            ( ~ ( member @ SY115 @ SV44 )
            | ( member @ SY115 @ SV32 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[116]) ).

thf(135,plain,
    ! [SV45: $i,SV33: $i,SV15: $i] :
      ( ( ~ ( intersection @ SV15 @ SV33 @ SV45 )
        | ! [SY116: $i] :
            ( ~ ( member @ SY116 @ SV33 )
            | ~ ( member @ SY116 @ SV15 )
            | ( member @ SY116 @ SV45 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[117]) ).

thf(136,plain,
    ! [SV46: $i,SV34: $i,SV16: $i] :
      ( ( ( member @ ( h @ SV16 @ SV34 @ SV46 ) @ SV46 )
        | ( intersection @ SV16 @ SV34 @ SV46 )
        | ( member @ ( h @ SV16 @ SV34 @ SV46 ) @ SV16 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[118]) ).

thf(137,plain,
    ! [SV47: $i,SV35: $i,SV17: $i] :
      ( ( ( member @ ( h @ SV17 @ SV35 @ SV47 ) @ SV47 )
        | ( intersection @ SV17 @ SV35 @ SV47 )
        | ( member @ ( h @ SV17 @ SV35 @ SV47 ) @ SV35 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[119]) ).

thf(138,plain,
    ! [SV48: $i,SV36: $i,SV18: $i] :
      ( ( ~ ( member @ ( h @ SV18 @ SV36 @ SV48 ) @ SV48 )
        | ~ ( member @ ( h @ SV18 @ SV36 @ SV48 ) @ SV36 )
        | ~ ( member @ ( h @ SV18 @ SV36 @ SV48 ) @ SV18 )
        | ( intersection @ SV18 @ SV36 @ SV48 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[120]) ).

thf(139,plain,
    ! [SV19: $i,SV1: $i] :
      ( ( ( member @ SV1 @ SV19 )
        = $false )
      | ( ( ! [SY92: $i] :
              ( ~ ( subset @ SV19 @ SY92 )
              | ( member @ SV1 @ SY92 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[121]) ).

thf(140,plain,
    ! [SV21: $i,SV3: $i] :
      ( ( ( member @ ( member_of_1_not_of_2 @ SV3 @ SV21 ) @ SV21 )
        = $false )
      | ( ( subset @ SV3 @ SV21 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[123]) ).

thf(141,plain,
    ! [SV22: $i,SV4: $i] :
      ( ( ( equal_sets @ SV4 @ SV22 )
        = $false )
      | ( ( subset @ SV4 @ SV22 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[124]) ).

thf(142,plain,
    ! [SV23: $i,SV5: $i] :
      ( ( ( equal_sets @ SV5 @ SV23 )
        = $false )
      | ( ( subset @ SV23 @ SV5 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[125]) ).

thf(143,plain,
    ! [SV24: $i,SV6: $i] :
      ( ( ( subset @ SV6 @ SV24 )
        = $false )
      | ( ( ~ ( subset @ SV24 @ SV6 )
          | ( equal_sets @ SV24 @ SV6 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[126]) ).

thf(144,plain,
    ! [SV37: $i,SV25: $i,SV7: $i] :
      ( ( ( ~ ( union @ SV7 @ SV25 @ SV37 ) )
        = $true )
      | ( ( ! [SY111: $i] :
              ( ~ ( member @ SY111 @ SV37 )
              | ( member @ SY111 @ SV7 )
              | ( member @ SY111 @ SV25 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[127]) ).

thf(145,plain,
    ! [SV38: $i,SV26: $i,SV8: $i] :
      ( ( ( ~ ( union @ SV8 @ SV26 @ SV38 ) )
        = $true )
      | ( ( ! [SY112: $i] :
              ( ~ ( member @ SY112 @ SV8 )
              | ( member @ SY112 @ SV38 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[128]) ).

thf(146,plain,
    ! [SV39: $i,SV27: $i,SV9: $i] :
      ( ( ( ~ ( union @ SV9 @ SV27 @ SV39 ) )
        = $true )
      | ( ( ! [SY113: $i] :
              ( ~ ( member @ SY113 @ SV27 )
              | ( member @ SY113 @ SV39 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[129]) ).

thf(147,plain,
    ! [SV40: $i,SV28: $i,SV10: $i] :
      ( ( ( union @ SV10 @ SV28 @ SV40 )
        = $true )
      | ( ( ( member @ ( g @ SV10 @ SV28 @ SV40 ) @ SV10 )
          | ( member @ ( g @ SV10 @ SV28 @ SV40 ) @ SV28 )
          | ( member @ ( g @ SV10 @ SV28 @ SV40 ) @ SV40 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[130]) ).

thf(148,plain,
    ! [SV41: $i,SV29: $i,SV11: $i] :
      ( ( ( ~ ( member @ ( g @ SV11 @ SV29 @ SV41 ) @ SV11 ) )
        = $true )
      | ( ( ~ ( member @ ( g @ SV11 @ SV29 @ SV41 ) @ SV41 )
          | ( union @ SV11 @ SV29 @ SV41 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[131]) ).

thf(149,plain,
    ! [SV42: $i,SV30: $i,SV12: $i] :
      ( ( ( ~ ( member @ ( g @ SV12 @ SV30 @ SV42 ) @ SV30 ) )
        = $true )
      | ( ( ~ ( member @ ( g @ SV12 @ SV30 @ SV42 ) @ SV42 )
          | ( union @ SV12 @ SV30 @ SV42 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[132]) ).

thf(150,plain,
    ! [SV43: $i,SV31: $i,SV13: $i] :
      ( ( ( ~ ( intersection @ SV13 @ SV31 @ SV43 ) )
        = $true )
      | ( ( ! [SY114: $i] :
              ( ~ ( member @ SY114 @ SV43 )
              | ( member @ SY114 @ SV13 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[133]) ).

thf(151,plain,
    ! [SV44: $i,SV32: $i,SV14: $i] :
      ( ( ( ~ ( intersection @ SV14 @ SV32 @ SV44 ) )
        = $true )
      | ( ( ! [SY115: $i] :
              ( ~ ( member @ SY115 @ SV44 )
              | ( member @ SY115 @ SV32 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[134]) ).

thf(152,plain,
    ! [SV45: $i,SV33: $i,SV15: $i] :
      ( ( ( ~ ( intersection @ SV15 @ SV33 @ SV45 ) )
        = $true )
      | ( ( ! [SY116: $i] :
              ( ~ ( member @ SY116 @ SV33 )
              | ~ ( member @ SY116 @ SV15 )
              | ( member @ SY116 @ SV45 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[135]) ).

thf(153,plain,
    ! [SV46: $i,SV34: $i,SV16: $i] :
      ( ( ( member @ ( h @ SV16 @ SV34 @ SV46 ) @ SV46 )
        = $true )
      | ( ( ( intersection @ SV16 @ SV34 @ SV46 )
          | ( member @ ( h @ SV16 @ SV34 @ SV46 ) @ SV16 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[136]) ).

thf(154,plain,
    ! [SV47: $i,SV35: $i,SV17: $i] :
      ( ( ( member @ ( h @ SV17 @ SV35 @ SV47 ) @ SV47 )
        = $true )
      | ( ( ( intersection @ SV17 @ SV35 @ SV47 )
          | ( member @ ( h @ SV17 @ SV35 @ SV47 ) @ SV35 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[137]) ).

thf(155,plain,
    ! [SV48: $i,SV36: $i,SV18: $i] :
      ( ( ( ~ ( member @ ( h @ SV18 @ SV36 @ SV48 ) @ SV48 ) )
        = $true )
      | ( ( ~ ( member @ ( h @ SV18 @ SV36 @ SV48 ) @ SV36 )
          | ~ ( member @ ( h @ SV18 @ SV36 @ SV48 ) @ SV18 )
          | ( intersection @ SV18 @ SV36 @ SV48 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[138]) ).

thf(156,plain,
    ! [SV1: $i,SV49: $i,SV19: $i] :
      ( ( ( ~ ( subset @ SV19 @ SV49 )
          | ( member @ SV1 @ SV49 ) )
        = $true )
      | ( ( member @ SV1 @ SV19 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[139]) ).

thf(157,plain,
    ! [SV6: $i,SV24: $i] :
      ( ( ( ~ ( subset @ SV24 @ SV6 ) )
        = $true )
      | ( ( equal_sets @ SV24 @ SV6 )
        = $true )
      | ( ( subset @ SV6 @ SV24 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[143]) ).

thf(158,plain,
    ! [SV37: $i,SV25: $i,SV7: $i] :
      ( ( ( union @ SV7 @ SV25 @ SV37 )
        = $false )
      | ( ( ! [SY111: $i] :
              ( ~ ( member @ SY111 @ SV37 )
              | ( member @ SY111 @ SV7 )
              | ( member @ SY111 @ SV25 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[144]) ).

thf(159,plain,
    ! [SV38: $i,SV26: $i,SV8: $i] :
      ( ( ( union @ SV8 @ SV26 @ SV38 )
        = $false )
      | ( ( ! [SY112: $i] :
              ( ~ ( member @ SY112 @ SV8 )
              | ( member @ SY112 @ SV38 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[145]) ).

thf(160,plain,
    ! [SV39: $i,SV27: $i,SV9: $i] :
      ( ( ( union @ SV9 @ SV27 @ SV39 )
        = $false )
      | ( ( ! [SY113: $i] :
              ( ~ ( member @ SY113 @ SV27 )
              | ( member @ SY113 @ SV39 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[146]) ).

thf(161,plain,
    ! [SV40: $i,SV28: $i,SV10: $i] :
      ( ( ( member @ ( g @ SV10 @ SV28 @ SV40 ) @ SV10 )
        = $true )
      | ( ( ( member @ ( g @ SV10 @ SV28 @ SV40 ) @ SV28 )
          | ( member @ ( g @ SV10 @ SV28 @ SV40 ) @ SV40 ) )
        = $true )
      | ( ( union @ SV10 @ SV28 @ SV40 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[147]) ).

thf(162,plain,
    ! [SV41: $i,SV29: $i,SV11: $i] :
      ( ( ( member @ ( g @ SV11 @ SV29 @ SV41 ) @ SV11 )
        = $false )
      | ( ( ~ ( member @ ( g @ SV11 @ SV29 @ SV41 ) @ SV41 )
          | ( union @ SV11 @ SV29 @ SV41 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[148]) ).

thf(163,plain,
    ! [SV42: $i,SV30: $i,SV12: $i] :
      ( ( ( member @ ( g @ SV12 @ SV30 @ SV42 ) @ SV30 )
        = $false )
      | ( ( ~ ( member @ ( g @ SV12 @ SV30 @ SV42 ) @ SV42 )
          | ( union @ SV12 @ SV30 @ SV42 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[149]) ).

thf(164,plain,
    ! [SV43: $i,SV31: $i,SV13: $i] :
      ( ( ( intersection @ SV13 @ SV31 @ SV43 )
        = $false )
      | ( ( ! [SY114: $i] :
              ( ~ ( member @ SY114 @ SV43 )
              | ( member @ SY114 @ SV13 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[150]) ).

thf(165,plain,
    ! [SV44: $i,SV32: $i,SV14: $i] :
      ( ( ( intersection @ SV14 @ SV32 @ SV44 )
        = $false )
      | ( ( ! [SY115: $i] :
              ( ~ ( member @ SY115 @ SV44 )
              | ( member @ SY115 @ SV32 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[151]) ).

thf(166,plain,
    ! [SV45: $i,SV33: $i,SV15: $i] :
      ( ( ( intersection @ SV15 @ SV33 @ SV45 )
        = $false )
      | ( ( ! [SY116: $i] :
              ( ~ ( member @ SY116 @ SV33 )
              | ~ ( member @ SY116 @ SV15 )
              | ( member @ SY116 @ SV45 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[152]) ).

thf(167,plain,
    ! [SV46: $i,SV34: $i,SV16: $i] :
      ( ( ( intersection @ SV16 @ SV34 @ SV46 )
        = $true )
      | ( ( member @ ( h @ SV16 @ SV34 @ SV46 ) @ SV16 )
        = $true )
      | ( ( member @ ( h @ SV16 @ SV34 @ SV46 ) @ SV46 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[153]) ).

thf(168,plain,
    ! [SV47: $i,SV35: $i,SV17: $i] :
      ( ( ( intersection @ SV17 @ SV35 @ SV47 )
        = $true )
      | ( ( member @ ( h @ SV17 @ SV35 @ SV47 ) @ SV35 )
        = $true )
      | ( ( member @ ( h @ SV17 @ SV35 @ SV47 ) @ SV47 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[154]) ).

thf(169,plain,
    ! [SV48: $i,SV36: $i,SV18: $i] :
      ( ( ( member @ ( h @ SV18 @ SV36 @ SV48 ) @ SV48 )
        = $false )
      | ( ( ~ ( member @ ( h @ SV18 @ SV36 @ SV48 ) @ SV36 )
          | ~ ( member @ ( h @ SV18 @ SV36 @ SV48 ) @ SV18 )
          | ( intersection @ SV18 @ SV36 @ SV48 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[155]) ).

thf(170,plain,
    ! [SV1: $i,SV49: $i,SV19: $i] :
      ( ( ( ~ ( subset @ SV19 @ SV49 ) )
        = $true )
      | ( ( member @ SV1 @ SV49 )
        = $true )
      | ( ( member @ SV1 @ SV19 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[156]) ).

thf(171,plain,
    ! [SV6: $i,SV24: $i] :
      ( ( ( subset @ SV24 @ SV6 )
        = $false )
      | ( ( equal_sets @ SV24 @ SV6 )
        = $true )
      | ( ( subset @ SV6 @ SV24 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[157]) ).

thf(172,plain,
    ! [SV25: $i,SV7: $i,SV37: $i,SV50: $i] :
      ( ( ( ~ ( member @ SV50 @ SV37 )
          | ( member @ SV50 @ SV7 )
          | ( member @ SV50 @ SV25 ) )
        = $true )
      | ( ( union @ SV7 @ SV25 @ SV37 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[158]) ).

thf(173,plain,
    ! [SV26: $i,SV38: $i,SV8: $i,SV51: $i] :
      ( ( ( ~ ( member @ SV51 @ SV8 )
          | ( member @ SV51 @ SV38 ) )
        = $true )
      | ( ( union @ SV8 @ SV26 @ SV38 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[159]) ).

thf(174,plain,
    ! [SV9: $i,SV39: $i,SV27: $i,SV52: $i] :
      ( ( ( ~ ( member @ SV52 @ SV27 )
          | ( member @ SV52 @ SV39 ) )
        = $true )
      | ( ( union @ SV9 @ SV27 @ SV39 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[160]) ).

thf(175,plain,
    ! [SV40: $i,SV28: $i,SV10: $i] :
      ( ( ( member @ ( g @ SV10 @ SV28 @ SV40 ) @ SV28 )
        = $true )
      | ( ( member @ ( g @ SV10 @ SV28 @ SV40 ) @ SV40 )
        = $true )
      | ( ( member @ ( g @ SV10 @ SV28 @ SV40 ) @ SV10 )
        = $true )
      | ( ( union @ SV10 @ SV28 @ SV40 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[161]) ).

thf(176,plain,
    ! [SV41: $i,SV29: $i,SV11: $i] :
      ( ( ( ~ ( member @ ( g @ SV11 @ SV29 @ SV41 ) @ SV41 ) )
        = $true )
      | ( ( union @ SV11 @ SV29 @ SV41 )
        = $true )
      | ( ( member @ ( g @ SV11 @ SV29 @ SV41 ) @ SV11 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[162]) ).

thf(177,plain,
    ! [SV42: $i,SV30: $i,SV12: $i] :
      ( ( ( ~ ( member @ ( g @ SV12 @ SV30 @ SV42 ) @ SV42 ) )
        = $true )
      | ( ( union @ SV12 @ SV30 @ SV42 )
        = $true )
      | ( ( member @ ( g @ SV12 @ SV30 @ SV42 ) @ SV30 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[163]) ).

thf(178,plain,
    ! [SV31: $i,SV13: $i,SV43: $i,SV53: $i] :
      ( ( ( ~ ( member @ SV53 @ SV43 )
          | ( member @ SV53 @ SV13 ) )
        = $true )
      | ( ( intersection @ SV13 @ SV31 @ SV43 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[164]) ).

thf(179,plain,
    ! [SV14: $i,SV32: $i,SV44: $i,SV54: $i] :
      ( ( ( ~ ( member @ SV54 @ SV44 )
          | ( member @ SV54 @ SV32 ) )
        = $true )
      | ( ( intersection @ SV14 @ SV32 @ SV44 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[165]) ).

thf(180,plain,
    ! [SV45: $i,SV15: $i,SV33: $i,SV55: $i] :
      ( ( ( ~ ( member @ SV55 @ SV33 )
          | ~ ( member @ SV55 @ SV15 )
          | ( member @ SV55 @ SV45 ) )
        = $true )
      | ( ( intersection @ SV15 @ SV33 @ SV45 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[166]) ).

thf(181,plain,
    ! [SV48: $i,SV36: $i,SV18: $i] :
      ( ( ( ~ ( member @ ( h @ SV18 @ SV36 @ SV48 ) @ SV36 ) )
        = $true )
      | ( ( ~ ( member @ ( h @ SV18 @ SV36 @ SV48 ) @ SV18 )
          | ( intersection @ SV18 @ SV36 @ SV48 ) )
        = $true )
      | ( ( member @ ( h @ SV18 @ SV36 @ SV48 ) @ SV48 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[169]) ).

thf(182,plain,
    ! [SV1: $i,SV49: $i,SV19: $i] :
      ( ( ( subset @ SV19 @ SV49 )
        = $false )
      | ( ( member @ SV1 @ SV49 )
        = $true )
      | ( ( member @ SV1 @ SV19 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[170]) ).

thf(183,plain,
    ! [SV25: $i,SV7: $i,SV37: $i,SV50: $i] :
      ( ( ( ~ ( member @ SV50 @ SV37 ) )
        = $true )
      | ( ( ( member @ SV50 @ SV7 )
          | ( member @ SV50 @ SV25 ) )
        = $true )
      | ( ( union @ SV7 @ SV25 @ SV37 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[172]) ).

thf(184,plain,
    ! [SV26: $i,SV38: $i,SV8: $i,SV51: $i] :
      ( ( ( ~ ( member @ SV51 @ SV8 ) )
        = $true )
      | ( ( member @ SV51 @ SV38 )
        = $true )
      | ( ( union @ SV8 @ SV26 @ SV38 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[173]) ).

thf(185,plain,
    ! [SV9: $i,SV39: $i,SV27: $i,SV52: $i] :
      ( ( ( ~ ( member @ SV52 @ SV27 ) )
        = $true )
      | ( ( member @ SV52 @ SV39 )
        = $true )
      | ( ( union @ SV9 @ SV27 @ SV39 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[174]) ).

thf(186,plain,
    ! [SV41: $i,SV29: $i,SV11: $i] :
      ( ( ( member @ ( g @ SV11 @ SV29 @ SV41 ) @ SV41 )
        = $false )
      | ( ( union @ SV11 @ SV29 @ SV41 )
        = $true )
      | ( ( member @ ( g @ SV11 @ SV29 @ SV41 ) @ SV11 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[176]) ).

thf(187,plain,
    ! [SV42: $i,SV30: $i,SV12: $i] :
      ( ( ( member @ ( g @ SV12 @ SV30 @ SV42 ) @ SV42 )
        = $false )
      | ( ( union @ SV12 @ SV30 @ SV42 )
        = $true )
      | ( ( member @ ( g @ SV12 @ SV30 @ SV42 ) @ SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[177]) ).

thf(188,plain,
    ! [SV31: $i,SV13: $i,SV43: $i,SV53: $i] :
      ( ( ( ~ ( member @ SV53 @ SV43 ) )
        = $true )
      | ( ( member @ SV53 @ SV13 )
        = $true )
      | ( ( intersection @ SV13 @ SV31 @ SV43 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[178]) ).

thf(189,plain,
    ! [SV14: $i,SV32: $i,SV44: $i,SV54: $i] :
      ( ( ( ~ ( member @ SV54 @ SV44 ) )
        = $true )
      | ( ( member @ SV54 @ SV32 )
        = $true )
      | ( ( intersection @ SV14 @ SV32 @ SV44 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[179]) ).

thf(190,plain,
    ! [SV45: $i,SV15: $i,SV33: $i,SV55: $i] :
      ( ( ( ~ ( member @ SV55 @ SV33 ) )
        = $true )
      | ( ( ~ ( member @ SV55 @ SV15 )
          | ( member @ SV55 @ SV45 ) )
        = $true )
      | ( ( intersection @ SV15 @ SV33 @ SV45 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[180]) ).

thf(191,plain,
    ! [SV48: $i,SV36: $i,SV18: $i] :
      ( ( ( member @ ( h @ SV18 @ SV36 @ SV48 ) @ SV36 )
        = $false )
      | ( ( ~ ( member @ ( h @ SV18 @ SV36 @ SV48 ) @ SV18 )
          | ( intersection @ SV18 @ SV36 @ SV48 ) )
        = $true )
      | ( ( member @ ( h @ SV18 @ SV36 @ SV48 ) @ SV48 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[181]) ).

thf(192,plain,
    ! [SV25: $i,SV7: $i,SV37: $i,SV50: $i] :
      ( ( ( member @ SV50 @ SV37 )
        = $false )
      | ( ( ( member @ SV50 @ SV7 )
          | ( member @ SV50 @ SV25 ) )
        = $true )
      | ( ( union @ SV7 @ SV25 @ SV37 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[183]) ).

thf(193,plain,
    ! [SV26: $i,SV38: $i,SV8: $i,SV51: $i] :
      ( ( ( member @ SV51 @ SV8 )
        = $false )
      | ( ( member @ SV51 @ SV38 )
        = $true )
      | ( ( union @ SV8 @ SV26 @ SV38 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[184]) ).

thf(194,plain,
    ! [SV9: $i,SV39: $i,SV27: $i,SV52: $i] :
      ( ( ( member @ SV52 @ SV27 )
        = $false )
      | ( ( member @ SV52 @ SV39 )
        = $true )
      | ( ( union @ SV9 @ SV27 @ SV39 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[185]) ).

thf(195,plain,
    ! [SV31: $i,SV13: $i,SV43: $i,SV53: $i] :
      ( ( ( member @ SV53 @ SV43 )
        = $false )
      | ( ( member @ SV53 @ SV13 )
        = $true )
      | ( ( intersection @ SV13 @ SV31 @ SV43 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[188]) ).

thf(196,plain,
    ! [SV14: $i,SV32: $i,SV44: $i,SV54: $i] :
      ( ( ( member @ SV54 @ SV44 )
        = $false )
      | ( ( member @ SV54 @ SV32 )
        = $true )
      | ( ( intersection @ SV14 @ SV32 @ SV44 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[189]) ).

thf(197,plain,
    ! [SV45: $i,SV15: $i,SV33: $i,SV55: $i] :
      ( ( ( member @ SV55 @ SV33 )
        = $false )
      | ( ( ~ ( member @ SV55 @ SV15 )
          | ( member @ SV55 @ SV45 ) )
        = $true )
      | ( ( intersection @ SV15 @ SV33 @ SV45 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[190]) ).

thf(198,plain,
    ! [SV48: $i,SV36: $i,SV18: $i] :
      ( ( ( ~ ( member @ ( h @ SV18 @ SV36 @ SV48 ) @ SV18 ) )
        = $true )
      | ( ( intersection @ SV18 @ SV36 @ SV48 )
        = $true )
      | ( ( member @ ( h @ SV18 @ SV36 @ SV48 ) @ SV36 )
        = $false )
      | ( ( member @ ( h @ SV18 @ SV36 @ SV48 ) @ SV48 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[191]) ).

thf(199,plain,
    ! [SV37: $i,SV25: $i,SV7: $i,SV50: $i] :
      ( ( ( member @ SV50 @ SV7 )
        = $true )
      | ( ( member @ SV50 @ SV25 )
        = $true )
      | ( ( member @ SV50 @ SV37 )
        = $false )
      | ( ( union @ SV7 @ SV25 @ SV37 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[192]) ).

thf(200,plain,
    ! [SV33: $i,SV45: $i,SV15: $i,SV55: $i] :
      ( ( ( ~ ( member @ SV55 @ SV15 ) )
        = $true )
      | ( ( member @ SV55 @ SV45 )
        = $true )
      | ( ( member @ SV55 @ SV33 )
        = $false )
      | ( ( intersection @ SV15 @ SV33 @ SV45 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[197]) ).

thf(201,plain,
    ! [SV48: $i,SV36: $i,SV18: $i] :
      ( ( ( member @ ( h @ SV18 @ SV36 @ SV48 ) @ SV18 )
        = $false )
      | ( ( intersection @ SV18 @ SV36 @ SV48 )
        = $true )
      | ( ( member @ ( h @ SV18 @ SV36 @ SV48 ) @ SV36 )
        = $false )
      | ( ( member @ ( h @ SV18 @ SV36 @ SV48 ) @ SV48 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[198]) ).

thf(202,plain,
    ! [SV33: $i,SV45: $i,SV15: $i,SV55: $i] :
      ( ( ( member @ SV55 @ SV15 )
        = $false )
      | ( ( member @ SV55 @ SV45 )
        = $true )
      | ( ( member @ SV55 @ SV33 )
        = $false )
      | ( ( intersection @ SV15 @ SV33 @ SV45 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[200]) ).

thf(203,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[78,202,201,199,196,195,194,193,187,186,182,175,171,168,167,142,141,140,122,102,83,81,80,79]) ).

thf(204,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[203]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET007-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n007.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jul 10 00:20:46 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.36  
% 0.13/0.36   No.of.Axioms: 23
% 0.13/0.36  
% 0.13/0.36   Length.of.Defs: 0
% 0.13/0.36  
% 0.13/0.36   Contains.Choice.Funs: false
% 0.13/0.38  (rf:0,axioms:23,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:25,loop_count:0,foatp_calls:0,translation:fof_full)...........
% 0.83/1.05  
% 0.83/1.05  ********************************
% 0.83/1.05  *   All subproblems solved!    *
% 0.83/1.05  ********************************
% 0.83/1.05  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:23,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:203,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.90/1.06  
% 0.90/1.06  %**** Beginning of derivation protocol ****
% 0.90/1.06  % SZS output start CNFRefutation
% See solution above
% 0.90/1.06  
% 0.90/1.06  %**** End of derivation protocol ****
% 0.90/1.06  %**** no. of clauses in derivation: 204 ****
% 0.90/1.06  %**** clause counter: 203 ****
% 0.90/1.06  
% 0.90/1.06  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:23,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:203,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------