TSTP Solution File: SEU130+2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU130+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n011.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 12:06:55 EDT 2022

% Result   : Theorem 0.63s 0.77s
% Output   : CNFRefutation 0.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   55
% Syntax   : Number of formulae    :  461 ( 255 unt;  17 typ;   0 def)
%            Number of atoms       : 2680 ( 906 equ;   0 cnn)
%            Maximal formula atoms :    6 (   6 avg)
%            Number of connectives : 5576 ( 989   ~; 857   |;  70   &;3615   @)
%                                         (  16 <=>;  29  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  24   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  17 usr;   7 con; 0-3 aty)
%            Number of variables   : 1194 (   0   ^1186   !;   8   ?;1194   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_disjoint,type,
    disjoint: $i > $i > $o ).

thf(tp_empty,type,
    empty: $i > $o ).

thf(tp_empty_set,type,
    empty_set: $i ).

thf(tp_in,type,
    in: $i > $i > $o ).

thf(tp_sK10_C,type,
    sK10_C: $i > $i > $i ).

thf(tp_sK1_A,type,
    sK1_A: $i ).

thf(tp_sK2_SY74,type,
    sK2_SY74: $i ).

thf(tp_sK3_A,type,
    sK3_A: $i ).

thf(tp_sK4_A,type,
    sK4_A: $i ).

thf(tp_sK5_D,type,
    sK5_D: $i > $i > $i > $i ).

thf(tp_sK6_C,type,
    sK6_C: $i > $i > $i ).

thf(tp_sK7_D,type,
    sK7_D: $i > $i > $i > $i ).

thf(tp_sK8_B,type,
    sK8_B: $i > $i ).

thf(tp_sK9_C,type,
    sK9_C: $i > $i > $i ).

thf(tp_set_intersection2,type,
    set_intersection2: $i > $i > $i ).

thf(tp_set_union2,type,
    set_union2: $i > $i > $i ).

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

thf(1,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( empty @ A )
        & ( A != B )
        & ( empty @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).

thf(2,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( in @ A @ B )
        & ( empty @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( empty @ A )
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( set_intersection2 @ A @ empty_set )
      = empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( set_union2 @ A @ empty_set )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( disjoint @ A @ B )
     => ( disjoint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).

thf(7,axiom,
    ! [A: $i,B: $i] : ( subset @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(8,axiom,
    ? [A: $i] :
      ~ ( empty @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(9,axiom,
    ? [A: $i] : ( empty @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(10,axiom,
    ! [A: $i,B: $i] :
      ( ( set_intersection2 @ A @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).

thf(11,axiom,
    ! [A: $i,B: $i] :
      ( ( set_union2 @ A @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).

thf(12,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( empty @ A )
     => ~ ( empty @ ( set_union2 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).

thf(13,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( empty @ A )
     => ~ ( empty @ ( set_union2 @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).

thf(14,axiom,
    empty @ empty_set,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).

thf(15,axiom,
    $true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_xboole_0) ).

thf(16,axiom,
    $true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_xboole_0) ).

thf(17,axiom,
    $true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).

thf(18,axiom,
    ! [A: $i,B: $i] :
      ( ( disjoint @ A @ B )
    <=> ( ( set_intersection2 @ A @ B )
        = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).

thf(19,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( set_intersection2 @ A @ B ) )
    <=> ! [D: $i] :
          ( ( in @ D @ C )
        <=> ( ( in @ D @ A )
            & ( in @ D @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).

thf(20,axiom,
    ! [A: $i,B: $i] :
      ( ( subset @ A @ B )
    <=> ! [C: $i] :
          ( ( in @ C @ A )
         => ( in @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

thf(21,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( set_union2 @ A @ B ) )
    <=> ! [D: $i] :
          ( ( in @ D @ C )
        <=> ( ( in @ D @ A )
            | ( in @ D @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).

thf(22,axiom,
    ! [A: $i] :
      ( ( A = empty_set )
    <=> ! [B: $i] :
          ~ ( in @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).

thf(23,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
    <=> ( ( subset @ A @ B )
        & ( subset @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).

thf(24,axiom,
    ! [A: $i,B: $i] :
      ( ( set_intersection2 @ A @ B )
      = ( set_intersection2 @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

thf(25,axiom,
    ! [A: $i,B: $i] :
      ( ( set_union2 @ A @ B )
      = ( set_union2 @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

thf(26,axiom,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(27,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( subset @ A @ B )
        & ( subset @ C @ B ) )
     => ( subset @ ( set_union2 @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).

thf(28,axiom,
    ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).

thf(29,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( ~ ( disjoint @ A @ B )
          & ! [C: $i] :
              ~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
      & ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
          & ( disjoint @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).

thf(30,axiom,
    ! [A: $i] :
      ( ( subset @ A @ empty_set )
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).

thf(31,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( ~ ( disjoint @ A @ B )
          & ! [C: $i] :
              ~ ( ( in @ C @ A )
                & ( in @ C @ B ) ) )
      & ~ ( ? [C: $i] :
              ( ( in @ C @ A )
              & ( in @ C @ B ) )
          & ( disjoint @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).

thf(32,axiom,
    ! [A: $i] : ( subset @ empty_set @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).

thf(33,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( subset @ A @ B )
     => ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).

thf(34,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( subset @ A @ B )
        & ( subset @ B @ C ) )
     => ( subset @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).

thf(35,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( subset @ A @ B )
        & ( subset @ A @ C ) )
     => ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).

thf(36,axiom,
    ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).

thf(37,axiom,
    ! [A: $i,B: $i] :
      ( ( subset @ A @ B )
     => ( ( set_union2 @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).

thf(38,conjecture,
    ! [A: $i,B: $i] :
      ( ( subset @ A @ B )
     => ( ( set_intersection2 @ A @ B )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).

thf(39,negated_conjecture,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( ( set_intersection2 @ A @ B )
            = A ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[38]) ).

thf(40,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( ( set_intersection2 @ A @ B )
            = A ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[39]) ).

thf(41,plain,
    ( ( ! [A: $i,B: $i] :
          ~ ( ( empty @ A )
            & ( A != B )
            & ( empty @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(42,plain,
    ( ( ! [A: $i,B: $i] :
          ~ ( ( in @ A @ B )
            & ( empty @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(43,plain,
    ( ( ! [A: $i] :
          ( ( empty @ A )
         => ( A = empty_set ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(44,plain,
    ( ( ! [A: $i] :
          ( ( set_intersection2 @ A @ empty_set )
          = empty_set ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(45,plain,
    ( ( ! [A: $i] :
          ( ( set_union2 @ A @ empty_set )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(46,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( disjoint @ A @ B )
         => ( disjoint @ B @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(47,plain,
    ( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(48,plain,
    ( ( ? [A: $i] :
          ~ ( empty @ A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(49,plain,
    ( ( ? [A: $i] : ( empty @ A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(50,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( set_intersection2 @ A @ A )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(51,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( set_union2 @ A @ A )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(52,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( empty @ A )
         => ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(53,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( empty @ A )
         => ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(54,plain,
    ( ( empty @ empty_set )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(55,plain,
    $true = $true,
    inference(unfold_def,[status(thm)],[15]) ).

thf(56,plain,
    $true = $true,
    inference(unfold_def,[status(thm)],[16]) ).

thf(57,plain,
    $true = $true,
    inference(unfold_def,[status(thm)],[17]) ).

thf(58,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( disjoint @ A @ B )
        <=> ( ( set_intersection2 @ A @ B )
            = empty_set ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(59,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( C
            = ( set_intersection2 @ A @ B ) )
        <=> ! [D: $i] :
              ( ( in @ D @ C )
            <=> ( ( in @ D @ A )
                & ( in @ D @ B ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(60,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
        <=> ! [C: $i] :
              ( ( in @ C @ A )
             => ( in @ C @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(61,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( C
            = ( set_union2 @ A @ B ) )
        <=> ! [D: $i] :
              ( ( in @ D @ C )
            <=> ( ( in @ D @ A )
                | ( in @ D @ B ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[21]) ).

thf(62,plain,
    ( ( ! [A: $i] :
          ( ( A = empty_set )
        <=> ! [B: $i] :
              ~ ( in @ B @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[22]) ).

thf(63,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A = B )
        <=> ( ( subset @ A @ B )
            & ( subset @ B @ A ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[23]) ).

thf(64,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( set_intersection2 @ A @ B )
          = ( set_intersection2 @ B @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[24]) ).

thf(65,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( set_union2 @ A @ B )
          = ( set_union2 @ B @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[25]) ).

thf(66,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( in @ A @ B )
         => ~ ( in @ B @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[26]) ).

thf(67,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( ( subset @ A @ B )
            & ( subset @ C @ B ) )
         => ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[27]) ).

thf(68,plain,
    ( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[28]) ).

thf(69,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( ~ ( disjoint @ A @ B )
              & ! [C: $i] :
                  ~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
          & ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
              & ( disjoint @ A @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[29]) ).

thf(70,plain,
    ( ( ! [A: $i] :
          ( ( subset @ A @ empty_set )
         => ( A = empty_set ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[30]) ).

thf(71,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( ~ ( disjoint @ A @ B )
              & ! [C: $i] :
                  ~ ( ( in @ C @ A )
                    & ( in @ C @ B ) ) )
          & ~ ( ? [C: $i] :
                  ( ( in @ C @ A )
                  & ( in @ C @ B ) )
              & ( disjoint @ A @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[31]) ).

thf(72,plain,
    ( ( ! [A: $i] : ( subset @ empty_set @ A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[32]) ).

thf(73,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( subset @ A @ B )
         => ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[33]) ).

thf(74,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( ( subset @ A @ B )
            & ( subset @ B @ C ) )
         => ( subset @ A @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[34]) ).

thf(75,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( ( subset @ A @ B )
            & ( subset @ A @ C ) )
         => ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[35]) ).

thf(76,plain,
    ( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[36]) ).

thf(77,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( ( set_union2 @ A @ B )
            = B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[37]) ).

thf(78,plain,
    ( ( ! [SY74: $i] :
          ( ( subset @ sK1_A @ SY74 )
         => ( ( set_intersection2 @ sK1_A @ SY74 )
            = sK1_A ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[40]) ).

thf(79,plain,
    ( ( ( subset @ sK1_A @ sK2_SY74 )
     => ( ( set_intersection2 @ sK1_A @ sK2_SY74 )
        = sK1_A ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[78]) ).

thf(80,plain,
    ( ( subset @ sK1_A @ sK2_SY74 )
    = $true ),
    inference(standard_cnf,[status(thm)],[79]) ).

thf(81,plain,
    ( ( ( set_intersection2 @ sK1_A @ sK2_SY74 )
      = sK1_A )
    = $false ),
    inference(standard_cnf,[status(thm)],[79]) ).

thf(82,plain,
    ( ( ( ( set_intersection2 @ sK1_A @ sK2_SY74 )
       != sK1_A ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[81]) ).

thf(83,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A = B )
          | ~ ( empty @ A )
          | ~ ( empty @ B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[41]) ).

thf(84,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( empty @ B )
          | ~ ( in @ A @ B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[42]) ).

thf(85,plain,
    ( ( ! [A: $i] :
          ( ~ ( empty @ A )
          | ( A = empty_set ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[43]) ).

thf(86,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( disjoint @ A @ B )
          | ( disjoint @ B @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[46]) ).

thf(87,plain,
    ( ( ! [A: $i] : ( subset @ A @ A ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[47]) ).

thf(88,plain,
    ( ( ~ ( empty @ sK3_A ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[48]) ).

thf(89,plain,
    ( ( empty @ sK4_A )
    = $true ),
    inference(extcnf_combined,[status(esa)],[49]) ).

thf(90,plain,
    ( ( ! [A: $i] :
          ( ( set_intersection2 @ A @ A )
          = A ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[50]) ).

thf(91,plain,
    ( ( ! [A: $i] :
          ( ( set_union2 @ A @ A )
          = A ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[51]) ).

thf(92,plain,
    ( ( ! [A: $i] :
          ( ( empty @ A )
          | ! [B: $i] :
              ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[52]) ).

thf(93,plain,
    ( ( ! [A: $i] :
          ( ( empty @ A )
          | ! [B: $i] :
              ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[53]) ).

thf(94,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( set_intersection2 @ A @ B )
           != empty_set )
          | ( disjoint @ A @ B ) )
      & ! [A: $i,B: $i] :
          ( ~ ( disjoint @ A @ B )
          | ( ( set_intersection2 @ A @ B )
            = empty_set ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[58]) ).

thf(95,plain,
    ( ( ! [A: $i] :
          ( ! [B: $i,C: $i] :
              ( ( ( ~ ( in @ ( sK5_D @ C @ B @ A ) @ A )
                  | ~ ( in @ ( sK5_D @ C @ B @ A ) @ B )
                  | ~ ( in @ ( sK5_D @ C @ B @ A ) @ C ) )
                & ( ( in @ ( sK5_D @ C @ B @ A ) @ A )
                  | ( in @ ( sK5_D @ C @ B @ A ) @ C ) )
                & ( ( in @ ( sK5_D @ C @ B @ A ) @ B )
                  | ( in @ ( sK5_D @ C @ B @ A ) @ C ) ) )
              | ( C
                = ( set_intersection2 @ A @ B ) ) )
          & ! [B: $i,C: $i] :
              ( ( C
               != ( set_intersection2 @ A @ B ) )
              | ( ! [D: $i] :
                    ( ~ ( in @ D @ A )
                    | ~ ( in @ D @ B )
                    | ( in @ D @ C ) )
                & ! [D: $i] :
                    ( ~ ( in @ D @ C )
                    | ( in @ D @ A ) )
                & ! [D: $i] :
                    ( ~ ( in @ D @ C )
                    | ( in @ D @ B ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[59]) ).

thf(96,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( in @ ( sK6_C @ B @ A ) @ A )
            & ~ ( in @ ( sK6_C @ B @ A ) @ B ) )
          | ( subset @ A @ B ) )
      & ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ! [C: $i] :
              ( ~ ( in @ C @ A )
              | ( in @ C @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[60]) ).

thf(97,plain,
    ( ( ! [A: $i] :
          ( ! [B: $i,C: $i] :
              ( ( ( ~ ( in @ ( sK7_D @ C @ B @ A ) @ C )
                  | ~ ( in @ ( sK7_D @ C @ B @ A ) @ A ) )
                & ( ~ ( in @ ( sK7_D @ C @ B @ A ) @ C )
                  | ~ ( in @ ( sK7_D @ C @ B @ A ) @ B ) )
                & ( ( in @ ( sK7_D @ C @ B @ A ) @ C )
                  | ( in @ ( sK7_D @ C @ B @ A ) @ A )
                  | ( in @ ( sK7_D @ C @ B @ A ) @ B ) ) )
              | ( C
                = ( set_union2 @ A @ B ) ) )
          & ! [B: $i,C: $i] :
              ( ( C
               != ( set_union2 @ A @ B ) )
              | ( ! [D: $i] :
                    ( ~ ( in @ D @ C )
                    | ( in @ D @ A )
                    | ( in @ D @ B ) )
                & ! [D: $i] :
                    ( ~ ( in @ D @ A )
                    | ( in @ D @ C ) )
                & ! [D: $i] :
                    ( ~ ( in @ D @ B )
                    | ( in @ D @ C ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[61]) ).

thf(98,plain,
    ( ( ! [A: $i] :
          ( ( in @ ( sK8_B @ A ) @ A )
          | ( A = empty_set ) )
      & ! [A: $i] :
          ( ( A != empty_set )
          | ! [B: $i] :
              ~ ( in @ B @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[62]) ).

thf(99,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ~ ( subset @ B @ A )
          | ( A = B ) )
      & ! [A: $i,B: $i] :
          ( ( A != B )
          | ( subset @ A @ B ) )
      & ! [A: $i,B: $i] :
          ( ( A != B )
          | ( subset @ B @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[63]) ).

thf(100,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ A @ B )
          | ~ ( in @ B @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[66]) ).

thf(101,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( subset @ A @ B )
          | ~ ( subset @ C @ B )
          | ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[67]) ).

thf(102,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( disjoint @ A @ B )
          | ( in @ ( sK9_C @ B @ A ) @ ( set_intersection2 @ A @ B ) ) )
      & ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ~ ( in @ C @ ( set_intersection2 @ A @ B ) )
          | ~ ( disjoint @ A @ B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[69]) ).

thf(103,plain,
    ( ( ! [A: $i] :
          ( ~ ( subset @ A @ empty_set )
          | ( A = empty_set ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[70]) ).

thf(104,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( disjoint @ A @ B )
          | ( ( in @ ( sK10_C @ B @ A ) @ A )
            & ( in @ ( sK10_C @ B @ A ) @ B ) ) )
      & ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ~ ( in @ C @ A )
              | ~ ( in @ C @ B ) )
          | ~ ( disjoint @ A @ B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[71]) ).

thf(105,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[73]) ).

thf(106,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( subset @ A @ B )
          | ~ ( subset @ B @ C )
          | ( subset @ A @ C ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[74]) ).

thf(107,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( subset @ A @ B )
          | ~ ( subset @ A @ C )
          | ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[75]) ).

thf(108,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ( ( set_union2 @ A @ B )
            = B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[77]) ).

thf(109,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ( ( set_union2 @ A @ B )
            = B ) ) )
    = $true ),
    inference(copy,[status(thm)],[108]) ).

thf(110,plain,
    ( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
    = $true ),
    inference(copy,[status(thm)],[76]) ).

thf(111,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( subset @ A @ B )
          | ~ ( subset @ A @ C )
          | ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[107]) ).

thf(112,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( subset @ A @ B )
          | ~ ( subset @ B @ C )
          | ( subset @ A @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[106]) ).

thf(113,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[105]) ).

thf(114,plain,
    ( ( ! [A: $i] : ( subset @ empty_set @ A ) )
    = $true ),
    inference(copy,[status(thm)],[72]) ).

thf(115,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( disjoint @ A @ B )
          | ( ( in @ ( sK10_C @ B @ A ) @ A )
            & ( in @ ( sK10_C @ B @ A ) @ B ) ) )
      & ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ~ ( in @ C @ A )
              | ~ ( in @ C @ B ) )
          | ~ ( disjoint @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[104]) ).

thf(116,plain,
    ( ( ! [A: $i] :
          ( ~ ( subset @ A @ empty_set )
          | ( A = empty_set ) ) )
    = $true ),
    inference(copy,[status(thm)],[103]) ).

thf(117,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( disjoint @ A @ B )
          | ( in @ ( sK9_C @ B @ A ) @ ( set_intersection2 @ A @ B ) ) )
      & ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ~ ( in @ C @ ( set_intersection2 @ A @ B ) )
          | ~ ( disjoint @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[102]) ).

thf(118,plain,
    ( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[68]) ).

thf(119,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( subset @ A @ B )
          | ~ ( subset @ C @ B )
          | ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[101]) ).

thf(120,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ A @ B )
          | ~ ( in @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[100]) ).

thf(121,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( set_union2 @ A @ B )
          = ( set_union2 @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[65]) ).

thf(122,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( set_intersection2 @ A @ B )
          = ( set_intersection2 @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[64]) ).

thf(123,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ~ ( subset @ B @ A )
          | ( A = B ) )
      & ! [A: $i,B: $i] :
          ( ( A != B )
          | ( subset @ A @ B ) )
      & ! [A: $i,B: $i] :
          ( ( A != B )
          | ( subset @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[99]) ).

thf(124,plain,
    ( ( ! [A: $i] :
          ( ( in @ ( sK8_B @ A ) @ A )
          | ( A = empty_set ) )
      & ! [A: $i] :
          ( ( A != empty_set )
          | ! [B: $i] :
              ~ ( in @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[98]) ).

thf(125,plain,
    ( ( ! [A: $i] :
          ( ! [B: $i,C: $i] :
              ( ( ( ~ ( in @ ( sK7_D @ C @ B @ A ) @ C )
                  | ~ ( in @ ( sK7_D @ C @ B @ A ) @ A ) )
                & ( ~ ( in @ ( sK7_D @ C @ B @ A ) @ C )
                  | ~ ( in @ ( sK7_D @ C @ B @ A ) @ B ) )
                & ( ( in @ ( sK7_D @ C @ B @ A ) @ C )
                  | ( in @ ( sK7_D @ C @ B @ A ) @ A )
                  | ( in @ ( sK7_D @ C @ B @ A ) @ B ) ) )
              | ( C
                = ( set_union2 @ A @ B ) ) )
          & ! [B: $i,C: $i] :
              ( ( C
               != ( set_union2 @ A @ B ) )
              | ( ! [D: $i] :
                    ( ~ ( in @ D @ C )
                    | ( in @ D @ A )
                    | ( in @ D @ B ) )
                & ! [D: $i] :
                    ( ~ ( in @ D @ A )
                    | ( in @ D @ C ) )
                & ! [D: $i] :
                    ( ~ ( in @ D @ B )
                    | ( in @ D @ C ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[97]) ).

thf(126,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( in @ ( sK6_C @ B @ A ) @ A )
            & ~ ( in @ ( sK6_C @ B @ A ) @ B ) )
          | ( subset @ A @ B ) )
      & ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ! [C: $i] :
              ( ~ ( in @ C @ A )
              | ( in @ C @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[96]) ).

thf(127,plain,
    ( ( ! [A: $i] :
          ( ! [B: $i,C: $i] :
              ( ( ( ~ ( in @ ( sK5_D @ C @ B @ A ) @ A )
                  | ~ ( in @ ( sK5_D @ C @ B @ A ) @ B )
                  | ~ ( in @ ( sK5_D @ C @ B @ A ) @ C ) )
                & ( ( in @ ( sK5_D @ C @ B @ A ) @ A )
                  | ( in @ ( sK5_D @ C @ B @ A ) @ C ) )
                & ( ( in @ ( sK5_D @ C @ B @ A ) @ B )
                  | ( in @ ( sK5_D @ C @ B @ A ) @ C ) ) )
              | ( C
                = ( set_intersection2 @ A @ B ) ) )
          & ! [B: $i,C: $i] :
              ( ( C
               != ( set_intersection2 @ A @ B ) )
              | ( ! [D: $i] :
                    ( ~ ( in @ D @ A )
                    | ~ ( in @ D @ B )
                    | ( in @ D @ C ) )
                & ! [D: $i] :
                    ( ~ ( in @ D @ C )
                    | ( in @ D @ A ) )
                & ! [D: $i] :
                    ( ~ ( in @ D @ C )
                    | ( in @ D @ B ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[95]) ).

thf(128,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( set_intersection2 @ A @ B )
           != empty_set )
          | ( disjoint @ A @ B ) )
      & ! [A: $i,B: $i] :
          ( ~ ( disjoint @ A @ B )
          | ( ( set_intersection2 @ A @ B )
            = empty_set ) ) )
    = $true ),
    inference(copy,[status(thm)],[94]) ).

thf(129,plain,
    $true = $true,
    inference(copy,[status(thm)],[57]) ).

thf(130,plain,
    $true = $true,
    inference(copy,[status(thm)],[56]) ).

thf(131,plain,
    $true = $true,
    inference(copy,[status(thm)],[55]) ).

thf(132,plain,
    ( ( empty @ empty_set )
    = $true ),
    inference(copy,[status(thm)],[54]) ).

thf(133,plain,
    ( ( ! [A: $i] :
          ( ( empty @ A )
          | ! [B: $i] :
              ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[93]) ).

thf(134,plain,
    ( ( ! [A: $i] :
          ( ( empty @ A )
          | ! [B: $i] :
              ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[92]) ).

thf(135,plain,
    ( ( ! [A: $i] :
          ( ( set_union2 @ A @ A )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[91]) ).

thf(136,plain,
    ( ( ! [A: $i] :
          ( ( set_intersection2 @ A @ A )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[90]) ).

thf(137,plain,
    ( ( empty @ sK4_A )
    = $true ),
    inference(copy,[status(thm)],[89]) ).

thf(138,plain,
    ( ( ~ ( empty @ sK3_A ) )
    = $true ),
    inference(copy,[status(thm)],[88]) ).

thf(139,plain,
    ( ( ! [A: $i] : ( subset @ A @ A ) )
    = $true ),
    inference(copy,[status(thm)],[87]) ).

thf(140,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( disjoint @ A @ B )
          | ( disjoint @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[86]) ).

thf(141,plain,
    ( ( ! [A: $i] :
          ( ( set_union2 @ A @ empty_set )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[45]) ).

thf(142,plain,
    ( ( ! [A: $i] :
          ( ( set_intersection2 @ A @ empty_set )
          = empty_set ) )
    = $true ),
    inference(copy,[status(thm)],[44]) ).

thf(143,plain,
    ( ( ! [A: $i] :
          ( ~ ( empty @ A )
          | ( A = empty_set ) ) )
    = $true ),
    inference(copy,[status(thm)],[85]) ).

thf(144,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( empty @ B )
          | ~ ( in @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[84]) ).

thf(145,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A = B )
          | ~ ( empty @ A )
          | ~ ( empty @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[83]) ).

thf(146,plain,
    ( ( subset @ sK1_A @ sK2_SY74 )
    = $true ),
    inference(copy,[status(thm)],[80]) ).

thf(147,plain,
    ( ( ( ( set_intersection2 @ sK1_A @ sK2_SY74 )
       != sK1_A ) )
    = $true ),
    inference(copy,[status(thm)],[82]) ).

thf(148,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( disjoint @ SX0 @ SX1 )
                | ~ ( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX0 )
                    | ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ! [SX2: $i] :
                    ( ~ ( in @ SX2 @ SX0 )
                    | ~ ( in @ SX2 @ SX1 ) )
                | ~ ( disjoint @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[115]) ).

thf(149,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( subset @ SX0 @ SX1 )
                | ~ ( subset @ SX1 @ SX0 )
                | ( SX0 = SX1 ) )
          | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                      ( ( SX0 != SX1 )
                      | ( subset @ SX0 @ SX1 ) )
                | ~ ! [SX0: $i,SX1: $i] :
                      ( ( SX0 != SX1 )
                      | ( subset @ SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[123]) ).

thf(150,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( ( set_intersection2 @ SX0 @ SX1 )
                 != empty_set )
                | ( disjoint @ SX0 @ SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( disjoint @ SX0 @ SX1 )
                | ( ( set_intersection2 @ SX0 @ SX1 )
                  = empty_set ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[128]) ).

thf(151,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX0 )
                    | ~ ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX1 ) )
                | ( subset @ SX0 @ SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( subset @ SX0 @ SX1 )
                | ! [SX2: $i] :
                    ( ~ ( in @ SX2 @ SX0 )
                    | ( in @ SX2 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[126]) ).

thf(152,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( ~ ( ~ ( in @ ( sK5_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
                          | ~ ( in @ ( sK5_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
                          | ~ ( in @ ( sK5_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
                      | ~ ~ ( ~ ( ( in @ ( sK5_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
                                | ( in @ ( sK5_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
                            | ~ ( ( in @ ( sK5_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
                                | ( in @ ( sK5_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
                  | ( SX2
                    = ( set_intersection2 @ SX0 @ SX1 ) ) )
            | ~ ! [SX1: $i,SX2: $i] :
                  ( ( SX2
                   != ( set_intersection2 @ SX0 @ SX1 ) )
                  | ~ ( ~ ! [SX3: $i] :
                            ( ~ ( in @ SX3 @ SX0 )
                            | ~ ( in @ SX3 @ SX1 )
                            | ( in @ SX3 @ SX2 ) )
                      | ~ ~ ( ~ ! [SX3: $i] :
                                  ( ~ ( in @ SX3 @ SX2 )
                                  | ( in @ SX3 @ SX0 ) )
                            | ~ ! [SX3: $i] :
                                  ( ~ ( in @ SX3 @ SX2 )
                                  | ( in @ SX3 @ SX1 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[127]) ).

thf(153,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( disjoint @ SX0 @ SX1 )
                | ( in @ ( sK9_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ! [SX2: $i] :
                    ~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
                | ~ ( disjoint @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[117]) ).

thf(154,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
                                | ~ ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
                            | ~ ( ~ ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
                                | ~ ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
                      | ~ ( ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
                          | ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
                          | ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
                  | ( SX2
                    = ( set_union2 @ SX0 @ SX1 ) ) )
            | ~ ! [SX1: $i,SX2: $i] :
                  ( ( SX2
                   != ( set_union2 @ SX0 @ SX1 ) )
                  | ~ ( ~ ! [SX3: $i] :
                            ( ~ ( in @ SX3 @ SX2 )
                            | ( in @ SX3 @ SX0 )
                            | ( in @ SX3 @ SX1 ) )
                      | ~ ~ ( ~ ! [SX3: $i] :
                                  ( ~ ( in @ SX3 @ SX0 )
                                  | ( in @ SX3 @ SX2 ) )
                            | ~ ! [SX3: $i] :
                                  ( ~ ( in @ SX3 @ SX1 )
                                  | ( in @ SX3 @ SX2 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[125]) ).

thf(155,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ( in @ ( sK8_B @ SX0 ) @ SX0 )
                | ( SX0 = empty_set ) )
          | ~ ! [SX0: $i] :
                ( ( SX0 != empty_set )
                | ! [SX1: $i] :
                    ~ ( in @ SX1 @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[124]) ).

thf(156,plain,
    ! [SV1: $i] :
      ( ( ! [SY75: $i] :
            ( ~ ( subset @ SV1 @ SY75 )
            | ( ( set_union2 @ SV1 @ SY75 )
              = SY75 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[109]) ).

thf(157,plain,
    ! [SV2: $i] :
      ( ( ! [SY76: $i] : ( subset @ ( set_intersection2 @ SV2 @ SY76 ) @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[110]) ).

thf(158,plain,
    ! [SV3: $i] :
      ( ( ! [SY77: $i,SY78: $i] :
            ( ~ ( subset @ SV3 @ SY77 )
            | ~ ( subset @ SV3 @ SY78 )
            | ( subset @ SV3 @ ( set_intersection2 @ SY77 @ SY78 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[111]) ).

thf(159,plain,
    ! [SV4: $i] :
      ( ( ! [SY79: $i,SY80: $i] :
            ( ~ ( subset @ SV4 @ SY79 )
            | ~ ( subset @ SY79 @ SY80 )
            | ( subset @ SV4 @ SY80 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[112]) ).

thf(160,plain,
    ! [SV5: $i] :
      ( ( ! [SY81: $i] :
            ( ~ ( subset @ SV5 @ SY81 )
            | ! [SY82: $i] : ( subset @ ( set_intersection2 @ SV5 @ SY82 ) @ ( set_intersection2 @ SY81 @ SY82 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[113]) ).

thf(161,plain,
    ! [SV6: $i] :
      ( ( subset @ empty_set @ SV6 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[114]) ).

thf(162,plain,
    ! [SV7: $i] :
      ( ( ~ ( subset @ SV7 @ empty_set )
        | ( SV7 = empty_set ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[116]) ).

thf(163,plain,
    ! [SV8: $i] :
      ( ( ! [SY83: $i] : ( subset @ SV8 @ ( set_union2 @ SV8 @ SY83 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[118]) ).

thf(164,plain,
    ! [SV9: $i] :
      ( ( ! [SY84: $i,SY85: $i] :
            ( ~ ( subset @ SV9 @ SY84 )
            | ~ ( subset @ SY85 @ SY84 )
            | ( subset @ ( set_union2 @ SV9 @ SY85 ) @ SY84 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[119]) ).

thf(165,plain,
    ! [SV10: $i] :
      ( ( ! [SY86: $i] :
            ( ~ ( in @ SV10 @ SY86 )
            | ~ ( in @ SY86 @ SV10 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[120]) ).

thf(166,plain,
    ! [SV11: $i] :
      ( ( ! [SY87: $i] :
            ( ( set_union2 @ SV11 @ SY87 )
            = ( set_union2 @ SY87 @ SV11 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[121]) ).

thf(167,plain,
    ! [SV12: $i] :
      ( ( ! [SY88: $i] :
            ( ( set_intersection2 @ SV12 @ SY88 )
            = ( set_intersection2 @ SY88 @ SV12 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[122]) ).

thf(168,plain,
    ! [SV13: $i] :
      ( ( ( empty @ SV13 )
        | ! [SY89: $i] :
            ~ ( empty @ ( set_union2 @ SV13 @ SY89 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[133]) ).

thf(169,plain,
    ! [SV14: $i] :
      ( ( ( empty @ SV14 )
        | ! [SY90: $i] :
            ~ ( empty @ ( set_union2 @ SY90 @ SV14 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[134]) ).

thf(170,plain,
    ! [SV15: $i] :
      ( ( ( set_union2 @ SV15 @ SV15 )
        = SV15 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[135]) ).

thf(171,plain,
    ! [SV16: $i] :
      ( ( ( set_intersection2 @ SV16 @ SV16 )
        = SV16 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[136]) ).

thf(172,plain,
    ( ( empty @ sK3_A )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[138]) ).

thf(173,plain,
    ! [SV17: $i] :
      ( ( subset @ SV17 @ SV17 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[139]) ).

thf(174,plain,
    ! [SV18: $i] :
      ( ( ! [SY91: $i] :
            ( ~ ( disjoint @ SV18 @ SY91 )
            | ( disjoint @ SY91 @ SV18 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[140]) ).

thf(175,plain,
    ! [SV19: $i] :
      ( ( ( set_union2 @ SV19 @ empty_set )
        = SV19 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[141]) ).

thf(176,plain,
    ! [SV20: $i] :
      ( ( ( set_intersection2 @ SV20 @ empty_set )
        = empty_set )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[142]) ).

thf(177,plain,
    ! [SV21: $i] :
      ( ( ~ ( empty @ SV21 )
        | ( SV21 = empty_set ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[143]) ).

thf(178,plain,
    ! [SV22: $i] :
      ( ( ! [SY92: $i] :
            ( ~ ( empty @ SY92 )
            | ~ ( in @ SV22 @ SY92 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[144]) ).

thf(179,plain,
    ! [SV23: $i] :
      ( ( ! [SY93: $i] :
            ( ( SV23 = SY93 )
            | ~ ( empty @ SV23 )
            | ~ ( empty @ SY93 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[145]) ).

thf(180,plain,
    ( ( ( set_intersection2 @ sK1_A @ sK2_SY74 )
      = sK1_A )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[147]) ).

thf(181,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( disjoint @ SX0 @ SX1 )
            | ~ ( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX0 )
                | ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ! [SX2: $i] :
                ( ~ ( in @ SX2 @ SX0 )
                | ~ ( in @ SX2 @ SX1 ) )
            | ~ ( disjoint @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[148]) ).

thf(182,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( subset @ SX0 @ SX1 )
            | ~ ( subset @ SX1 @ SX0 )
            | ( SX0 = SX1 ) )
      | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ( SX0 != SX1 )
                  | ( subset @ SX0 @ SX1 ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ( SX0 != SX1 )
                  | ( subset @ SX1 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[149]) ).

thf(183,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( set_intersection2 @ SX0 @ SX1 )
             != empty_set )
            | ( disjoint @ SX0 @ SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( disjoint @ SX0 @ SX1 )
            | ( ( set_intersection2 @ SX0 @ SX1 )
              = empty_set ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[150]) ).

thf(184,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX0 )
                | ~ ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX1 ) )
            | ( subset @ SX0 @ SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( subset @ SX0 @ SX1 )
            | ! [SX2: $i] :
                ( ~ ( in @ SX2 @ SX0 )
                | ( in @ SX2 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[151]) ).

thf(185,plain,
    ! [SV24: $i] :
      ( ( ~ ( ~ ! [SY94: $i,SY95: $i] :
                  ( ~ ( ~ ( ~ ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SV24 )
                          | ~ ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SY94 )
                          | ~ ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SY95 ) )
                      | ~ ~ ( ~ ( ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SV24 )
                                | ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SY95 ) )
                            | ~ ( ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SY94 )
                                | ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SY95 ) ) ) )
                  | ( SY95
                    = ( set_intersection2 @ SV24 @ SY94 ) ) )
            | ~ ! [SY96: $i,SY97: $i] :
                  ( ( SY97
                   != ( set_intersection2 @ SV24 @ SY96 ) )
                  | ~ ( ~ ! [SY98: $i] :
                            ( ~ ( in @ SY98 @ SV24 )
                            | ~ ( in @ SY98 @ SY96 )
                            | ( in @ SY98 @ SY97 ) )
                      | ~ ~ ( ~ ! [SY99: $i] :
                                  ( ~ ( in @ SY99 @ SY97 )
                                  | ( in @ SY99 @ SV24 ) )
                            | ~ ! [SX3: $i] :
                                  ( ~ ( in @ SX3 @ SY97 )
                                  | ( in @ SX3 @ SY96 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[152]) ).

thf(186,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( disjoint @ SX0 @ SX1 )
            | ( in @ ( sK9_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ! [SX2: $i] :
                ~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
            | ~ ( disjoint @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[153]) ).

thf(187,plain,
    ! [SV25: $i] :
      ( ( ~ ( ~ ! [SY101: $i,SY102: $i] :
                  ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SY102 )
                                | ~ ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SV25 ) )
                            | ~ ( ~ ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SY102 )
                                | ~ ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SY101 ) ) )
                      | ~ ( ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SY102 )
                          | ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SV25 )
                          | ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SY101 ) ) )
                  | ( SY102
                    = ( set_union2 @ SV25 @ SY101 ) ) )
            | ~ ! [SY103: $i,SY104: $i] :
                  ( ( SY104
                   != ( set_union2 @ SV25 @ SY103 ) )
                  | ~ ( ~ ! [SY105: $i] :
                            ( ~ ( in @ SY105 @ SY104 )
                            | ( in @ SY105 @ SV25 )
                            | ( in @ SY105 @ SY103 ) )
                      | ~ ~ ( ~ ! [SY106: $i] :
                                  ( ~ ( in @ SY106 @ SV25 )
                                  | ( in @ SY106 @ SY104 ) )
                            | ~ ! [SX3: $i] :
                                  ( ~ ( in @ SX3 @ SY103 )
                                  | ( in @ SX3 @ SY104 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[154]) ).

thf(188,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( in @ ( sK8_B @ SX0 ) @ SX0 )
            | ( SX0 = empty_set ) )
      | ~ ! [SX0: $i] :
            ( ( SX0 != empty_set )
            | ! [SX1: $i] :
                ~ ( in @ SX1 @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[155]) ).

thf(189,plain,
    ! [SV26: $i,SV1: $i] :
      ( ( ~ ( subset @ SV1 @ SV26 )
        | ( ( set_union2 @ SV1 @ SV26 )
          = SV26 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[156]) ).

thf(190,plain,
    ! [SV27: $i,SV2: $i] :
      ( ( subset @ ( set_intersection2 @ SV2 @ SV27 ) @ SV2 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[157]) ).

thf(191,plain,
    ! [SV28: $i,SV3: $i] :
      ( ( ! [SY108: $i] :
            ( ~ ( subset @ SV3 @ SV28 )
            | ~ ( subset @ SV3 @ SY108 )
            | ( subset @ SV3 @ ( set_intersection2 @ SV28 @ SY108 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[158]) ).

thf(192,plain,
    ! [SV29: $i,SV4: $i] :
      ( ( ! [SY109: $i] :
            ( ~ ( subset @ SV4 @ SV29 )
            | ~ ( subset @ SV29 @ SY109 )
            | ( subset @ SV4 @ SY109 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[159]) ).

thf(193,plain,
    ! [SV30: $i,SV5: $i] :
      ( ( ~ ( subset @ SV5 @ SV30 )
        | ! [SY110: $i] : ( subset @ ( set_intersection2 @ SV5 @ SY110 ) @ ( set_intersection2 @ SV30 @ SY110 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[160]) ).

thf(194,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( subset @ SV7 @ empty_set ) )
        = $true )
      | ( ( SV7 = empty_set )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[162]) ).

thf(195,plain,
    ! [SV31: $i,SV8: $i] :
      ( ( subset @ SV8 @ ( set_union2 @ SV8 @ SV31 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[163]) ).

thf(196,plain,
    ! [SV32: $i,SV9: $i] :
      ( ( ! [SY111: $i] :
            ( ~ ( subset @ SV9 @ SV32 )
            | ~ ( subset @ SY111 @ SV32 )
            | ( subset @ ( set_union2 @ SV9 @ SY111 ) @ SV32 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[164]) ).

thf(197,plain,
    ! [SV33: $i,SV10: $i] :
      ( ( ~ ( in @ SV10 @ SV33 )
        | ~ ( in @ SV33 @ SV10 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[165]) ).

thf(198,plain,
    ! [SV34: $i,SV11: $i] :
      ( ( ( set_union2 @ SV11 @ SV34 )
        = ( set_union2 @ SV34 @ SV11 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[166]) ).

thf(199,plain,
    ! [SV35: $i,SV12: $i] :
      ( ( ( set_intersection2 @ SV12 @ SV35 )
        = ( set_intersection2 @ SV35 @ SV12 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[167]) ).

thf(200,plain,
    ! [SV13: $i] :
      ( ( ( empty @ SV13 )
        = $true )
      | ( ( ! [SY89: $i] :
              ~ ( empty @ ( set_union2 @ SV13 @ SY89 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[168]) ).

thf(201,plain,
    ! [SV14: $i] :
      ( ( ( empty @ SV14 )
        = $true )
      | ( ( ! [SY90: $i] :
              ~ ( empty @ ( set_union2 @ SY90 @ SV14 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[169]) ).

thf(202,plain,
    ! [SV36: $i,SV18: $i] :
      ( ( ~ ( disjoint @ SV18 @ SV36 )
        | ( disjoint @ SV36 @ SV18 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[174]) ).

thf(203,plain,
    ! [SV21: $i] :
      ( ( ( ~ ( empty @ SV21 ) )
        = $true )
      | ( ( SV21 = empty_set )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[177]) ).

thf(204,plain,
    ! [SV22: $i,SV37: $i] :
      ( ( ~ ( empty @ SV37 )
        | ~ ( in @ SV22 @ SV37 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[178]) ).

thf(205,plain,
    ! [SV38: $i,SV23: $i] :
      ( ( ( SV23 = SV38 )
        | ~ ( empty @ SV23 )
        | ~ ( empty @ SV38 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[179]) ).

thf(206,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( disjoint @ SX0 @ SX1 )
            | ~ ( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX0 )
                | ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[181]) ).

thf(207,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ! [SX2: $i] :
                ( ~ ( in @ SX2 @ SX0 )
                | ~ ( in @ SX2 @ SX1 ) )
            | ~ ( disjoint @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[181]) ).

thf(208,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( subset @ SX0 @ SX1 )
            | ~ ( subset @ SX1 @ SX0 )
            | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[182]) ).

thf(209,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ( SX0 != SX1 )
                  | ( subset @ SX0 @ SX1 ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ( SX0 != SX1 )
                  | ( subset @ SX1 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[182]) ).

thf(210,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( set_intersection2 @ SX0 @ SX1 )
             != empty_set )
            | ( disjoint @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[183]) ).

thf(211,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( disjoint @ SX0 @ SX1 )
            | ( ( set_intersection2 @ SX0 @ SX1 )
              = empty_set ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[183]) ).

thf(212,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX0 )
                | ~ ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX1 ) )
            | ( subset @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[184]) ).

thf(213,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( subset @ SX0 @ SX1 )
            | ! [SX2: $i] :
                ( ~ ( in @ SX2 @ SX0 )
                | ( in @ SX2 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[184]) ).

thf(214,plain,
    ! [SV24: $i] :
      ( ( ~ ! [SY94: $i,SY95: $i] :
              ( ~ ( ~ ( ~ ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SV24 )
                      | ~ ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SY94 )
                      | ~ ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SY95 ) )
                  | ~ ~ ( ~ ( ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SV24 )
                            | ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SY95 ) )
                        | ~ ( ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SY94 )
                            | ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SY95 ) ) ) )
              | ( SY95
                = ( set_intersection2 @ SV24 @ SY94 ) ) )
        | ~ ! [SY96: $i,SY97: $i] :
              ( ( SY97
               != ( set_intersection2 @ SV24 @ SY96 ) )
              | ~ ( ~ ! [SY98: $i] :
                        ( ~ ( in @ SY98 @ SV24 )
                        | ~ ( in @ SY98 @ SY96 )
                        | ( in @ SY98 @ SY97 ) )
                  | ~ ~ ( ~ ! [SY99: $i] :
                              ( ~ ( in @ SY99 @ SY97 )
                              | ( in @ SY99 @ SV24 ) )
                        | ~ ! [SX3: $i] :
                              ( ~ ( in @ SX3 @ SY97 )
                              | ( in @ SX3 @ SY96 ) ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[185]) ).

thf(215,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( disjoint @ SX0 @ SX1 )
            | ( in @ ( sK9_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[186]) ).

thf(216,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ! [SX2: $i] :
                ~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
            | ~ ( disjoint @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[186]) ).

thf(217,plain,
    ! [SV25: $i] :
      ( ( ~ ! [SY101: $i,SY102: $i] :
              ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SY102 )
                            | ~ ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SV25 ) )
                        | ~ ( ~ ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SY102 )
                            | ~ ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SY101 ) ) )
                  | ~ ( ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SY102 )
                      | ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SV25 )
                      | ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SY101 ) ) )
              | ( SY102
                = ( set_union2 @ SV25 @ SY101 ) ) )
        | ~ ! [SY103: $i,SY104: $i] :
              ( ( SY104
               != ( set_union2 @ SV25 @ SY103 ) )
              | ~ ( ~ ! [SY105: $i] :
                        ( ~ ( in @ SY105 @ SY104 )
                        | ( in @ SY105 @ SV25 )
                        | ( in @ SY105 @ SY103 ) )
                  | ~ ~ ( ~ ! [SY106: $i] :
                              ( ~ ( in @ SY106 @ SV25 )
                              | ( in @ SY106 @ SY104 ) )
                        | ~ ! [SX3: $i] :
                              ( ~ ( in @ SX3 @ SY103 )
                              | ( in @ SX3 @ SY104 ) ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[187]) ).

thf(218,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( in @ ( sK8_B @ SX0 ) @ SX0 )
            | ( SX0 = empty_set ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[188]) ).

thf(219,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( SX0 != empty_set )
            | ! [SX1: $i] :
                ~ ( in @ SX1 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[188]) ).

thf(220,plain,
    ! [SV26: $i,SV1: $i] :
      ( ( ( ~ ( subset @ SV1 @ SV26 ) )
        = $true )
      | ( ( ( set_union2 @ SV1 @ SV26 )
          = SV26 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[189]) ).

thf(221,plain,
    ! [SV39: $i,SV28: $i,SV3: $i] :
      ( ( ~ ( subset @ SV3 @ SV28 )
        | ~ ( subset @ SV3 @ SV39 )
        | ( subset @ SV3 @ ( set_intersection2 @ SV28 @ SV39 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[191]) ).

thf(222,plain,
    ! [SV40: $i,SV29: $i,SV4: $i] :
      ( ( ~ ( subset @ SV4 @ SV29 )
        | ~ ( subset @ SV29 @ SV40 )
        | ( subset @ SV4 @ SV40 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[192]) ).

thf(223,plain,
    ! [SV30: $i,SV5: $i] :
      ( ( ( ~ ( subset @ SV5 @ SV30 ) )
        = $true )
      | ( ( ! [SY110: $i] : ( subset @ ( set_intersection2 @ SV5 @ SY110 ) @ ( set_intersection2 @ SV30 @ SY110 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[193]) ).

thf(224,plain,
    ! [SV7: $i] :
      ( ( ( subset @ SV7 @ empty_set )
        = $false )
      | ( ( SV7 = empty_set )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[194]) ).

thf(225,plain,
    ! [SV41: $i,SV32: $i,SV9: $i] :
      ( ( ~ ( subset @ SV9 @ SV32 )
        | ~ ( subset @ SV41 @ SV32 )
        | ( subset @ ( set_union2 @ SV9 @ SV41 ) @ SV32 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[196]) ).

thf(226,plain,
    ! [SV33: $i,SV10: $i] :
      ( ( ( ~ ( in @ SV10 @ SV33 ) )
        = $true )
      | ( ( ~ ( in @ SV33 @ SV10 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[197]) ).

thf(227,plain,
    ! [SV42: $i,SV13: $i] :
      ( ( ( ~ ( empty @ ( set_union2 @ SV13 @ SV42 ) ) )
        = $true )
      | ( ( empty @ SV13 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[200]) ).

thf(228,plain,
    ! [SV14: $i,SV43: $i] :
      ( ( ( ~ ( empty @ ( set_union2 @ SV43 @ SV14 ) ) )
        = $true )
      | ( ( empty @ SV14 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[201]) ).

thf(229,plain,
    ! [SV36: $i,SV18: $i] :
      ( ( ( ~ ( disjoint @ SV18 @ SV36 ) )
        = $true )
      | ( ( disjoint @ SV36 @ SV18 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[202]) ).

thf(230,plain,
    ! [SV21: $i] :
      ( ( ( empty @ SV21 )
        = $false )
      | ( ( SV21 = empty_set )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[203]) ).

thf(231,plain,
    ! [SV22: $i,SV37: $i] :
      ( ( ( ~ ( empty @ SV37 ) )
        = $true )
      | ( ( ~ ( in @ SV22 @ SV37 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[204]) ).

thf(232,plain,
    ! [SV38: $i,SV23: $i] :
      ( ( ( ( SV23 = SV38 )
          | ~ ( empty @ SV23 ) )
        = $true )
      | ( ( ~ ( empty @ SV38 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[205]) ).

thf(233,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( disjoint @ SX0 @ SX1 )
          | ~ ( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX0 )
              | ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[206]) ).

thf(234,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ! [SX2: $i] :
              ( ~ ( in @ SX2 @ SX0 )
              | ~ ( in @ SX2 @ SX1 ) )
          | ~ ( disjoint @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[207]) ).

thf(235,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( subset @ SX0 @ SX1 )
          | ~ ( subset @ SX1 @ SX0 )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[208]) ).

thf(236,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( SX0 != SX1 )
                | ( subset @ SX0 @ SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ( SX0 != SX1 )
                | ( subset @ SX1 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[209]) ).

thf(237,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( set_intersection2 @ SX0 @ SX1 )
           != empty_set )
          | ( disjoint @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[210]) ).

thf(238,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( disjoint @ SX0 @ SX1 )
          | ( ( set_intersection2 @ SX0 @ SX1 )
            = empty_set ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[211]) ).

thf(239,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX0 )
              | ~ ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX1 ) )
          | ( subset @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[212]) ).

thf(240,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( subset @ SX0 @ SX1 )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ SX0 )
              | ( in @ SX2 @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[213]) ).

thf(241,plain,
    ! [SV24: $i] :
      ( ( ~ ! [SY94: $i,SY95: $i] :
              ( ~ ( ~ ( ~ ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SV24 )
                      | ~ ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SY94 )
                      | ~ ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SY95 ) )
                  | ~ ~ ( ~ ( ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SV24 )
                            | ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SY95 ) )
                        | ~ ( ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SY94 )
                            | ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SY95 ) ) ) )
              | ( SY95
                = ( set_intersection2 @ SV24 @ SY94 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[214]) ).

thf(242,plain,
    ! [SV24: $i] :
      ( ( ~ ! [SY96: $i,SY97: $i] :
              ( ( SY97
               != ( set_intersection2 @ SV24 @ SY96 ) )
              | ~ ( ~ ! [SY98: $i] :
                        ( ~ ( in @ SY98 @ SV24 )
                        | ~ ( in @ SY98 @ SY96 )
                        | ( in @ SY98 @ SY97 ) )
                  | ~ ~ ( ~ ! [SY99: $i] :
                              ( ~ ( in @ SY99 @ SY97 )
                              | ( in @ SY99 @ SV24 ) )
                        | ~ ! [SX3: $i] :
                              ( ~ ( in @ SX3 @ SY97 )
                              | ( in @ SX3 @ SY96 ) ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[214]) ).

thf(243,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( disjoint @ SX0 @ SX1 )
          | ( in @ ( sK9_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[215]) ).

thf(244,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ! [SX2: $i] :
              ~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
          | ~ ( disjoint @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[216]) ).

thf(245,plain,
    ! [SV25: $i] :
      ( ( ~ ! [SY101: $i,SY102: $i] :
              ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SY102 )
                            | ~ ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SV25 ) )
                        | ~ ( ~ ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SY102 )
                            | ~ ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SY101 ) ) )
                  | ~ ( ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SY102 )
                      | ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SV25 )
                      | ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SY101 ) ) )
              | ( SY102
                = ( set_union2 @ SV25 @ SY101 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[217]) ).

thf(246,plain,
    ! [SV25: $i] :
      ( ( ~ ! [SY103: $i,SY104: $i] :
              ( ( SY104
               != ( set_union2 @ SV25 @ SY103 ) )
              | ~ ( ~ ! [SY105: $i] :
                        ( ~ ( in @ SY105 @ SY104 )
                        | ( in @ SY105 @ SV25 )
                        | ( in @ SY105 @ SY103 ) )
                  | ~ ~ ( ~ ! [SY106: $i] :
                              ( ~ ( in @ SY106 @ SV25 )
                              | ( in @ SY106 @ SY104 ) )
                        | ~ ! [SX3: $i] :
                              ( ~ ( in @ SX3 @ SY103 )
                              | ( in @ SX3 @ SY104 ) ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[217]) ).

thf(247,plain,
    ( ( ! [SX0: $i] :
          ( ( in @ ( sK8_B @ SX0 ) @ SX0 )
          | ( SX0 = empty_set ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[218]) ).

thf(248,plain,
    ( ( ! [SX0: $i] :
          ( ( SX0 != empty_set )
          | ! [SX1: $i] :
              ~ ( in @ SX1 @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[219]) ).

thf(249,plain,
    ! [SV26: $i,SV1: $i] :
      ( ( ( subset @ SV1 @ SV26 )
        = $false )
      | ( ( ( set_union2 @ SV1 @ SV26 )
          = SV26 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[220]) ).

thf(250,plain,
    ! [SV39: $i,SV28: $i,SV3: $i] :
      ( ( ( ~ ( subset @ SV3 @ SV28 )
          | ~ ( subset @ SV3 @ SV39 ) )
        = $true )
      | ( ( subset @ SV3 @ ( set_intersection2 @ SV28 @ SV39 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[221]) ).

thf(251,plain,
    ! [SV40: $i,SV29: $i,SV4: $i] :
      ( ( ( ~ ( subset @ SV4 @ SV29 )
          | ~ ( subset @ SV29 @ SV40 ) )
        = $true )
      | ( ( subset @ SV4 @ SV40 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[222]) ).

thf(252,plain,
    ! [SV30: $i,SV5: $i] :
      ( ( ( subset @ SV5 @ SV30 )
        = $false )
      | ( ( ! [SY110: $i] : ( subset @ ( set_intersection2 @ SV5 @ SY110 ) @ ( set_intersection2 @ SV30 @ SY110 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[223]) ).

thf(253,plain,
    ! [SV41: $i,SV32: $i,SV9: $i] :
      ( ( ( ~ ( subset @ SV9 @ SV32 )
          | ~ ( subset @ SV41 @ SV32 ) )
        = $true )
      | ( ( subset @ ( set_union2 @ SV9 @ SV41 ) @ SV32 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[225]) ).

thf(254,plain,
    ! [SV33: $i,SV10: $i] :
      ( ( ( in @ SV10 @ SV33 )
        = $false )
      | ( ( ~ ( in @ SV33 @ SV10 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[226]) ).

thf(255,plain,
    ! [SV42: $i,SV13: $i] :
      ( ( ( empty @ ( set_union2 @ SV13 @ SV42 ) )
        = $false )
      | ( ( empty @ SV13 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[227]) ).

thf(256,plain,
    ! [SV14: $i,SV43: $i] :
      ( ( ( empty @ ( set_union2 @ SV43 @ SV14 ) )
        = $false )
      | ( ( empty @ SV14 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[228]) ).

thf(257,plain,
    ! [SV36: $i,SV18: $i] :
      ( ( ( disjoint @ SV18 @ SV36 )
        = $false )
      | ( ( disjoint @ SV36 @ SV18 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[229]) ).

thf(258,plain,
    ! [SV22: $i,SV37: $i] :
      ( ( ( empty @ SV37 )
        = $false )
      | ( ( ~ ( in @ SV22 @ SV37 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[231]) ).

thf(259,plain,
    ! [SV38: $i,SV23: $i] :
      ( ( ( SV23 = SV38 )
        = $true )
      | ( ( ~ ( empty @ SV23 ) )
        = $true )
      | ( ( ~ ( empty @ SV38 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[232]) ).

thf(260,plain,
    ! [SV44: $i] :
      ( ( ! [SY112: $i] :
            ( ( disjoint @ SV44 @ SY112 )
            | ~ ( ~ ( in @ ( sK10_C @ SY112 @ SV44 ) @ SV44 )
                | ~ ( in @ ( sK10_C @ SY112 @ SV44 ) @ SY112 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[233]) ).

thf(261,plain,
    ! [SV45: $i] :
      ( ( ! [SY113: $i] :
            ( ! [SY114: $i] :
                ( ~ ( in @ SY114 @ SV45 )
                | ~ ( in @ SY114 @ SY113 ) )
            | ~ ( disjoint @ SV45 @ SY113 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[234]) ).

thf(262,plain,
    ! [SV46: $i] :
      ( ( ! [SY115: $i] :
            ( ~ ( subset @ SV46 @ SY115 )
            | ~ ( subset @ SY115 @ SV46 )
            | ( SV46 = SY115 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[235]) ).

thf(263,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ( subset @ SX0 @ SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ( subset @ SX1 @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[236]) ).

thf(264,plain,
    ! [SV47: $i] :
      ( ( ! [SY116: $i] :
            ( ( ( set_intersection2 @ SV47 @ SY116 )
             != empty_set )
            | ( disjoint @ SV47 @ SY116 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[237]) ).

thf(265,plain,
    ! [SV48: $i] :
      ( ( ! [SY117: $i] :
            ( ~ ( disjoint @ SV48 @ SY117 )
            | ( ( set_intersection2 @ SV48 @ SY117 )
              = empty_set ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[238]) ).

thf(266,plain,
    ! [SV49: $i] :
      ( ( ! [SY118: $i] :
            ( ~ ( ~ ( in @ ( sK6_C @ SY118 @ SV49 ) @ SV49 )
                | ~ ~ ( in @ ( sK6_C @ SY118 @ SV49 ) @ SY118 ) )
            | ( subset @ SV49 @ SY118 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[239]) ).

thf(267,plain,
    ! [SV50: $i] :
      ( ( ! [SY119: $i] :
            ( ~ ( subset @ SV50 @ SY119 )
            | ! [SY120: $i] :
                ( ~ ( in @ SY120 @ SV50 )
                | ( in @ SY120 @ SY119 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[240]) ).

thf(268,plain,
    ! [SV24: $i] :
      ( ( ! [SY94: $i,SY95: $i] :
            ( ~ ( ~ ( ~ ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SV24 )
                    | ~ ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SY94 )
                    | ~ ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SY95 ) )
                | ~ ~ ( ~ ( ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SV24 )
                          | ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SY95 ) )
                      | ~ ( ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SY94 )
                          | ( in @ ( sK5_D @ SY95 @ SY94 @ SV24 ) @ SY95 ) ) ) )
            | ( SY95
              = ( set_intersection2 @ SV24 @ SY94 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[241]) ).

thf(269,plain,
    ! [SV24: $i] :
      ( ( ! [SY96: $i,SY97: $i] :
            ( ( SY97
             != ( set_intersection2 @ SV24 @ SY96 ) )
            | ~ ( ~ ! [SY98: $i] :
                      ( ~ ( in @ SY98 @ SV24 )
                      | ~ ( in @ SY98 @ SY96 )
                      | ( in @ SY98 @ SY97 ) )
                | ~ ~ ( ~ ! [SY99: $i] :
                            ( ~ ( in @ SY99 @ SY97 )
                            | ( in @ SY99 @ SV24 ) )
                      | ~ ! [SX3: $i] :
                            ( ~ ( in @ SX3 @ SY97 )
                            | ( in @ SX3 @ SY96 ) ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[242]) ).

thf(270,plain,
    ! [SV51: $i] :
      ( ( ! [SY121: $i] :
            ( ( disjoint @ SV51 @ SY121 )
            | ( in @ ( sK9_C @ SY121 @ SV51 ) @ ( set_intersection2 @ SV51 @ SY121 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[243]) ).

thf(271,plain,
    ! [SV52: $i] :
      ( ( ! [SY122: $i] :
            ( ! [SY123: $i] :
                ~ ( in @ SY123 @ ( set_intersection2 @ SV52 @ SY122 ) )
            | ~ ( disjoint @ SV52 @ SY122 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[244]) ).

thf(272,plain,
    ! [SV25: $i] :
      ( ( ! [SY101: $i,SY102: $i] :
            ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SY102 )
                          | ~ ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SV25 ) )
                      | ~ ( ~ ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SY102 )
                          | ~ ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SY101 ) ) )
                | ~ ( ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SY102 )
                    | ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SV25 )
                    | ( in @ ( sK7_D @ SY102 @ SY101 @ SV25 ) @ SY101 ) ) )
            | ( SY102
              = ( set_union2 @ SV25 @ SY101 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[245]) ).

thf(273,plain,
    ! [SV25: $i] :
      ( ( ! [SY103: $i,SY104: $i] :
            ( ( SY104
             != ( set_union2 @ SV25 @ SY103 ) )
            | ~ ( ~ ! [SY105: $i] :
                      ( ~ ( in @ SY105 @ SY104 )
                      | ( in @ SY105 @ SV25 )
                      | ( in @ SY105 @ SY103 ) )
                | ~ ~ ( ~ ! [SY106: $i] :
                            ( ~ ( in @ SY106 @ SV25 )
                            | ( in @ SY106 @ SY104 ) )
                      | ~ ! [SX3: $i] :
                            ( ~ ( in @ SX3 @ SY103 )
                            | ( in @ SX3 @ SY104 ) ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[246]) ).

thf(274,plain,
    ! [SV53: $i] :
      ( ( ( in @ ( sK8_B @ SV53 ) @ SV53 )
        | ( SV53 = empty_set ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[247]) ).

thf(275,plain,
    ! [SV54: $i] :
      ( ( ( SV54 != empty_set )
        | ! [SY124: $i] :
            ~ ( in @ SY124 @ SV54 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[248]) ).

thf(276,plain,
    ! [SV39: $i,SV28: $i,SV3: $i] :
      ( ( ( ~ ( subset @ SV3 @ SV28 ) )
        = $true )
      | ( ( ~ ( subset @ SV3 @ SV39 ) )
        = $true )
      | ( ( subset @ SV3 @ ( set_intersection2 @ SV28 @ SV39 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[250]) ).

thf(277,plain,
    ! [SV40: $i,SV29: $i,SV4: $i] :
      ( ( ( ~ ( subset @ SV4 @ SV29 ) )
        = $true )
      | ( ( ~ ( subset @ SV29 @ SV40 ) )
        = $true )
      | ( ( subset @ SV4 @ SV40 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[251]) ).

thf(278,plain,
    ! [SV30: $i,SV55: $i,SV5: $i] :
      ( ( ( subset @ ( set_intersection2 @ SV5 @ SV55 ) @ ( set_intersection2 @ SV30 @ SV55 ) )
        = $true )
      | ( ( subset @ SV5 @ SV30 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[252]) ).

thf(279,plain,
    ! [SV41: $i,SV32: $i,SV9: $i] :
      ( ( ( ~ ( subset @ SV9 @ SV32 ) )
        = $true )
      | ( ( ~ ( subset @ SV41 @ SV32 ) )
        = $true )
      | ( ( subset @ ( set_union2 @ SV9 @ SV41 ) @ SV32 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[253]) ).

thf(280,plain,
    ! [SV10: $i,SV33: $i] :
      ( ( ( in @ SV33 @ SV10 )
        = $false )
      | ( ( in @ SV10 @ SV33 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[254]) ).

thf(281,plain,
    ! [SV37: $i,SV22: $i] :
      ( ( ( in @ SV22 @ SV37 )
        = $false )
      | ( ( empty @ SV37 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[258]) ).

thf(282,plain,
    ! [SV38: $i,SV23: $i] :
      ( ( ( empty @ SV23 )
        = $false )
      | ( ( SV23 = SV38 )
        = $true )
      | ( ( ~ ( empty @ SV38 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[259]) ).

thf(283,plain,
    ! [SV56: $i,SV44: $i] :
      ( ( ( disjoint @ SV44 @ SV56 )
        | ~ ( ~ ( in @ ( sK10_C @ SV56 @ SV44 ) @ SV44 )
            | ~ ( in @ ( sK10_C @ SV56 @ SV44 ) @ SV56 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[260]) ).

thf(284,plain,
    ! [SV57: $i,SV45: $i] :
      ( ( ! [SY125: $i] :
            ( ~ ( in @ SY125 @ SV45 )
            | ~ ( in @ SY125 @ SV57 ) )
        | ~ ( disjoint @ SV45 @ SV57 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[261]) ).

thf(285,plain,
    ! [SV58: $i,SV46: $i] :
      ( ( ~ ( subset @ SV46 @ SV58 )
        | ~ ( subset @ SV58 @ SV46 )
        | ( SV46 = SV58 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[262]) ).

thf(286,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ( subset @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[263]) ).

thf(287,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ( subset @ SX1 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[263]) ).

thf(288,plain,
    ! [SV59: $i,SV47: $i] :
      ( ( ( ( set_intersection2 @ SV47 @ SV59 )
         != empty_set )
        | ( disjoint @ SV47 @ SV59 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[264]) ).

thf(289,plain,
    ! [SV60: $i,SV48: $i] :
      ( ( ~ ( disjoint @ SV48 @ SV60 )
        | ( ( set_intersection2 @ SV48 @ SV60 )
          = empty_set ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[265]) ).

thf(290,plain,
    ! [SV49: $i,SV61: $i] :
      ( ( ~ ( ~ ( in @ ( sK6_C @ SV61 @ SV49 ) @ SV49 )
            | ~ ~ ( in @ ( sK6_C @ SV61 @ SV49 ) @ SV61 ) )
        | ( subset @ SV49 @ SV61 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[266]) ).

thf(291,plain,
    ! [SV62: $i,SV50: $i] :
      ( ( ~ ( subset @ SV50 @ SV62 )
        | ! [SY126: $i] :
            ( ~ ( in @ SY126 @ SV50 )
            | ( in @ SY126 @ SV62 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[267]) ).

thf(292,plain,
    ! [SV24: $i,SV63: $i] :
      ( ( ! [SY127: $i] :
            ( ~ ( ~ ( ~ ( in @ ( sK5_D @ SY127 @ SV63 @ SV24 ) @ SV24 )
                    | ~ ( in @ ( sK5_D @ SY127 @ SV63 @ SV24 ) @ SV63 )
                    | ~ ( in @ ( sK5_D @ SY127 @ SV63 @ SV24 ) @ SY127 ) )
                | ~ ~ ( ~ ( ( in @ ( sK5_D @ SY127 @ SV63 @ SV24 ) @ SV24 )
                          | ( in @ ( sK5_D @ SY127 @ SV63 @ SV24 ) @ SY127 ) )
                      | ~ ( ( in @ ( sK5_D @ SY127 @ SV63 @ SV24 ) @ SV63 )
                          | ( in @ ( sK5_D @ SY127 @ SV63 @ SV24 ) @ SY127 ) ) ) )
            | ( SY127
              = ( set_intersection2 @ SV24 @ SV63 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[268]) ).

thf(293,plain,
    ! [SV64: $i,SV24: $i] :
      ( ( ! [SY128: $i] :
            ( ( SY128
             != ( set_intersection2 @ SV24 @ SV64 ) )
            | ~ ( ~ ! [SY129: $i] :
                      ( ~ ( in @ SY129 @ SV24 )
                      | ~ ( in @ SY129 @ SV64 )
                      | ( in @ SY129 @ SY128 ) )
                | ~ ~ ( ~ ! [SY99: $i] :
                            ( ~ ( in @ SY99 @ SY128 )
                            | ( in @ SY99 @ SV24 ) )
                      | ~ ! [SY131: $i] :
                            ( ~ ( in @ SY131 @ SY128 )
                            | ( in @ SY131 @ SV64 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[269]) ).

thf(294,plain,
    ! [SV65: $i,SV51: $i] :
      ( ( ( disjoint @ SV51 @ SV65 )
        | ( in @ ( sK9_C @ SV65 @ SV51 ) @ ( set_intersection2 @ SV51 @ SV65 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[270]) ).

thf(295,plain,
    ! [SV66: $i,SV52: $i] :
      ( ( ! [SY132: $i] :
            ~ ( in @ SY132 @ ( set_intersection2 @ SV52 @ SV66 ) )
        | ~ ( disjoint @ SV52 @ SV66 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[271]) ).

thf(296,plain,
    ! [SV25: $i,SV67: $i] :
      ( ( ! [SY133: $i] :
            ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SY133 @ SV67 @ SV25 ) @ SY133 )
                          | ~ ( in @ ( sK7_D @ SY133 @ SV67 @ SV25 ) @ SV25 ) )
                      | ~ ( ~ ( in @ ( sK7_D @ SY133 @ SV67 @ SV25 ) @ SY133 )
                          | ~ ( in @ ( sK7_D @ SY133 @ SV67 @ SV25 ) @ SV67 ) ) )
                | ~ ( ( in @ ( sK7_D @ SY133 @ SV67 @ SV25 ) @ SY133 )
                    | ( in @ ( sK7_D @ SY133 @ SV67 @ SV25 ) @ SV25 )
                    | ( in @ ( sK7_D @ SY133 @ SV67 @ SV25 ) @ SV67 ) ) )
            | ( SY133
              = ( set_union2 @ SV25 @ SV67 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[272]) ).

thf(297,plain,
    ! [SV68: $i,SV25: $i] :
      ( ( ! [SY134: $i] :
            ( ( SY134
             != ( set_union2 @ SV25 @ SV68 ) )
            | ~ ( ~ ! [SY135: $i] :
                      ( ~ ( in @ SY135 @ SY134 )
                      | ( in @ SY135 @ SV25 )
                      | ( in @ SY135 @ SV68 ) )
                | ~ ~ ( ~ ! [SY106: $i] :
                            ( ~ ( in @ SY106 @ SV25 )
                            | ( in @ SY106 @ SY134 ) )
                      | ~ ! [SY137: $i] :
                            ( ~ ( in @ SY137 @ SV68 )
                            | ( in @ SY137 @ SY134 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[273]) ).

thf(298,plain,
    ! [SV53: $i] :
      ( ( ( in @ ( sK8_B @ SV53 ) @ SV53 )
        = $true )
      | ( ( SV53 = empty_set )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[274]) ).

thf(299,plain,
    ! [SV54: $i] :
      ( ( ( ( SV54 != empty_set ) )
        = $true )
      | ( ( ! [SY124: $i] :
              ~ ( in @ SY124 @ SV54 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[275]) ).

thf(300,plain,
    ! [SV39: $i,SV28: $i,SV3: $i] :
      ( ( ( subset @ SV3 @ SV28 )
        = $false )
      | ( ( ~ ( subset @ SV3 @ SV39 ) )
        = $true )
      | ( ( subset @ SV3 @ ( set_intersection2 @ SV28 @ SV39 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[276]) ).

thf(301,plain,
    ! [SV40: $i,SV29: $i,SV4: $i] :
      ( ( ( subset @ SV4 @ SV29 )
        = $false )
      | ( ( ~ ( subset @ SV29 @ SV40 ) )
        = $true )
      | ( ( subset @ SV4 @ SV40 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[277]) ).

thf(302,plain,
    ! [SV41: $i,SV32: $i,SV9: $i] :
      ( ( ( subset @ SV9 @ SV32 )
        = $false )
      | ( ( ~ ( subset @ SV41 @ SV32 ) )
        = $true )
      | ( ( subset @ ( set_union2 @ SV9 @ SV41 ) @ SV32 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[279]) ).

thf(303,plain,
    ! [SV23: $i,SV38: $i] :
      ( ( ( empty @ SV38 )
        = $false )
      | ( ( SV23 = SV38 )
        = $true )
      | ( ( empty @ SV23 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[282]) ).

thf(304,plain,
    ! [SV56: $i,SV44: $i] :
      ( ( ( disjoint @ SV44 @ SV56 )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK10_C @ SV56 @ SV44 ) @ SV44 )
              | ~ ( in @ ( sK10_C @ SV56 @ SV44 ) @ SV56 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[283]) ).

thf(305,plain,
    ! [SV57: $i,SV45: $i] :
      ( ( ( ! [SY125: $i] :
              ( ~ ( in @ SY125 @ SV45 )
              | ~ ( in @ SY125 @ SV57 ) ) )
        = $true )
      | ( ( ~ ( disjoint @ SV45 @ SV57 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[284]) ).

thf(306,plain,
    ! [SV58: $i,SV46: $i] :
      ( ( ( ~ ( subset @ SV46 @ SV58 )
          | ~ ( subset @ SV58 @ SV46 ) )
        = $true )
      | ( ( SV46 = SV58 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[285]) ).

thf(307,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( subset @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[286]) ).

thf(308,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( subset @ SX1 @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[287]) ).

thf(309,plain,
    ! [SV59: $i,SV47: $i] :
      ( ( ( ( ( set_intersection2 @ SV47 @ SV59 )
           != empty_set ) )
        = $true )
      | ( ( disjoint @ SV47 @ SV59 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[288]) ).

thf(310,plain,
    ! [SV60: $i,SV48: $i] :
      ( ( ( ~ ( disjoint @ SV48 @ SV60 ) )
        = $true )
      | ( ( ( set_intersection2 @ SV48 @ SV60 )
          = empty_set )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[289]) ).

thf(311,plain,
    ! [SV49: $i,SV61: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK6_C @ SV61 @ SV49 ) @ SV49 )
              | ~ ~ ( in @ ( sK6_C @ SV61 @ SV49 ) @ SV61 ) ) )
        = $true )
      | ( ( subset @ SV49 @ SV61 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[290]) ).

thf(312,plain,
    ! [SV62: $i,SV50: $i] :
      ( ( ( ~ ( subset @ SV50 @ SV62 ) )
        = $true )
      | ( ( ! [SY126: $i] :
              ( ~ ( in @ SY126 @ SV50 )
              | ( in @ SY126 @ SV62 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[291]) ).

thf(313,plain,
    ! [SV24: $i,SV63: $i,SV69: $i] :
      ( ( ~ ( ~ ( ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV24 )
                | ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV63 )
                | ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) )
            | ~ ~ ( ~ ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV24 )
                      | ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) )
                  | ~ ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV63 )
                      | ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) ) ) )
        | ( SV69
          = ( set_intersection2 @ SV24 @ SV63 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[292]) ).

thf(314,plain,
    ! [SV64: $i,SV24: $i,SV70: $i] :
      ( ( ( SV70
         != ( set_intersection2 @ SV24 @ SV64 ) )
        | ~ ( ~ ! [SY138: $i] :
                  ( ~ ( in @ SY138 @ SV24 )
                  | ~ ( in @ SY138 @ SV64 )
                  | ( in @ SY138 @ SV70 ) )
            | ~ ~ ( ~ ! [SY139: $i] :
                        ( ~ ( in @ SY139 @ SV70 )
                        | ( in @ SY139 @ SV24 ) )
                  | ~ ! [SY140: $i] :
                        ( ~ ( in @ SY140 @ SV70 )
                        | ( in @ SY140 @ SV64 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[293]) ).

thf(315,plain,
    ! [SV65: $i,SV51: $i] :
      ( ( ( disjoint @ SV51 @ SV65 )
        = $true )
      | ( ( in @ ( sK9_C @ SV65 @ SV51 ) @ ( set_intersection2 @ SV51 @ SV65 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[294]) ).

thf(316,plain,
    ! [SV66: $i,SV52: $i] :
      ( ( ( ! [SY132: $i] :
              ~ ( in @ SY132 @ ( set_intersection2 @ SV52 @ SV66 ) ) )
        = $true )
      | ( ( ~ ( disjoint @ SV52 @ SV66 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[295]) ).

thf(317,plain,
    ! [SV25: $i,SV67: $i,SV71: $i] :
      ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
                      | ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV25 ) )
                  | ~ ( ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
                      | ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV67 ) ) )
            | ~ ( ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
                | ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV25 )
                | ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV67 ) ) )
        | ( SV71
          = ( set_union2 @ SV25 @ SV67 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[296]) ).

thf(318,plain,
    ! [SV68: $i,SV25: $i,SV72: $i] :
      ( ( ( SV72
         != ( set_union2 @ SV25 @ SV68 ) )
        | ~ ( ~ ! [SY141: $i] :
                  ( ~ ( in @ SY141 @ SV72 )
                  | ( in @ SY141 @ SV25 )
                  | ( in @ SY141 @ SV68 ) )
            | ~ ~ ( ~ ! [SY142: $i] :
                        ( ~ ( in @ SY142 @ SV25 )
                        | ( in @ SY142 @ SV72 ) )
                  | ~ ! [SY143: $i] :
                        ( ~ ( in @ SY143 @ SV68 )
                        | ( in @ SY143 @ SV72 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[297]) ).

thf(319,plain,
    ! [SV54: $i] :
      ( ( ( SV54 = empty_set )
        = $false )
      | ( ( ! [SY124: $i] :
              ~ ( in @ SY124 @ SV54 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[299]) ).

thf(320,plain,
    ! [SV28: $i,SV39: $i,SV3: $i] :
      ( ( ( subset @ SV3 @ SV39 )
        = $false )
      | ( ( subset @ SV3 @ SV28 )
        = $false )
      | ( ( subset @ SV3 @ ( set_intersection2 @ SV28 @ SV39 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[300]) ).

thf(321,plain,
    ! [SV4: $i,SV40: $i,SV29: $i] :
      ( ( ( subset @ SV29 @ SV40 )
        = $false )
      | ( ( subset @ SV4 @ SV29 )
        = $false )
      | ( ( subset @ SV4 @ SV40 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[301]) ).

thf(322,plain,
    ! [SV9: $i,SV32: $i,SV41: $i] :
      ( ( ( subset @ SV41 @ SV32 )
        = $false )
      | ( ( subset @ SV9 @ SV32 )
        = $false )
      | ( ( subset @ ( set_union2 @ SV9 @ SV41 ) @ SV32 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[302]) ).

thf(323,plain,
    ! [SV44: $i,SV56: $i] :
      ( ( ( ~ ( in @ ( sK10_C @ SV56 @ SV44 ) @ SV44 )
          | ~ ( in @ ( sK10_C @ SV56 @ SV44 ) @ SV56 ) )
        = $false )
      | ( ( disjoint @ SV44 @ SV56 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[304]) ).

thf(324,plain,
    ! [SV57: $i,SV45: $i,SV73: $i] :
      ( ( ( ~ ( in @ SV73 @ SV45 )
          | ~ ( in @ SV73 @ SV57 ) )
        = $true )
      | ( ( ~ ( disjoint @ SV45 @ SV57 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[305]) ).

thf(325,plain,
    ! [SV58: $i,SV46: $i] :
      ( ( ( ~ ( subset @ SV46 @ SV58 ) )
        = $true )
      | ( ( ~ ( subset @ SV58 @ SV46 ) )
        = $true )
      | ( ( SV46 = SV58 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[306]) ).

thf(326,plain,
    ! [SV74: $i] :
      ( ( ! [SY144: $i] :
            ( ( SV74 != SY144 )
            | ( subset @ SV74 @ SY144 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[307]) ).

thf(327,plain,
    ! [SV75: $i] :
      ( ( ! [SY145: $i] :
            ( ( SV75 != SY145 )
            | ( subset @ SY145 @ SV75 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[308]) ).

thf(328,plain,
    ! [SV59: $i,SV47: $i] :
      ( ( ( ( set_intersection2 @ SV47 @ SV59 )
          = empty_set )
        = $false )
      | ( ( disjoint @ SV47 @ SV59 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[309]) ).

thf(329,plain,
    ! [SV60: $i,SV48: $i] :
      ( ( ( disjoint @ SV48 @ SV60 )
        = $false )
      | ( ( ( set_intersection2 @ SV48 @ SV60 )
          = empty_set )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[310]) ).

thf(330,plain,
    ! [SV49: $i,SV61: $i] :
      ( ( ( ~ ( in @ ( sK6_C @ SV61 @ SV49 ) @ SV49 )
          | ~ ~ ( in @ ( sK6_C @ SV61 @ SV49 ) @ SV61 ) )
        = $false )
      | ( ( subset @ SV49 @ SV61 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[311]) ).

thf(331,plain,
    ! [SV62: $i,SV50: $i] :
      ( ( ( subset @ SV50 @ SV62 )
        = $false )
      | ( ( ! [SY126: $i] :
              ( ~ ( in @ SY126 @ SV50 )
              | ( in @ SY126 @ SV62 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[312]) ).

thf(332,plain,
    ! [SV24: $i,SV63: $i,SV69: $i] :
      ( ( ( ~ ( ~ ( ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV24 )
                  | ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV63 )
                  | ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) )
              | ~ ~ ( ~ ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV24 )
                        | ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) )
                    | ~ ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV63 )
                        | ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) ) ) ) )
        = $true )
      | ( ( SV69
          = ( set_intersection2 @ SV24 @ SV63 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[313]) ).

thf(333,plain,
    ! [SV64: $i,SV24: $i,SV70: $i] :
      ( ( ( ( SV70
           != ( set_intersection2 @ SV24 @ SV64 ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY138: $i] :
                    ( ~ ( in @ SY138 @ SV24 )
                    | ~ ( in @ SY138 @ SV64 )
                    | ( in @ SY138 @ SV70 ) )
              | ~ ~ ( ~ ! [SY139: $i] :
                          ( ~ ( in @ SY139 @ SV70 )
                          | ( in @ SY139 @ SV24 ) )
                    | ~ ! [SY140: $i] :
                          ( ~ ( in @ SY140 @ SV70 )
                          | ( in @ SY140 @ SV64 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[314]) ).

thf(334,plain,
    ! [SV66: $i,SV52: $i,SV76: $i] :
      ( ( ( ~ ( in @ SV76 @ ( set_intersection2 @ SV52 @ SV66 ) ) )
        = $true )
      | ( ( ~ ( disjoint @ SV52 @ SV66 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[316]) ).

thf(335,plain,
    ! [SV25: $i,SV67: $i,SV71: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
                        | ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV25 ) )
                    | ~ ( ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
                        | ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV67 ) ) )
              | ~ ( ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
                  | ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV25 )
                  | ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV67 ) ) ) )
        = $true )
      | ( ( SV71
          = ( set_union2 @ SV25 @ SV67 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[317]) ).

thf(336,plain,
    ! [SV68: $i,SV25: $i,SV72: $i] :
      ( ( ( ( SV72
           != ( set_union2 @ SV25 @ SV68 ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY141: $i] :
                    ( ~ ( in @ SY141 @ SV72 )
                    | ( in @ SY141 @ SV25 )
                    | ( in @ SY141 @ SV68 ) )
              | ~ ~ ( ~ ! [SY142: $i] :
                          ( ~ ( in @ SY142 @ SV25 )
                          | ( in @ SY142 @ SV72 ) )
                    | ~ ! [SY143: $i] :
                          ( ~ ( in @ SY143 @ SV68 )
                          | ( in @ SY143 @ SV72 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[318]) ).

thf(337,plain,
    ! [SV54: $i,SV77: $i] :
      ( ( ( ~ ( in @ SV77 @ SV54 ) )
        = $true )
      | ( ( SV54 = empty_set )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[319]) ).

thf(338,plain,
    ! [SV44: $i,SV56: $i] :
      ( ( ( ~ ( in @ ( sK10_C @ SV56 @ SV44 ) @ SV44 ) )
        = $false )
      | ( ( disjoint @ SV44 @ SV56 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[323]) ).

thf(339,plain,
    ! [SV44: $i,SV56: $i] :
      ( ( ( ~ ( in @ ( sK10_C @ SV56 @ SV44 ) @ SV56 ) )
        = $false )
      | ( ( disjoint @ SV44 @ SV56 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[323]) ).

thf(340,plain,
    ! [SV57: $i,SV45: $i,SV73: $i] :
      ( ( ( ~ ( in @ SV73 @ SV45 ) )
        = $true )
      | ( ( ~ ( in @ SV73 @ SV57 ) )
        = $true )
      | ( ( ~ ( disjoint @ SV45 @ SV57 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[324]) ).

thf(341,plain,
    ! [SV58: $i,SV46: $i] :
      ( ( ( subset @ SV46 @ SV58 )
        = $false )
      | ( ( ~ ( subset @ SV58 @ SV46 ) )
        = $true )
      | ( ( SV46 = SV58 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[325]) ).

thf(342,plain,
    ! [SV78: $i,SV74: $i] :
      ( ( ( SV74 != SV78 )
        | ( subset @ SV74 @ SV78 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[326]) ).

thf(343,plain,
    ! [SV79: $i,SV75: $i] :
      ( ( ( SV75 != SV79 )
        | ( subset @ SV79 @ SV75 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[327]) ).

thf(344,plain,
    ! [SV49: $i,SV61: $i] :
      ( ( ( ~ ( in @ ( sK6_C @ SV61 @ SV49 ) @ SV49 ) )
        = $false )
      | ( ( subset @ SV49 @ SV61 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[330]) ).

thf(345,plain,
    ! [SV49: $i,SV61: $i] :
      ( ( ( ~ ~ ( in @ ( sK6_C @ SV61 @ SV49 ) @ SV61 ) )
        = $false )
      | ( ( subset @ SV49 @ SV61 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[330]) ).

thf(346,plain,
    ! [SV62: $i,SV50: $i,SV80: $i] :
      ( ( ( ~ ( in @ SV80 @ SV50 )
          | ( in @ SV80 @ SV62 ) )
        = $true )
      | ( ( subset @ SV50 @ SV62 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[331]) ).

thf(347,plain,
    ! [SV24: $i,SV63: $i,SV69: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV24 )
              | ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV63 )
              | ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) )
          | ~ ~ ( ~ ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV24 )
                    | ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) )
                | ~ ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV63 )
                    | ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) ) ) )
        = $false )
      | ( ( SV69
          = ( set_intersection2 @ SV24 @ SV63 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[332]) ).

thf(348,plain,
    ! [SV64: $i,SV24: $i,SV70: $i] :
      ( ( ( SV70
          = ( set_intersection2 @ SV24 @ SV64 ) )
        = $false )
      | ( ( ~ ( ~ ! [SY138: $i] :
                    ( ~ ( in @ SY138 @ SV24 )
                    | ~ ( in @ SY138 @ SV64 )
                    | ( in @ SY138 @ SV70 ) )
              | ~ ~ ( ~ ! [SY139: $i] :
                          ( ~ ( in @ SY139 @ SV70 )
                          | ( in @ SY139 @ SV24 ) )
                    | ~ ! [SY140: $i] :
                          ( ~ ( in @ SY140 @ SV70 )
                          | ( in @ SY140 @ SV64 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[333]) ).

thf(349,plain,
    ! [SV66: $i,SV52: $i,SV76: $i] :
      ( ( ( in @ SV76 @ ( set_intersection2 @ SV52 @ SV66 ) )
        = $false )
      | ( ( ~ ( disjoint @ SV52 @ SV66 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[334]) ).

thf(350,plain,
    ! [SV25: $i,SV67: $i,SV71: $i] :
      ( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
                    | ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV25 ) )
                | ~ ( ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
                    | ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV67 ) ) )
          | ~ ( ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
              | ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV25 )
              | ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV67 ) ) )
        = $false )
      | ( ( SV71
          = ( set_union2 @ SV25 @ SV67 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[335]) ).

thf(351,plain,
    ! [SV68: $i,SV25: $i,SV72: $i] :
      ( ( ( SV72
          = ( set_union2 @ SV25 @ SV68 ) )
        = $false )
      | ( ( ~ ( ~ ! [SY141: $i] :
                    ( ~ ( in @ SY141 @ SV72 )
                    | ( in @ SY141 @ SV25 )
                    | ( in @ SY141 @ SV68 ) )
              | ~ ~ ( ~ ! [SY142: $i] :
                          ( ~ ( in @ SY142 @ SV25 )
                          | ( in @ SY142 @ SV72 ) )
                    | ~ ! [SY143: $i] :
                          ( ~ ( in @ SY143 @ SV68 )
                          | ( in @ SY143 @ SV72 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[336]) ).

thf(352,plain,
    ! [SV54: $i,SV77: $i] :
      ( ( ( in @ SV77 @ SV54 )
        = $false )
      | ( ( SV54 = empty_set )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[337]) ).

thf(353,plain,
    ! [SV44: $i,SV56: $i] :
      ( ( ( in @ ( sK10_C @ SV56 @ SV44 ) @ SV44 )
        = $true )
      | ( ( disjoint @ SV44 @ SV56 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[338]) ).

thf(354,plain,
    ! [SV44: $i,SV56: $i] :
      ( ( ( in @ ( sK10_C @ SV56 @ SV44 ) @ SV56 )
        = $true )
      | ( ( disjoint @ SV44 @ SV56 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[339]) ).

thf(355,plain,
    ! [SV57: $i,SV45: $i,SV73: $i] :
      ( ( ( in @ SV73 @ SV45 )
        = $false )
      | ( ( ~ ( in @ SV73 @ SV57 ) )
        = $true )
      | ( ( ~ ( disjoint @ SV45 @ SV57 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[340]) ).

thf(356,plain,
    ! [SV46: $i,SV58: $i] :
      ( ( ( subset @ SV58 @ SV46 )
        = $false )
      | ( ( subset @ SV46 @ SV58 )
        = $false )
      | ( ( SV46 = SV58 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[341]) ).

thf(357,plain,
    ! [SV78: $i,SV74: $i] :
      ( ( ( ( SV74 != SV78 ) )
        = $true )
      | ( ( subset @ SV74 @ SV78 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[342]) ).

thf(358,plain,
    ! [SV79: $i,SV75: $i] :
      ( ( ( ( SV75 != SV79 ) )
        = $true )
      | ( ( subset @ SV79 @ SV75 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[343]) ).

thf(359,plain,
    ! [SV49: $i,SV61: $i] :
      ( ( ( in @ ( sK6_C @ SV61 @ SV49 ) @ SV49 )
        = $true )
      | ( ( subset @ SV49 @ SV61 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[344]) ).

thf(360,plain,
    ! [SV49: $i,SV61: $i] :
      ( ( ( ~ ( in @ ( sK6_C @ SV61 @ SV49 ) @ SV61 ) )
        = $true )
      | ( ( subset @ SV49 @ SV61 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[345]) ).

thf(361,plain,
    ! [SV62: $i,SV50: $i,SV80: $i] :
      ( ( ( ~ ( in @ SV80 @ SV50 ) )
        = $true )
      | ( ( in @ SV80 @ SV62 )
        = $true )
      | ( ( subset @ SV50 @ SV62 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[346]) ).

thf(362,plain,
    ! [SV24: $i,SV63: $i,SV69: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV24 )
              | ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV63 )
              | ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) ) )
        = $false )
      | ( ( SV69
          = ( set_intersection2 @ SV24 @ SV63 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[347]) ).

thf(363,plain,
    ! [SV24: $i,SV63: $i,SV69: $i] :
      ( ( ( ~ ~ ( ~ ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV24 )
                    | ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) )
                | ~ ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV63 )
                    | ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) ) ) )
        = $false )
      | ( ( SV69
          = ( set_intersection2 @ SV24 @ SV63 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[347]) ).

thf(364,plain,
    ! [SV70: $i,SV64: $i,SV24: $i] :
      ( ( ( ~ ! [SY138: $i] :
                ( ~ ( in @ SY138 @ SV24 )
                | ~ ( in @ SY138 @ SV64 )
                | ( in @ SY138 @ SV70 ) )
          | ~ ~ ( ~ ! [SY139: $i] :
                      ( ~ ( in @ SY139 @ SV70 )
                      | ( in @ SY139 @ SV24 ) )
                | ~ ! [SY140: $i] :
                      ( ~ ( in @ SY140 @ SV70 )
                      | ( in @ SY140 @ SV64 ) ) ) )
        = $false )
      | ( ( SV70
          = ( set_intersection2 @ SV24 @ SV64 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[348]) ).

thf(365,plain,
    ! [SV76: $i,SV66: $i,SV52: $i] :
      ( ( ( disjoint @ SV52 @ SV66 )
        = $false )
      | ( ( in @ SV76 @ ( set_intersection2 @ SV52 @ SV66 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[349]) ).

thf(366,plain,
    ! [SV25: $i,SV67: $i,SV71: $i] :
      ( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
                    | ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV25 ) )
                | ~ ( ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
                    | ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV67 ) ) ) )
        = $false )
      | ( ( SV71
          = ( set_union2 @ SV25 @ SV67 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[350]) ).

thf(367,plain,
    ! [SV25: $i,SV67: $i,SV71: $i] :
      ( ( ( ~ ( ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
              | ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV25 )
              | ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV67 ) ) )
        = $false )
      | ( ( SV71
          = ( set_union2 @ SV25 @ SV67 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[350]) ).

thf(368,plain,
    ! [SV68: $i,SV25: $i,SV72: $i] :
      ( ( ( ~ ! [SY141: $i] :
                ( ~ ( in @ SY141 @ SV72 )
                | ( in @ SY141 @ SV25 )
                | ( in @ SY141 @ SV68 ) )
          | ~ ~ ( ~ ! [SY142: $i] :
                      ( ~ ( in @ SY142 @ SV25 )
                      | ( in @ SY142 @ SV72 ) )
                | ~ ! [SY143: $i] :
                      ( ~ ( in @ SY143 @ SV68 )
                      | ( in @ SY143 @ SV72 ) ) ) )
        = $false )
      | ( ( SV72
          = ( set_union2 @ SV25 @ SV68 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[351]) ).

thf(369,plain,
    ! [SV45: $i,SV57: $i,SV73: $i] :
      ( ( ( in @ SV73 @ SV57 )
        = $false )
      | ( ( in @ SV73 @ SV45 )
        = $false )
      | ( ( ~ ( disjoint @ SV45 @ SV57 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[355]) ).

thf(370,plain,
    ! [SV78: $i,SV74: $i] :
      ( ( ( SV74 = SV78 )
        = $false )
      | ( ( subset @ SV74 @ SV78 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[357]) ).

thf(371,plain,
    ! [SV79: $i,SV75: $i] :
      ( ( ( SV75 = SV79 )
        = $false )
      | ( ( subset @ SV79 @ SV75 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[358]) ).

thf(372,plain,
    ! [SV49: $i,SV61: $i] :
      ( ( ( in @ ( sK6_C @ SV61 @ SV49 ) @ SV61 )
        = $false )
      | ( ( subset @ SV49 @ SV61 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[360]) ).

thf(373,plain,
    ! [SV62: $i,SV50: $i,SV80: $i] :
      ( ( ( in @ SV80 @ SV50 )
        = $false )
      | ( ( in @ SV80 @ SV62 )
        = $true )
      | ( ( subset @ SV50 @ SV62 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[361]) ).

thf(374,plain,
    ! [SV24: $i,SV63: $i,SV69: $i] :
      ( ( ( ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV24 )
          | ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV63 )
          | ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) )
        = $true )
      | ( ( SV69
          = ( set_intersection2 @ SV24 @ SV63 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[362]) ).

thf(375,plain,
    ! [SV24: $i,SV63: $i,SV69: $i] :
      ( ( ( ~ ( ~ ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV24 )
                  | ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) )
              | ~ ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV63 )
                  | ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) ) ) )
        = $true )
      | ( ( SV69
          = ( set_intersection2 @ SV24 @ SV63 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[363]) ).

thf(376,plain,
    ! [SV70: $i,SV64: $i,SV24: $i] :
      ( ( ( ~ ! [SY138: $i] :
                ( ~ ( in @ SY138 @ SV24 )
                | ~ ( in @ SY138 @ SV64 )
                | ( in @ SY138 @ SV70 ) ) )
        = $false )
      | ( ( SV70
          = ( set_intersection2 @ SV24 @ SV64 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[364]) ).

thf(377,plain,
    ! [SV64: $i,SV24: $i,SV70: $i] :
      ( ( ( ~ ~ ( ~ ! [SY139: $i] :
                      ( ~ ( in @ SY139 @ SV70 )
                      | ( in @ SY139 @ SV24 ) )
                | ~ ! [SY140: $i] :
                      ( ~ ( in @ SY140 @ SV70 )
                      | ( in @ SY140 @ SV64 ) ) ) )
        = $false )
      | ( ( SV70
          = ( set_intersection2 @ SV24 @ SV64 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[364]) ).

thf(378,plain,
    ! [SV25: $i,SV67: $i,SV71: $i] :
      ( ( ( ~ ( ~ ( ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
                  | ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV25 ) )
              | ~ ( ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
                  | ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV67 ) ) ) )
        = $true )
      | ( ( SV71
          = ( set_union2 @ SV25 @ SV67 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[366]) ).

thf(379,plain,
    ! [SV25: $i,SV67: $i,SV71: $i] :
      ( ( ( ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
          | ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV25 )
          | ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV67 ) )
        = $true )
      | ( ( SV71
          = ( set_union2 @ SV25 @ SV67 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[367]) ).

thf(380,plain,
    ! [SV68: $i,SV25: $i,SV72: $i] :
      ( ( ( ~ ! [SY141: $i] :
                ( ~ ( in @ SY141 @ SV72 )
                | ( in @ SY141 @ SV25 )
                | ( in @ SY141 @ SV68 ) ) )
        = $false )
      | ( ( SV72
          = ( set_union2 @ SV25 @ SV68 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[368]) ).

thf(381,plain,
    ! [SV68: $i,SV72: $i,SV25: $i] :
      ( ( ( ~ ~ ( ~ ! [SY142: $i] :
                      ( ~ ( in @ SY142 @ SV25 )
                      | ( in @ SY142 @ SV72 ) )
                | ~ ! [SY143: $i] :
                      ( ~ ( in @ SY143 @ SV68 )
                      | ( in @ SY143 @ SV72 ) ) ) )
        = $false )
      | ( ( SV72
          = ( set_union2 @ SV25 @ SV68 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[368]) ).

thf(382,plain,
    ! [SV73: $i,SV57: $i,SV45: $i] :
      ( ( ( disjoint @ SV45 @ SV57 )
        = $false )
      | ( ( in @ SV73 @ SV45 )
        = $false )
      | ( ( in @ SV73 @ SV57 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[369]) ).

thf(383,plain,
    ! [SV24: $i,SV63: $i,SV69: $i] :
      ( ( ( ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV24 )
          | ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV63 ) )
        = $true )
      | ( ( ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) )
        = $true )
      | ( ( SV69
          = ( set_intersection2 @ SV24 @ SV63 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[374]) ).

thf(384,plain,
    ! [SV24: $i,SV63: $i,SV69: $i] :
      ( ( ( ~ ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV24 )
              | ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) )
          | ~ ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV63 )
              | ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) ) )
        = $false )
      | ( ( SV69
          = ( set_intersection2 @ SV24 @ SV63 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[375]) ).

thf(385,plain,
    ! [SV70: $i,SV64: $i,SV24: $i] :
      ( ( ( ! [SY138: $i] :
              ( ~ ( in @ SY138 @ SV24 )
              | ~ ( in @ SY138 @ SV64 )
              | ( in @ SY138 @ SV70 ) ) )
        = $true )
      | ( ( SV70
          = ( set_intersection2 @ SV24 @ SV64 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[376]) ).

thf(386,plain,
    ! [SV64: $i,SV24: $i,SV70: $i] :
      ( ( ( ~ ( ~ ! [SY139: $i] :
                    ( ~ ( in @ SY139 @ SV70 )
                    | ( in @ SY139 @ SV24 ) )
              | ~ ! [SY140: $i] :
                    ( ~ ( in @ SY140 @ SV70 )
                    | ( in @ SY140 @ SV64 ) ) ) )
        = $true )
      | ( ( SV70
          = ( set_intersection2 @ SV24 @ SV64 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[377]) ).

thf(387,plain,
    ! [SV25: $i,SV67: $i,SV71: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
              | ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV25 ) )
          | ~ ( ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
              | ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV67 ) ) )
        = $false )
      | ( ( SV71
          = ( set_union2 @ SV25 @ SV67 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[378]) ).

thf(388,plain,
    ! [SV25: $i,SV67: $i,SV71: $i] :
      ( ( ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
        = $true )
      | ( ( ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV25 )
          | ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV67 ) )
        = $true )
      | ( ( SV71
          = ( set_union2 @ SV25 @ SV67 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[379]) ).

thf(389,plain,
    ! [SV68: $i,SV25: $i,SV72: $i] :
      ( ( ( ! [SY141: $i] :
              ( ~ ( in @ SY141 @ SV72 )
              | ( in @ SY141 @ SV25 )
              | ( in @ SY141 @ SV68 ) ) )
        = $true )
      | ( ( SV72
          = ( set_union2 @ SV25 @ SV68 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[380]) ).

thf(390,plain,
    ! [SV68: $i,SV72: $i,SV25: $i] :
      ( ( ( ~ ( ~ ! [SY142: $i] :
                    ( ~ ( in @ SY142 @ SV25 )
                    | ( in @ SY142 @ SV72 ) )
              | ~ ! [SY143: $i] :
                    ( ~ ( in @ SY143 @ SV68 )
                    | ( in @ SY143 @ SV72 ) ) ) )
        = $true )
      | ( ( SV72
          = ( set_union2 @ SV25 @ SV68 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[381]) ).

thf(391,plain,
    ! [SV24: $i,SV63: $i,SV69: $i] :
      ( ( ( ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV24 ) )
        = $true )
      | ( ( ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV63 ) )
        = $true )
      | ( ( ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) )
        = $true )
      | ( ( SV69
          = ( set_intersection2 @ SV24 @ SV63 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[383]) ).

thf(392,plain,
    ! [SV24: $i,SV63: $i,SV69: $i] :
      ( ( ( ~ ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV24 )
              | ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) ) )
        = $false )
      | ( ( SV69
          = ( set_intersection2 @ SV24 @ SV63 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[384]) ).

thf(393,plain,
    ! [SV24: $i,SV63: $i,SV69: $i] :
      ( ( ( ~ ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV63 )
              | ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) ) )
        = $false )
      | ( ( SV69
          = ( set_intersection2 @ SV24 @ SV63 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[384]) ).

thf(394,plain,
    ! [SV70: $i,SV64: $i,SV24: $i,SV81: $i] :
      ( ( ( ~ ( in @ SV81 @ SV24 )
          | ~ ( in @ SV81 @ SV64 )
          | ( in @ SV81 @ SV70 ) )
        = $true )
      | ( ( SV70
          = ( set_intersection2 @ SV24 @ SV64 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[385]) ).

thf(395,plain,
    ! [SV64: $i,SV24: $i,SV70: $i] :
      ( ( ( ~ ! [SY139: $i] :
                ( ~ ( in @ SY139 @ SV70 )
                | ( in @ SY139 @ SV24 ) )
          | ~ ! [SY140: $i] :
                ( ~ ( in @ SY140 @ SV70 )
                | ( in @ SY140 @ SV64 ) ) )
        = $false )
      | ( ( SV70
          = ( set_intersection2 @ SV24 @ SV64 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[386]) ).

thf(396,plain,
    ! [SV25: $i,SV67: $i,SV71: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
              | ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV25 ) ) )
        = $false )
      | ( ( SV71
          = ( set_union2 @ SV25 @ SV67 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[387]) ).

thf(397,plain,
    ! [SV25: $i,SV67: $i,SV71: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
              | ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV67 ) ) )
        = $false )
      | ( ( SV71
          = ( set_union2 @ SV25 @ SV67 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[387]) ).

thf(398,plain,
    ! [SV25: $i,SV67: $i,SV71: $i] :
      ( ( ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV25 )
        = $true )
      | ( ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV67 )
        = $true )
      | ( ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
        = $true )
      | ( ( SV71
          = ( set_union2 @ SV25 @ SV67 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[388]) ).

thf(399,plain,
    ! [SV68: $i,SV25: $i,SV72: $i,SV82: $i] :
      ( ( ( ~ ( in @ SV82 @ SV72 )
          | ( in @ SV82 @ SV25 )
          | ( in @ SV82 @ SV68 ) )
        = $true )
      | ( ( SV72
          = ( set_union2 @ SV25 @ SV68 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[389]) ).

thf(400,plain,
    ! [SV68: $i,SV72: $i,SV25: $i] :
      ( ( ( ~ ! [SY142: $i] :
                ( ~ ( in @ SY142 @ SV25 )
                | ( in @ SY142 @ SV72 ) )
          | ~ ! [SY143: $i] :
                ( ~ ( in @ SY143 @ SV68 )
                | ( in @ SY143 @ SV72 ) ) )
        = $false )
      | ( ( SV72
          = ( set_union2 @ SV25 @ SV68 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[390]) ).

thf(401,plain,
    ! [SV24: $i,SV63: $i,SV69: $i] :
      ( ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV24 )
        = $false )
      | ( ( ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV63 ) )
        = $true )
      | ( ( ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) )
        = $true )
      | ( ( SV69
          = ( set_intersection2 @ SV24 @ SV63 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[391]) ).

thf(402,plain,
    ! [SV24: $i,SV63: $i,SV69: $i] :
      ( ( ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV24 )
          | ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) )
        = $true )
      | ( ( SV69
          = ( set_intersection2 @ SV24 @ SV63 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[392]) ).

thf(403,plain,
    ! [SV24: $i,SV63: $i,SV69: $i] :
      ( ( ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV63 )
          | ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) )
        = $true )
      | ( ( SV69
          = ( set_intersection2 @ SV24 @ SV63 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[393]) ).

thf(404,plain,
    ! [SV70: $i,SV64: $i,SV24: $i,SV81: $i] :
      ( ( ( ~ ( in @ SV81 @ SV24 )
          | ~ ( in @ SV81 @ SV64 ) )
        = $true )
      | ( ( in @ SV81 @ SV70 )
        = $true )
      | ( ( SV70
          = ( set_intersection2 @ SV24 @ SV64 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[394]) ).

thf(405,plain,
    ! [SV64: $i,SV24: $i,SV70: $i] :
      ( ( ( ~ ! [SY139: $i] :
                ( ~ ( in @ SY139 @ SV70 )
                | ( in @ SY139 @ SV24 ) ) )
        = $false )
      | ( ( SV70
          = ( set_intersection2 @ SV24 @ SV64 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[395]) ).

thf(406,plain,
    ! [SV24: $i,SV64: $i,SV70: $i] :
      ( ( ( ~ ! [SY140: $i] :
                ( ~ ( in @ SY140 @ SV70 )
                | ( in @ SY140 @ SV64 ) ) )
        = $false )
      | ( ( SV70
          = ( set_intersection2 @ SV24 @ SV64 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[395]) ).

thf(407,plain,
    ! [SV25: $i,SV67: $i,SV71: $i] :
      ( ( ( ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
          | ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV25 ) )
        = $true )
      | ( ( SV71
          = ( set_union2 @ SV25 @ SV67 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[396]) ).

thf(408,plain,
    ! [SV25: $i,SV67: $i,SV71: $i] :
      ( ( ( ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
          | ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV67 ) )
        = $true )
      | ( ( SV71
          = ( set_union2 @ SV25 @ SV67 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[397]) ).

thf(409,plain,
    ! [SV68: $i,SV25: $i,SV72: $i,SV82: $i] :
      ( ( ( ~ ( in @ SV82 @ SV72 ) )
        = $true )
      | ( ( ( in @ SV82 @ SV25 )
          | ( in @ SV82 @ SV68 ) )
        = $true )
      | ( ( SV72
          = ( set_union2 @ SV25 @ SV68 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[399]) ).

thf(410,plain,
    ! [SV68: $i,SV72: $i,SV25: $i] :
      ( ( ( ~ ! [SY142: $i] :
                ( ~ ( in @ SY142 @ SV25 )
                | ( in @ SY142 @ SV72 ) ) )
        = $false )
      | ( ( SV72
          = ( set_union2 @ SV25 @ SV68 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[400]) ).

thf(411,plain,
    ! [SV25: $i,SV72: $i,SV68: $i] :
      ( ( ( ~ ! [SY143: $i] :
                ( ~ ( in @ SY143 @ SV68 )
                | ( in @ SY143 @ SV72 ) ) )
        = $false )
      | ( ( SV72
          = ( set_union2 @ SV25 @ SV68 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[400]) ).

thf(412,plain,
    ! [SV24: $i,SV63: $i,SV69: $i] :
      ( ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV63 )
        = $false )
      | ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV24 )
        = $false )
      | ( ( ~ ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 ) )
        = $true )
      | ( ( SV69
          = ( set_intersection2 @ SV24 @ SV63 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[401]) ).

thf(413,plain,
    ! [SV24: $i,SV63: $i,SV69: $i] :
      ( ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV24 )
        = $true )
      | ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 )
        = $true )
      | ( ( SV69
          = ( set_intersection2 @ SV24 @ SV63 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[402]) ).

thf(414,plain,
    ! [SV24: $i,SV63: $i,SV69: $i] :
      ( ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV63 )
        = $true )
      | ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 )
        = $true )
      | ( ( SV69
          = ( set_intersection2 @ SV24 @ SV63 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[403]) ).

thf(415,plain,
    ! [SV70: $i,SV64: $i,SV24: $i,SV81: $i] :
      ( ( ( ~ ( in @ SV81 @ SV24 ) )
        = $true )
      | ( ( ~ ( in @ SV81 @ SV64 ) )
        = $true )
      | ( ( in @ SV81 @ SV70 )
        = $true )
      | ( ( SV70
          = ( set_intersection2 @ SV24 @ SV64 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[404]) ).

thf(416,plain,
    ! [SV64: $i,SV24: $i,SV70: $i] :
      ( ( ( ! [SY139: $i] :
              ( ~ ( in @ SY139 @ SV70 )
              | ( in @ SY139 @ SV24 ) ) )
        = $true )
      | ( ( SV70
          = ( set_intersection2 @ SV24 @ SV64 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[405]) ).

thf(417,plain,
    ! [SV24: $i,SV64: $i,SV70: $i] :
      ( ( ( ! [SY140: $i] :
              ( ~ ( in @ SY140 @ SV70 )
              | ( in @ SY140 @ SV64 ) ) )
        = $true )
      | ( ( SV70
          = ( set_intersection2 @ SV24 @ SV64 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[406]) ).

thf(418,plain,
    ! [SV25: $i,SV67: $i,SV71: $i] :
      ( ( ( ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 ) )
        = $true )
      | ( ( ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV25 ) )
        = $true )
      | ( ( SV71
          = ( set_union2 @ SV25 @ SV67 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[407]) ).

thf(419,plain,
    ! [SV25: $i,SV67: $i,SV71: $i] :
      ( ( ( ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 ) )
        = $true )
      | ( ( ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV67 ) )
        = $true )
      | ( ( SV71
          = ( set_union2 @ SV25 @ SV67 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[408]) ).

thf(420,plain,
    ! [SV68: $i,SV25: $i,SV72: $i,SV82: $i] :
      ( ( ( in @ SV82 @ SV72 )
        = $false )
      | ( ( ( in @ SV82 @ SV25 )
          | ( in @ SV82 @ SV68 ) )
        = $true )
      | ( ( SV72
          = ( set_union2 @ SV25 @ SV68 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[409]) ).

thf(421,plain,
    ! [SV68: $i,SV72: $i,SV25: $i] :
      ( ( ( ! [SY142: $i] :
              ( ~ ( in @ SY142 @ SV25 )
              | ( in @ SY142 @ SV72 ) ) )
        = $true )
      | ( ( SV72
          = ( set_union2 @ SV25 @ SV68 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[410]) ).

thf(422,plain,
    ! [SV25: $i,SV72: $i,SV68: $i] :
      ( ( ( ! [SY143: $i] :
              ( ~ ( in @ SY143 @ SV68 )
              | ( in @ SY143 @ SV72 ) ) )
        = $true )
      | ( ( SV72
          = ( set_union2 @ SV25 @ SV68 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[411]) ).

thf(423,plain,
    ! [SV24: $i,SV63: $i,SV69: $i] :
      ( ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV69 )
        = $false )
      | ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV24 )
        = $false )
      | ( ( in @ ( sK5_D @ SV69 @ SV63 @ SV24 ) @ SV63 )
        = $false )
      | ( ( SV69
          = ( set_intersection2 @ SV24 @ SV63 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[412]) ).

thf(424,plain,
    ! [SV70: $i,SV64: $i,SV24: $i,SV81: $i] :
      ( ( ( in @ SV81 @ SV24 )
        = $false )
      | ( ( ~ ( in @ SV81 @ SV64 ) )
        = $true )
      | ( ( in @ SV81 @ SV70 )
        = $true )
      | ( ( SV70
          = ( set_intersection2 @ SV24 @ SV64 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[415]) ).

thf(425,plain,
    ! [SV64: $i,SV24: $i,SV70: $i,SV83: $i] :
      ( ( ( ~ ( in @ SV83 @ SV70 )
          | ( in @ SV83 @ SV24 ) )
        = $true )
      | ( ( SV70
          = ( set_intersection2 @ SV24 @ SV64 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[416]) ).

thf(426,plain,
    ! [SV24: $i,SV64: $i,SV70: $i,SV84: $i] :
      ( ( ( ~ ( in @ SV84 @ SV70 )
          | ( in @ SV84 @ SV64 ) )
        = $true )
      | ( ( SV70
          = ( set_intersection2 @ SV24 @ SV64 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[417]) ).

thf(427,plain,
    ! [SV25: $i,SV67: $i,SV71: $i] :
      ( ( ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
        = $false )
      | ( ( ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV25 ) )
        = $true )
      | ( ( SV71
          = ( set_union2 @ SV25 @ SV67 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[418]) ).

thf(428,plain,
    ! [SV25: $i,SV67: $i,SV71: $i] :
      ( ( ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
        = $false )
      | ( ( ~ ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV67 ) )
        = $true )
      | ( ( SV71
          = ( set_union2 @ SV25 @ SV67 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[419]) ).

thf(429,plain,
    ! [SV72: $i,SV68: $i,SV25: $i,SV82: $i] :
      ( ( ( in @ SV82 @ SV25 )
        = $true )
      | ( ( in @ SV82 @ SV68 )
        = $true )
      | ( ( in @ SV82 @ SV72 )
        = $false )
      | ( ( SV72
          = ( set_union2 @ SV25 @ SV68 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[420]) ).

thf(430,plain,
    ! [SV68: $i,SV72: $i,SV25: $i,SV85: $i] :
      ( ( ( ~ ( in @ SV85 @ SV25 )
          | ( in @ SV85 @ SV72 ) )
        = $true )
      | ( ( SV72
          = ( set_union2 @ SV25 @ SV68 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[421]) ).

thf(431,plain,
    ! [SV25: $i,SV72: $i,SV68: $i,SV86: $i] :
      ( ( ( ~ ( in @ SV86 @ SV68 )
          | ( in @ SV86 @ SV72 ) )
        = $true )
      | ( ( SV72
          = ( set_union2 @ SV25 @ SV68 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[422]) ).

thf(432,plain,
    ! [SV70: $i,SV24: $i,SV64: $i,SV81: $i] :
      ( ( ( in @ SV81 @ SV64 )
        = $false )
      | ( ( in @ SV81 @ SV24 )
        = $false )
      | ( ( in @ SV81 @ SV70 )
        = $true )
      | ( ( SV70
          = ( set_intersection2 @ SV24 @ SV64 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[424]) ).

thf(433,plain,
    ! [SV64: $i,SV24: $i,SV70: $i,SV83: $i] :
      ( ( ( ~ ( in @ SV83 @ SV70 ) )
        = $true )
      | ( ( in @ SV83 @ SV24 )
        = $true )
      | ( ( SV70
          = ( set_intersection2 @ SV24 @ SV64 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[425]) ).

thf(434,plain,
    ! [SV24: $i,SV64: $i,SV70: $i,SV84: $i] :
      ( ( ( ~ ( in @ SV84 @ SV70 ) )
        = $true )
      | ( ( in @ SV84 @ SV64 )
        = $true )
      | ( ( SV70
          = ( set_intersection2 @ SV24 @ SV64 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[426]) ).

thf(435,plain,
    ! [SV25: $i,SV67: $i,SV71: $i] :
      ( ( ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV25 )
        = $false )
      | ( ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
        = $false )
      | ( ( SV71
          = ( set_union2 @ SV25 @ SV67 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[427]) ).

thf(436,plain,
    ! [SV25: $i,SV67: $i,SV71: $i] :
      ( ( ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV67 )
        = $false )
      | ( ( in @ ( sK7_D @ SV71 @ SV67 @ SV25 ) @ SV71 )
        = $false )
      | ( ( SV71
          = ( set_union2 @ SV25 @ SV67 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[428]) ).

thf(437,plain,
    ! [SV68: $i,SV72: $i,SV25: $i,SV85: $i] :
      ( ( ( ~ ( in @ SV85 @ SV25 ) )
        = $true )
      | ( ( in @ SV85 @ SV72 )
        = $true )
      | ( ( SV72
          = ( set_union2 @ SV25 @ SV68 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[430]) ).

thf(438,plain,
    ! [SV25: $i,SV72: $i,SV68: $i,SV86: $i] :
      ( ( ( ~ ( in @ SV86 @ SV68 ) )
        = $true )
      | ( ( in @ SV86 @ SV72 )
        = $true )
      | ( ( SV72
          = ( set_union2 @ SV25 @ SV68 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[431]) ).

thf(439,plain,
    ! [SV64: $i,SV24: $i,SV70: $i,SV83: $i] :
      ( ( ( in @ SV83 @ SV70 )
        = $false )
      | ( ( in @ SV83 @ SV24 )
        = $true )
      | ( ( SV70
          = ( set_intersection2 @ SV24 @ SV64 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[433]) ).

thf(440,plain,
    ! [SV24: $i,SV64: $i,SV70: $i,SV84: $i] :
      ( ( ( in @ SV84 @ SV70 )
        = $false )
      | ( ( in @ SV84 @ SV64 )
        = $true )
      | ( ( SV70
          = ( set_intersection2 @ SV24 @ SV64 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[434]) ).

thf(441,plain,
    ! [SV68: $i,SV72: $i,SV25: $i,SV85: $i] :
      ( ( ( in @ SV85 @ SV25 )
        = $false )
      | ( ( in @ SV85 @ SV72 )
        = $true )
      | ( ( SV72
          = ( set_union2 @ SV25 @ SV68 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[437]) ).

thf(442,plain,
    ! [SV25: $i,SV72: $i,SV68: $i,SV86: $i] :
      ( ( ( in @ SV86 @ SV68 )
        = $false )
      | ( ( in @ SV86 @ SV72 )
        = $true )
      | ( ( SV72
          = ( set_union2 @ SV25 @ SV68 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[438]) ).

thf(443,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[129,442,441,440,439,436,435,432,429,423,414,413,398,382,373,372,371,370,365,359,356,354,353,352,329,328,322,321,320,315,303,298,281,280,278,257,256,255,249,230,224,199,198,195,190,180,176,175,173,172,171,170,161,146,137,132,131,130]) ).

thf(444,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[443]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : SEU130+2 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.15  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.16/0.36  % Computer : n011.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 600
% 0.16/0.36  % DateTime : Sun Jun 19 03:23:53 EDT 2022
% 0.16/0.36  % CPUTime  : 
% 0.16/0.39  
% 0.16/0.39   No.of.Axioms: 37
% 0.16/0.39  
% 0.16/0.39   Length.of.Defs: 0
% 0.16/0.39  
% 0.16/0.39   Contains.Choice.Funs: false
% 0.16/0.39  .
% 0.16/0.40  (rf:0,axioms:37,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:39,loop_count:0,foatp_calls:0,translation:fof_full).............................
% 0.63/0.77  
% 0.63/0.77  ********************************
% 0.63/0.77  *   All subproblems solved!    *
% 0.63/0.77  ********************************
% 0.63/0.77  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:38,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:443,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.71/0.88  
% 0.71/0.88  %**** Beginning of derivation protocol ****
% 0.71/0.88  % SZS output start CNFRefutation
% See solution above
% 0.71/0.88  
% 0.71/0.88  %**** End of derivation protocol ****
% 0.71/0.88  %**** no. of clauses in derivation: 444 ****
% 0.71/0.88  %**** clause counter: 443 ****
% 0.71/0.88  
% 0.71/0.88  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:38,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:443,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------