TSTP Solution File: SET600+3 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET600+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 03:06:24 EDT 2024

% Result   : Theorem 68.50s 10.73s
% Output   : Refutation 68.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   60
%            Number of leaves      :   19
% Syntax   : Number of formulae    :  197 (  24 unt;  12 typ;   0 def)
%            Number of atoms       :  546 ( 173 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives : 1372 ( 274   ~; 241   |;  21   &; 805   @)
%                                         (   6 <=>;  25  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  12 usr;   8 con; 0-2 aty)
%            Number of variables   :  195 (   0   ^ 192   !;   3   ?; 195   :)

% Comments : 
%------------------------------------------------------------------------------
thf(union_type,type,
    union: $i > $i > $i ).

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

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

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

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

thf(sk1_type,type,
    sk1: $o ).

thf(sk2_type,type,
    sk2: $i ).

thf(sk3_type,type,
    sk3: $i ).

thf(sk4_type,type,
    sk4: $i ).

thf(sk5_type,type,
    sk5: $i ).

thf(sk6_type,type,
    sk6: $i > $i > $i ).

thf(sk7_type,type,
    sk7: $i > $i ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ( subset @ A @ B )
    <=> ! [C: $i] :
          ( ( member @ C @ A )
         => ( member @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).

thf(47,plain,
    ! [A: $i,B: $i] :
      ( ( ( subset @ A @ B )
       => ! [C: $i] :
            ( ( member @ C @ A )
           => ( member @ C @ B ) ) )
      & ( ! [C: $i] :
            ( ( member @ C @ A )
           => ( member @ C @ B ) )
       => ( subset @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(48,plain,
    ( ! [A: $i,B: $i] :
        ( ( subset @ A @ B )
       => ! [C: $i] :
            ( ( member @ C @ A )
           => ( member @ C @ B ) ) )
    & ! [A: $i,B: $i] :
        ( ! [C: $i] :
            ( ( member @ C @ A )
           => ( member @ C @ B ) )
       => ( subset @ A @ B ) ) ),
    inference(miniscope,[status(thm)],[47]) ).

thf(49,plain,
    ! [B: $i,A: $i] :
      ( ( member @ ( sk6 @ B @ A ) @ A )
      | ( subset @ A @ B ) ),
    inference(cnf,[status(esa)],[48]) ).

thf(52,plain,
    ! [B: $i,A: $i] :
      ( ( member @ ( sk6 @ B @ A ) @ A )
      | ( subset @ A @ B ) ),
    inference(simp,[status(thm)],[49]) ).

thf(4,axiom,
    ! [A: $i] :
      ~ ( member @ A @ empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).

thf(30,plain,
    ! [A: $i] :
      ~ ( member @ A @ empty_set ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(31,plain,
    ~ ? [A: $i] : ( member @ A @ empty_set ),
    inference(miniscope,[status(thm)],[30]) ).

thf(32,plain,
    ! [A: $i] :
      ~ ( member @ A @ empty_set ),
    inference(cnf,[status(esa)],[31]) ).

thf(363,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( subset @ A @ B )
      | ( ( member @ ( sk6 @ B @ A ) @ A )
       != ( member @ C @ empty_set ) ) ),
    inference(paramod_ordered,[status(thm)],[52,32]) ).

thf(364,plain,
    ! [A: $i] : ( subset @ empty_set @ A ),
    inference(pattern_uni,[status(thm)],[363:[bind(A,$thf( empty_set )),bind(B,$thf( D )),bind(C,$thf( sk6 @ D @ empty_set ))]]) ).

thf(384,plain,
    ! [A: $i] : ( subset @ empty_set @ A ),
    inference(simp,[status(thm)],[364]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
    <=> ( ( subset @ A @ B )
        & ( subset @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).

thf(33,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
       => ( ( subset @ A @ B )
          & ( subset @ B @ A ) ) )
      & ( ( ( subset @ A @ B )
          & ( subset @ B @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(34,plain,
    ( ! [A: $i,B: $i] :
        ( ( A = B )
       => ( ( subset @ A @ B )
          & ( subset @ B @ A ) ) )
    & ! [A: $i,B: $i] :
        ( ( ( subset @ A @ B )
          & ( subset @ B @ A ) )
       => ( A = B ) ) ),
    inference(miniscope,[status(thm)],[33]) ).

thf(35,plain,
    ! [B: $i,A: $i] :
      ( ~ ( subset @ A @ B )
      | ~ ( subset @ B @ A )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[34]) ).

thf(38,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( subset @ A @ B )
      | ~ ( subset @ B @ A ) ),
    inference(lifteq,[status(thm)],[35]) ).

thf(39,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( subset @ A @ B )
      | ~ ( subset @ B @ A ) ),
    inference(simp,[status(thm)],[38]) ).

thf(465,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( subset @ C @ B )
      | ( ( subset @ empty_set @ A )
       != ( subset @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[384,39]) ).

thf(466,plain,
    ! [A: $i] :
      ( ( empty_set = A )
      | ~ ( subset @ A @ empty_set ) ),
    inference(pattern_uni,[status(thm)],[465:[bind(A,$thf( A )),bind(B,$thf( empty_set )),bind(C,$thf( A ))]]) ).

thf(1,conjecture,
    ! [A: $i,B: $i] :
      ( ( ( union @ A @ B )
        = empty_set )
    <=> ( ( A = empty_set )
        & ( B = empty_set ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th59) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i] :
        ( ( ( union @ A @ B )
          = empty_set )
      <=> ( ( A = empty_set )
          & ( B = empty_set ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(11,plain,
    ~ ! [A: $i,B: $i] :
        ( ( ( ( union @ A @ B )
            = empty_set )
         => ( ( A = empty_set )
            & ( B = empty_set ) ) )
        & ( ( ( A = empty_set )
            & ( B = empty_set ) )
         => ( ( union @ A @ B )
            = empty_set ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(12,plain,
    ~ ( ! [A: $i,B: $i] :
          ( ( ( union @ A @ B )
            = empty_set )
         => ( ( A = empty_set )
            & ( B = empty_set ) ) )
      & ! [A: $i,B: $i] :
          ( ( ( A = empty_set )
            & ( B = empty_set ) )
         => ( ( union @ A @ B )
            = empty_set ) ) ),
    inference(miniscope,[status(thm)],[11]) ).

thf(16,plain,
    ( ( ( union @ sk2 @ sk3 )
      = empty_set )
    | ~ sk1 ),
    inference(cnf,[status(esa)],[12]) ).

thf(21,plain,
    ( ( ( union @ sk2 @ sk3 )
      = empty_set )
    | ~ sk1 ),
    inference(lifteq,[status(thm)],[16]) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( union @ A @ B )
      = ( union @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).

thf(44,plain,
    ! [A: $i,B: $i] :
      ( ( union @ A @ B )
      = ( union @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(45,plain,
    ! [B: $i,A: $i] :
      ( ( union @ A @ B )
      = ( union @ B @ A ) ),
    inference(cnf,[status(esa)],[44]) ).

thf(46,plain,
    ! [B: $i,A: $i] :
      ( ( union @ A @ B )
      = ( union @ B @ A ) ),
    inference(lifteq,[status(thm)],[45]) ).

thf(88,plain,
    ! [B: $i,A: $i] :
      ( ~ sk1
      | ( ( union @ B @ A )
        = empty_set )
      | ( ( union @ sk2 @ sk3 )
       != ( union @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[21,46]) ).

thf(89,plain,
    ( ~ sk1
    | ( ( union @ sk3 @ sk2 )
      = empty_set ) ),
    inference(pattern_uni,[status(thm)],[88:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).

thf(17,plain,
    ( sk1
    | ( sk4 = empty_set ) ),
    inference(cnf,[status(esa)],[12]) ).

thf(20,plain,
    ( ( sk4 = empty_set )
    | sk1 ),
    inference(lifteq,[status(thm)],[17]) ).

thf(13,plain,
    ( sk1
    | ( sk5 = empty_set ) ),
    inference(cnf,[status(esa)],[12]) ).

thf(19,plain,
    ( ( sk5 = empty_set )
    | sk1 ),
    inference(lifteq,[status(thm)],[13]) ).

thf(14,plain,
    ( sk1
    | ( ( union @ sk4 @ sk5 )
     != empty_set ) ),
    inference(cnf,[status(esa)],[12]) ).

thf(18,plain,
    ( ( ( union @ sk4 @ sk5 )
     != empty_set )
    | sk1 ),
    inference(lifteq,[status(thm)],[14]) ).

thf(83,plain,
    ( sk1
    | ( ( union @ sk4 @ empty_set )
     != empty_set )
    | ( sk5 != sk5 ) ),
    inference(paramod_ordered,[status(thm)],[19,18]) ).

thf(84,plain,
    ( sk1
    | ( ( union @ sk4 @ empty_set )
     != empty_set ) ),
    inference(pattern_uni,[status(thm)],[83:[]]) ).

thf(487,plain,
    ! [A: $i] :
      ( ~ ( subset @ A @ empty_set )
      | sk1
      | ( A
       != ( union @ sk4 @ empty_set ) ) ),
    inference(paramod_ordered,[status(thm)],[466,84]) ).

thf(488,plain,
    ( ~ ( subset @ ( union @ sk4 @ empty_set ) @ empty_set )
    | sk1 ),
    inference(pattern_uni,[status(thm)],[487:[bind(A,$thf( union @ sk4 @ empty_set ))]]) ).

thf(593,plain,
    ! [B: $i,A: $i] :
      ( ( member @ ( sk6 @ B @ A ) @ A )
      | sk1
      | ( ( subset @ A @ B )
       != ( subset @ ( union @ sk4 @ empty_set ) @ empty_set ) ) ),
    inference(paramod_ordered,[status(thm)],[52,488]) ).

thf(594,plain,
    ( ( member @ ( sk6 @ empty_set @ ( union @ sk4 @ empty_set ) ) @ ( union @ sk4 @ empty_set ) )
    | sk1 ),
    inference(pattern_uni,[status(thm)],[593:[bind(A,$thf( union @ sk4 @ empty_set )),bind(B,$thf( empty_set ))]]) ).

thf(763,plain,
    ( sk1
    | ( member @ ( sk6 @ empty_set @ ( union @ sk4 @ empty_set ) ) @ ( union @ empty_set @ empty_set ) )
    | ( sk4 != sk4 ) ),
    inference(paramod_ordered,[status(thm)],[20,594]) ).

thf(764,plain,
    ( sk1
    | ( member @ ( sk6 @ empty_set @ ( union @ sk4 @ empty_set ) ) @ ( union @ empty_set @ empty_set ) ) ),
    inference(pattern_uni,[status(thm)],[763:[]]) ).

thf(3,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( member @ C @ ( union @ A @ B ) )
    <=> ( ( member @ C @ A )
        | ( member @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).

thf(23,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( member @ C @ ( union @ A @ B ) )
       => ( ( member @ C @ A )
          | ( member @ C @ B ) ) )
      & ( ( ( member @ C @ A )
          | ( member @ C @ B ) )
       => ( member @ C @ ( union @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(24,plain,
    ( ! [A: $i,B: $i,C: $i] :
        ( ( member @ C @ ( union @ A @ B ) )
       => ( ( member @ C @ A )
          | ( member @ C @ B ) ) )
    & ! [A: $i,B: $i,C: $i] :
        ( ( ( member @ C @ A )
          | ( member @ C @ B ) )
       => ( member @ C @ ( union @ A @ B ) ) ) ),
    inference(miniscope,[status(thm)],[23]) ).

thf(27,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ C @ ( union @ A @ B ) )
      | ( member @ C @ A )
      | ( member @ C @ B ) ),
    inference(cnf,[status(esa)],[24]) ).

thf(1382,plain,
    ! [C: $i,B: $i,A: $i] :
      ( sk1
      | ( member @ C @ A )
      | ( member @ C @ B )
      | ( ( member @ ( sk6 @ empty_set @ ( union @ sk4 @ empty_set ) ) @ ( union @ empty_set @ empty_set ) )
       != ( member @ C @ ( union @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[764,27]) ).

thf(1383,plain,
    ( sk1
    | ( member @ ( sk6 @ empty_set @ ( union @ sk4 @ empty_set ) ) @ empty_set )
    | ( member @ ( sk6 @ empty_set @ ( union @ sk4 @ empty_set ) ) @ empty_set ) ),
    inference(pattern_uni,[status(thm)],[1382:[bind(A,$thf( empty_set )),bind(B,$thf( empty_set )),bind(C,$thf( sk6 @ empty_set @ ( union @ sk4 @ empty_set ) ))]]) ).

thf(1422,plain,
    ( sk1
    | ( member @ ( sk6 @ empty_set @ ( union @ sk4 @ empty_set ) ) @ empty_set ) ),
    inference(simp,[status(thm)],[1383]) ).

thf(1509,plain,
    ( sk1
    | $false ),
    inference(rewrite,[status(thm)],[1422,32]) ).

thf(1510,plain,
    sk1,
    inference(simp,[status(thm)],[1509]) ).

thf(1513,plain,
    ( ~ $true
    | ( ( union @ sk3 @ sk2 )
      = empty_set ) ),
    inference(rewrite,[status(thm)],[89,1510]) ).

thf(1514,plain,
    ( ( union @ sk3 @ sk2 )
    = empty_set ),
    inference(simp,[status(thm)],[1513]) ).

thf(1533,plain,
    ! [A: $i] :
      ( ~ ( subset @ A @ empty_set )
      | ( ( union @ sk3 @ empty_set )
        = empty_set )
      | ( A != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[466,1514]) ).

thf(1534,plain,
    ( ~ ( subset @ sk2 @ empty_set )
    | ( ( union @ sk3 @ empty_set )
      = empty_set ) ),
    inference(pattern_uni,[status(thm)],[1533:[bind(A,$thf( sk2 ))]]) ).

thf(3726,plain,
    ! [B: $i,A: $i] :
      ( ( member @ ( sk6 @ B @ A ) @ A )
      | ( ( union @ sk3 @ empty_set )
        = empty_set )
      | ( ( subset @ A @ B )
       != ( subset @ sk2 @ empty_set ) ) ),
    inference(paramod_ordered,[status(thm)],[52,1534]) ).

thf(3727,plain,
    ( ( member @ ( sk6 @ empty_set @ sk2 ) @ sk2 )
    | ( ( union @ sk3 @ empty_set )
      = empty_set ) ),
    inference(pattern_uni,[status(thm)],[3726:[bind(A,$thf( sk2 )),bind(B,$thf( empty_set ))]]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( empty @ A )
    <=> ! [B: $i] :
          ~ ( member @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).

thf(56,plain,
    ! [A: $i] :
      ( ( ( empty @ A )
       => ! [B: $i] :
            ~ ( member @ B @ A ) )
      & ( ! [B: $i] :
            ~ ( member @ B @ A )
       => ( empty @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(57,plain,
    ( ! [A: $i] :
        ( ( empty @ A )
       => ~ ? [B: $i] : ( member @ B @ A ) )
    & ! [A: $i] :
        ( ~ ? [B: $i] : ( member @ B @ A )
       => ( empty @ A ) ) ),
    inference(miniscope,[status(thm)],[56]) ).

thf(59,plain,
    ! [B: $i,A: $i] :
      ( ~ ( empty @ A )
      | ~ ( member @ B @ A ) ),
    inference(cnf,[status(esa)],[57]) ).

thf(5526,plain,
    ! [B: $i,A: $i] :
      ( ( ( union @ sk3 @ empty_set )
        = empty_set )
      | ~ ( empty @ A )
      | ( ( member @ ( sk6 @ empty_set @ sk2 ) @ sk2 )
       != ( member @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3727,59]) ).

thf(5527,plain,
    ( ( ( union @ sk3 @ empty_set )
      = empty_set )
    | ~ ( empty @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[5526:[bind(A,$thf( sk2 )),bind(B,$thf( sk6 @ empty_set @ sk2 ))]]) ).

thf(5675,plain,
    ! [B: $i,A: $i] :
      ( ~ ( empty @ sk2 )
      | ( ( union @ B @ A )
        = empty_set )
      | ( ( union @ sk3 @ empty_set )
       != ( union @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[5527,46]) ).

thf(5676,plain,
    ( ~ ( empty @ sk2 )
    | ( ( union @ empty_set @ sk3 )
      = empty_set ) ),
    inference(pattern_uni,[status(thm)],[5675:[bind(A,$thf( sk3 )),bind(B,$thf( empty_set ))]]) ).

thf(58,plain,
    ! [A: $i] :
      ( ( member @ ( sk7 @ A ) @ A )
      | ( empty @ A ) ),
    inference(cnf,[status(esa)],[57]) ).

thf(60,plain,
    ! [A: $i] :
      ( ( member @ ( sk7 @ A ) @ A )
      | ( empty @ A ) ),
    inference(simp,[status(thm)],[58]) ).

thf(280,plain,
    ! [B: $i,A: $i] :
      ( ( empty @ A )
      | ( ( member @ ( sk7 @ A ) @ A )
       != ( member @ B @ empty_set ) ) ),
    inference(paramod_ordered,[status(thm)],[60,32]) ).

thf(281,plain,
    empty @ empty_set,
    inference(pattern_uni,[status(thm)],[280:[bind(A,$thf( empty_set )),bind(B,$thf( sk7 @ empty_set ))]]) ).

thf(15,plain,
    ( ( sk2 != empty_set )
    | ( sk3 != empty_set )
    | ~ sk1 ),
    inference(cnf,[status(esa)],[12]) ).

thf(22,plain,
    ( ( sk2 != empty_set )
    | ( sk3 != empty_set )
    | ~ sk1 ),
    inference(lifteq,[status(thm)],[15]) ).

thf(205,plain,
    ! [B: $i,A: $i] :
      ( ~ ( subset @ A @ B )
      | ~ ( subset @ B @ A )
      | ( sk2 != empty_set )
      | ( B != empty_set )
      | ~ sk1
      | ( A != sk3 ) ),
    inference(paramod_ordered,[status(thm)],[39,22]) ).

thf(206,plain,
    ! [A: $i] :
      ( ~ ( subset @ sk3 @ A )
      | ~ ( subset @ A @ sk3 )
      | ( sk2 != empty_set )
      | ( A != empty_set )
      | ~ sk1 ),
    inference(pattern_uni,[status(thm)],[205:[bind(A,$thf( sk3 ))]]) ).

thf(222,plain,
    ( ~ ( subset @ sk3 @ empty_set )
    | ~ ( subset @ empty_set @ sk3 )
    | ( sk2 != empty_set )
    | ~ sk1 ),
    inference(simp,[status(thm)],[206]) ).

thf(461,plain,
    ( ~ ( subset @ sk3 @ empty_set )
    | ~ $true
    | ( sk2 != empty_set )
    | ~ sk1 ),
    inference(rewrite,[status(thm)],[222,384]) ).

thf(462,plain,
    ( ~ ( subset @ sk3 @ empty_set )
    | ( sk2 != empty_set )
    | ~ sk1 ),
    inference(simp,[status(thm)],[461]) ).

thf(1515,plain,
    ( ~ ( subset @ sk3 @ empty_set )
    | ( sk2 != empty_set )
    | ~ $true ),
    inference(rewrite,[status(thm)],[462,1510]) ).

thf(1516,plain,
    ( ~ ( subset @ sk3 @ empty_set )
    | ( sk2 != empty_set ) ),
    inference(simp,[status(thm)],[1515]) ).

thf(1844,plain,
    ! [B: $i,A: $i] :
      ( ( member @ ( sk6 @ B @ A ) @ A )
      | ( sk2 != empty_set )
      | ( ( subset @ A @ B )
       != ( subset @ sk3 @ empty_set ) ) ),
    inference(paramod_ordered,[status(thm)],[52,1516]) ).

thf(1845,plain,
    ( ( member @ ( sk6 @ empty_set @ sk3 ) @ sk3 )
    | ( sk2 != empty_set ) ),
    inference(pattern_uni,[status(thm)],[1844:[bind(A,$thf( sk3 )),bind(B,$thf( empty_set ))]]) ).

thf(5120,plain,
    ! [B: $i,A: $i] :
      ( ( sk2 != empty_set )
      | ~ ( empty @ A )
      | ( ( member @ ( sk6 @ empty_set @ sk3 ) @ sk3 )
       != ( member @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1845,59]) ).

thf(5121,plain,
    ( ( sk2 != empty_set )
    | ~ ( empty @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[5120:[bind(A,$thf( sk3 )),bind(B,$thf( sk6 @ empty_set @ sk3 ))]]) ).

thf(5213,plain,
    ! [A: $i] :
      ( ~ ( subset @ A @ empty_set )
      | ~ ( empty @ sk3 )
      | ( A != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[466,5121]) ).

thf(5214,plain,
    ( ~ ( subset @ sk2 @ empty_set )
    | ~ ( empty @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[5213:[bind(A,$thf( sk2 ))]]) ).

thf(5283,plain,
    ! [B: $i,A: $i] :
      ( ( member @ ( sk6 @ B @ A ) @ A )
      | ~ ( empty @ sk3 )
      | ( ( subset @ A @ B )
       != ( subset @ sk2 @ empty_set ) ) ),
    inference(paramod_ordered,[status(thm)],[52,5214]) ).

thf(5284,plain,
    ( ( member @ ( sk6 @ empty_set @ sk2 ) @ sk2 )
    | ~ ( empty @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[5283:[bind(A,$thf( sk2 )),bind(B,$thf( empty_set ))]]) ).

thf(7690,plain,
    ! [B: $i,A: $i] :
      ( ~ ( empty @ sk3 )
      | ~ ( empty @ A )
      | ( ( member @ ( sk6 @ empty_set @ sk2 ) @ sk2 )
       != ( member @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5284,59]) ).

thf(7691,plain,
    ( ~ ( empty @ sk3 )
    | ~ ( empty @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[7690:[bind(A,$thf( sk2 )),bind(B,$thf( sk6 @ empty_set @ sk2 ))]]) ).

thf(7843,plain,
    ( ~ ( empty @ sk2 )
    | ( ( empty @ sk3 )
     != ( empty @ sk2 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[7691]) ).

thf(7846,plain,
    ( ~ ( empty @ sk2 )
    | ( ( empty @ sk3 )
     != ( empty @ sk2 ) ) ),
    inference(simp,[status(thm)],[7843]) ).

thf(7889,plain,
    ( ( ( empty @ sk3 )
     != ( empty @ sk2 ) )
    | ( ( empty @ sk2 )
     != ( empty @ empty_set ) ) ),
    inference(paramod_ordered,[status(thm)],[281,7846]) ).

thf(7913,plain,
    ( ( ( empty @ sk3 )
     != ( empty @ sk2 ) )
    | ( sk2 != empty_set ) ),
    inference(simp,[status(thm)],[7889]) ).

thf(7929,plain,
    ( ( sk2 != empty_set )
    | ( empty @ sk3 )
    | ( empty @ sk2 ) ),
    inference(bool_ext,[status(thm)],[7913]) ).

thf(8465,plain,
    ( ( sk2 != empty_set )
    | ( empty @ sk2 )
    | ( ( empty @ sk3 )
     != ( empty @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[7929,5121]) ).

thf(8466,plain,
    ( ( sk2 != empty_set )
    | ( empty @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[8465:[]]) ).

thf(8525,plain,
    ! [A: $i] :
      ( ~ ( subset @ A @ empty_set )
      | ( empty @ sk2 )
      | ( A != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[466,8466]) ).

thf(8526,plain,
    ( ~ ( subset @ sk2 @ empty_set )
    | ( empty @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[8525:[bind(A,$thf( sk2 ))]]) ).

thf(8629,plain,
    ! [B: $i,A: $i] :
      ( ( member @ ( sk6 @ B @ A ) @ A )
      | ( empty @ sk2 )
      | ( ( subset @ A @ B )
       != ( subset @ sk2 @ empty_set ) ) ),
    inference(paramod_ordered,[status(thm)],[52,8526]) ).

thf(8630,plain,
    ( ( member @ ( sk6 @ empty_set @ sk2 ) @ sk2 )
    | ( empty @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[8629:[bind(A,$thf( sk2 )),bind(B,$thf( empty_set ))]]) ).

thf(26,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ C @ B )
      | ( member @ C @ ( union @ A @ B ) ) ),
    inference(cnf,[status(esa)],[24]) ).

thf(29,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ C @ B )
      | ( member @ C @ ( union @ A @ B ) ) ),
    inference(simp,[status(thm)],[26]) ).

thf(8841,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty @ sk2 )
      | ( member @ C @ ( union @ A @ B ) )
      | ( ( member @ ( sk6 @ empty_set @ sk2 ) @ sk2 )
       != ( member @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[8630,29]) ).

thf(8842,plain,
    ! [A: $i] :
      ( ( empty @ sk2 )
      | ( member @ ( sk6 @ empty_set @ sk2 ) @ ( union @ A @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[8841:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk6 @ empty_set @ sk2 ))]]) ).

thf(18478,plain,
    ! [A: $i] :
      ( ( empty @ sk2 )
      | ( member @ ( sk6 @ empty_set @ sk2 ) @ empty_set )
      | ( ( union @ sk3 @ sk2 )
       != ( union @ A @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[1514,8842]) ).

thf(18479,plain,
    ( ( empty @ sk2 )
    | ( member @ ( sk6 @ empty_set @ sk2 ) @ empty_set ) ),
    inference(pattern_uni,[status(thm)],[18478:[bind(A,$thf( sk3 ))]]) ).

thf(18795,plain,
    ( ( empty @ sk2 )
    | $false ),
    inference(rewrite,[status(thm)],[18479,32]) ).

thf(18796,plain,
    empty @ sk2,
    inference(simp,[status(thm)],[18795]) ).

thf(18801,plain,
    ( ~ $true
    | ( ( union @ empty_set @ sk3 )
      = empty_set ) ),
    inference(rewrite,[status(thm)],[5676,18796]) ).

thf(18802,plain,
    ( ( union @ empty_set @ sk3 )
    = empty_set ),
    inference(simp,[status(thm)],[18801]) ).

thf(203,plain,
    ! [B: $i,A: $i] :
      ( ~ ( subset @ A @ B )
      | ~ ( subset @ B @ A )
      | ( B != empty_set )
      | ( sk3 != empty_set )
      | ~ sk1
      | ( A != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[39,22]) ).

thf(204,plain,
    ! [A: $i] :
      ( ~ ( subset @ sk2 @ A )
      | ~ ( subset @ A @ sk2 )
      | ( A != empty_set )
      | ( sk3 != empty_set )
      | ~ sk1 ),
    inference(pattern_uni,[status(thm)],[203:[bind(A,$thf( sk2 ))]]) ).

thf(221,plain,
    ( ~ ( subset @ sk2 @ empty_set )
    | ~ ( subset @ empty_set @ sk2 )
    | ( sk3 != empty_set )
    | ~ sk1 ),
    inference(simp,[status(thm)],[204]) ).

thf(463,plain,
    ( ~ ( subset @ sk2 @ empty_set )
    | ~ $true
    | ( sk3 != empty_set )
    | ~ sk1 ),
    inference(rewrite,[status(thm)],[221,384]) ).

thf(464,plain,
    ( ~ ( subset @ sk2 @ empty_set )
    | ( sk3 != empty_set )
    | ~ sk1 ),
    inference(simp,[status(thm)],[463]) ).

thf(1519,plain,
    ( ~ ( subset @ sk2 @ empty_set )
    | ( sk3 != empty_set )
    | ~ $true ),
    inference(rewrite,[status(thm)],[464,1510]) ).

thf(1520,plain,
    ( ~ ( subset @ sk2 @ empty_set )
    | ( sk3 != empty_set ) ),
    inference(simp,[status(thm)],[1519]) ).

thf(1894,plain,
    ! [B: $i,A: $i] :
      ( ( member @ ( sk6 @ B @ A ) @ A )
      | ( sk3 != empty_set )
      | ( ( subset @ A @ B )
       != ( subset @ sk2 @ empty_set ) ) ),
    inference(paramod_ordered,[status(thm)],[52,1520]) ).

thf(1895,plain,
    ( ( member @ ( sk6 @ empty_set @ sk2 ) @ sk2 )
    | ( sk3 != empty_set ) ),
    inference(pattern_uni,[status(thm)],[1894:[bind(A,$thf( sk2 )),bind(B,$thf( empty_set ))]]) ).

thf(6049,plain,
    ! [B: $i,A: $i] :
      ( ( sk3 != empty_set )
      | ~ ( empty @ A )
      | ( ( member @ ( sk6 @ empty_set @ sk2 ) @ sk2 )
       != ( member @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1895,59]) ).

thf(6050,plain,
    ( ( sk3 != empty_set )
    | ~ ( empty @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[6049:[bind(A,$thf( sk2 )),bind(B,$thf( sk6 @ empty_set @ sk2 ))]]) ).

thf(6142,plain,
    ! [A: $i] :
      ( ~ ( subset @ A @ empty_set )
      | ~ ( empty @ sk2 )
      | ( A != sk3 ) ),
    inference(paramod_ordered,[status(thm)],[466,6050]) ).

thf(6143,plain,
    ( ~ ( subset @ sk3 @ empty_set )
    | ~ ( empty @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[6142:[bind(A,$thf( sk3 ))]]) ).

thf(6212,plain,
    ! [B: $i,A: $i] :
      ( ( member @ ( sk6 @ B @ A ) @ A )
      | ~ ( empty @ sk2 )
      | ( ( subset @ A @ B )
       != ( subset @ sk3 @ empty_set ) ) ),
    inference(paramod_ordered,[status(thm)],[52,6143]) ).

thf(6213,plain,
    ( ( member @ ( sk6 @ empty_set @ sk3 ) @ sk3 )
    | ~ ( empty @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[6212:[bind(A,$thf( sk3 )),bind(B,$thf( empty_set ))]]) ).

thf(18820,plain,
    ( ( member @ ( sk6 @ empty_set @ sk3 ) @ sk3 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[6213,18796]) ).

thf(18821,plain,
    member @ ( sk6 @ empty_set @ sk3 ) @ sk3,
    inference(simp,[status(thm)],[18820]) ).

thf(19605,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( member @ C @ ( union @ A @ B ) )
      | ( ( member @ ( sk6 @ empty_set @ sk3 ) @ sk3 )
       != ( member @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[18821,29]) ).

thf(19606,plain,
    ! [A: $i] : ( member @ ( sk6 @ empty_set @ sk3 ) @ ( union @ A @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[19605:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( sk6 @ empty_set @ sk3 ))]]) ).

thf(20005,plain,
    ! [A: $i] :
      ( ( member @ ( sk6 @ empty_set @ sk3 ) @ empty_set )
      | ( ( union @ empty_set @ sk3 )
       != ( union @ A @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[18802,19606]) ).

thf(20006,plain,
    member @ ( sk6 @ empty_set @ sk3 ) @ empty_set,
    inference(pattern_uni,[status(thm)],[20005:[bind(A,$thf( empty_set ))]]) ).

thf(50,plain,
    ! [B: $i,A: $i] :
      ( ~ ( member @ ( sk6 @ B @ A ) @ B )
      | ( subset @ A @ B ) ),
    inference(cnf,[status(esa)],[48]) ).

thf(53,plain,
    ! [B: $i,A: $i] :
      ( ~ ( member @ ( sk6 @ B @ A ) @ B )
      | ( subset @ A @ B ) ),
    inference(simp,[status(thm)],[50]) ).

thf(8570,plain,
    ! [B: $i,A: $i] :
      ( ( sk2 != empty_set )
      | ~ ( member @ B @ A )
      | ( ( empty @ sk2 )
       != ( empty @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8466,59]) ).

thf(8571,plain,
    ! [A: $i] :
      ( ( sk2 != empty_set )
      | ~ ( member @ A @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[8570:[bind(A,$thf( sk2 ))]]) ).

thf(8617,plain,
    ! [A: $i] :
      ( ( sk2 != empty_set )
      | ~ ( member @ A @ sk2 ) ),
    inference(simp,[status(thm)],[8571]) ).

thf(9216,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( subset @ A @ B )
      | ( sk2 != empty_set )
      | ( ( member @ ( sk6 @ B @ A ) @ A )
       != ( member @ C @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[52,8617]) ).

thf(9217,plain,
    ! [A: $i] :
      ( ( subset @ sk2 @ A )
      | ( sk2 != empty_set ) ),
    inference(pattern_uni,[status(thm)],[9216:[bind(A,$thf( sk2 )),bind(B,$thf( D )),bind(C,$thf( sk6 @ D @ sk2 ))]]) ).

thf(9290,plain,
    ! [A: $i] :
      ( ( subset @ sk2 @ A )
      | ( sk2 != empty_set ) ),
    inference(simp,[status(thm)],[9217]) ).

thf(36,plain,
    ! [B: $i,A: $i] :
      ( ( A != B )
      | ( subset @ A @ B ) ),
    inference(cnf,[status(esa)],[34]) ).

thf(40,plain,
    ! [B: $i,A: $i] :
      ( ( A != B )
      | ( subset @ A @ B ) ),
    inference(lifteq,[status(thm)],[36]) ).

thf(41,plain,
    ! [A: $i] : ( subset @ A @ A ),
    inference(simp,[status(thm)],[40]) ).

thf(650,plain,
    ! [A: $i] :
      ( ~ ( subset @ A @ empty_set )
      | ~ ( subset @ sk3 @ empty_set )
      | ~ sk1
      | ( A != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[466,462]) ).

thf(651,plain,
    ( ~ ( subset @ sk2 @ empty_set )
    | ~ ( subset @ sk3 @ empty_set )
    | ~ sk1 ),
    inference(pattern_uni,[status(thm)],[650:[bind(A,$thf( sk2 ))]]) ).

thf(1289,plain,
    ( ~ ( subset @ sk2 @ empty_set )
    | ~ sk1
    | ( ( subset @ sk3 @ empty_set )
     != ( subset @ sk2 @ empty_set ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[651]) ).

thf(1292,plain,
    ( ~ ( subset @ sk2 @ empty_set )
    | ~ sk1
    | ( sk3 != sk2 )
    | ( empty_set != empty_set ) ),
    inference(simp,[status(thm)],[1289]) ).

thf(1297,plain,
    ( ~ ( subset @ sk2 @ empty_set )
    | ~ sk1
    | ( sk3 != sk2 ) ),
    inference(simp,[status(thm)],[1292]) ).

thf(1328,plain,
    ! [A: $i] :
      ( ~ sk1
      | ( sk3 != sk2 )
      | ( ( subset @ A @ A )
       != ( subset @ sk2 @ empty_set ) ) ),
    inference(paramod_ordered,[status(thm)],[41,1297]) ).

thf(1329,plain,
    ! [A: $i] :
      ( ~ sk1
      | ( sk3 != sk2 )
      | ( A != sk2 )
      | ( A != empty_set ) ),
    inference(simp,[status(thm)],[1328]) ).

thf(1335,plain,
    ( ~ sk1
    | ( sk3 != sk2 )
    | ( sk2 != empty_set ) ),
    inference(simp,[status(thm)],[1329]) ).

thf(1517,plain,
    ( ~ $true
    | ( sk3 != sk2 )
    | ( sk2 != empty_set ) ),
    inference(rewrite,[status(thm)],[1335,1510]) ).

thf(1518,plain,
    ( ( sk3 != sk2 )
    | ( sk2 != empty_set ) ),
    inference(simp,[status(thm)],[1517]) ).

thf(1609,plain,
    ! [B: $i,A: $i] :
      ( ~ ( subset @ A @ B )
      | ~ ( subset @ B @ A )
      | ( B != sk2 )
      | ( sk2 != empty_set )
      | ( A != sk3 ) ),
    inference(paramod_ordered,[status(thm)],[39,1518]) ).

thf(1610,plain,
    ! [A: $i] :
      ( ~ ( subset @ sk3 @ A )
      | ~ ( subset @ A @ sk3 )
      | ( A != sk2 )
      | ( sk2 != empty_set ) ),
    inference(pattern_uni,[status(thm)],[1609:[bind(A,$thf( sk3 ))]]) ).

thf(1618,plain,
    ( ~ ( subset @ sk3 @ sk2 )
    | ~ ( subset @ sk2 @ sk3 )
    | ( sk2 != empty_set ) ),
    inference(simp,[status(thm)],[1610]) ).

thf(12075,plain,
    ! [A: $i] :
      ( ( sk2 != empty_set )
      | ~ ( subset @ sk3 @ sk2 )
      | ( ( subset @ sk2 @ A )
       != ( subset @ sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[9290,1618]) ).

thf(12076,plain,
    ( ( sk2 != empty_set )
    | ~ ( subset @ sk3 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[12075:[bind(A,$thf( sk3 ))]]) ).

thf(12235,plain,
    ! [A: $i] :
      ( ~ ( subset @ A @ empty_set )
      | ~ ( subset @ sk3 @ sk2 )
      | ( A != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[466,12076]) ).

thf(12236,plain,
    ( ~ ( subset @ sk2 @ empty_set )
    | ~ ( subset @ sk3 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[12235:[bind(A,$thf( sk2 ))]]) ).

thf(12304,plain,
    ! [B: $i,A: $i] :
      ( ( member @ ( sk6 @ B @ A ) @ A )
      | ~ ( subset @ sk3 @ sk2 )
      | ( ( subset @ A @ B )
       != ( subset @ sk2 @ empty_set ) ) ),
    inference(paramod_ordered,[status(thm)],[52,12236]) ).

thf(12305,plain,
    ( ( member @ ( sk6 @ empty_set @ sk2 ) @ sk2 )
    | ~ ( subset @ sk3 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[12304:[bind(A,$thf( sk2 )),bind(B,$thf( empty_set ))]]) ).

thf(12964,plain,
    ! [B: $i,A: $i] :
      ( ~ ( subset @ sk3 @ sk2 )
      | ~ ( empty @ A )
      | ( ( member @ ( sk6 @ empty_set @ sk2 ) @ sk2 )
       != ( member @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[12305,59]) ).

thf(12965,plain,
    ( ~ ( subset @ sk3 @ sk2 )
    | ~ ( empty @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[12964:[bind(A,$thf( sk2 )),bind(B,$thf( sk6 @ empty_set @ sk2 ))]]) ).

thf(13156,plain,
    ! [B: $i,A: $i] :
      ( ~ ( member @ ( sk6 @ B @ A ) @ B )
      | ~ ( empty @ sk2 )
      | ( ( subset @ A @ B )
       != ( subset @ sk3 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[53,12965]) ).

thf(13157,plain,
    ( ~ ( member @ ( sk6 @ sk2 @ sk3 ) @ sk2 )
    | ~ ( empty @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[13156:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 ))]]) ).

thf(18811,plain,
    ( ~ ( member @ ( sk6 @ sk2 @ sk3 ) @ sk2 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[13157,18796]) ).

thf(18812,plain,
    ~ ( member @ ( sk6 @ sk2 @ sk3 ) @ sk2 ),
    inference(simp,[status(thm)],[18811]) ).

thf(9621,plain,
    ! [B: $i,A: $i] :
      ( ~ ( subset @ A @ empty_set )
      | ( subset @ sk2 @ B )
      | ( A != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[466,9290]) ).

thf(9622,plain,
    ! [A: $i] :
      ( ~ ( subset @ sk2 @ empty_set )
      | ( subset @ sk2 @ A ) ),
    inference(pattern_uni,[status(thm)],[9621:[bind(A,$thf( sk2 ))]]) ).

thf(9681,plain,
    ! [A: $i] :
      ( ~ ( subset @ sk2 @ empty_set )
      | ( subset @ sk2 @ A ) ),
    inference(simp,[status(thm)],[9622]) ).

thf(10377,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( member @ ( sk6 @ B @ A ) @ A )
      | ( subset @ sk2 @ C )
      | ( ( subset @ A @ B )
       != ( subset @ sk2 @ empty_set ) ) ),
    inference(paramod_ordered,[status(thm)],[52,9681]) ).

thf(10378,plain,
    ! [A: $i] :
      ( ( member @ ( sk6 @ empty_set @ sk2 ) @ sk2 )
      | ( subset @ sk2 @ A ) ),
    inference(pattern_uni,[status(thm)],[10377:[bind(A,$thf( sk2 )),bind(B,$thf( empty_set ))]]) ).

thf(10517,plain,
    ! [A: $i] :
      ( ( member @ ( sk6 @ empty_set @ sk2 ) @ sk2 )
      | ( subset @ sk2 @ A ) ),
    inference(simp,[status(thm)],[10378]) ).

thf(15314,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( subset @ sk2 @ A )
      | ~ ( empty @ B )
      | ( ( member @ ( sk6 @ empty_set @ sk2 ) @ sk2 )
       != ( member @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[10517,59]) ).

thf(15315,plain,
    ! [A: $i] :
      ( ( subset @ sk2 @ A )
      | ~ ( empty @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[15314:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk6 @ empty_set @ sk2 ))]]) ).

thf(15625,plain,
    ! [B: $i,A: $i] :
      ( ~ ( empty @ sk2 )
      | ( empty_set = B )
      | ( ( subset @ sk2 @ A )
       != ( subset @ B @ empty_set ) ) ),
    inference(paramod_ordered,[status(thm)],[15315,466]) ).

thf(15626,plain,
    ( ~ ( empty @ sk2 )
    | ( sk2 = empty_set ) ),
    inference(pattern_uni,[status(thm)],[15625:[bind(A,$thf( empty_set )),bind(B,$thf( sk2 ))]]) ).

thf(18816,plain,
    ( ~ $true
    | ( sk2 = empty_set ) ),
    inference(rewrite,[status(thm)],[15626,18796]) ).

thf(18817,plain,
    sk2 = empty_set,
    inference(simp,[status(thm)],[18816]) ).

thf(19154,plain,
    ~ ( member @ ( sk6 @ empty_set @ sk3 ) @ empty_set ),
    inference(rewrite,[status(thm)],[18812,18817]) ).

thf(20175,plain,
    $false,
    inference(rewrite,[status(thm)],[20006,19154]) ).

thf(20176,plain,
    $false,
    inference(simp,[status(thm)],[20175]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12  % Problem  : SET600+3 : TPTP v8.2.0. Released v2.2.0.
% 0.09/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n017.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon May 20 11:31:39 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.91/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.24/1.01  % [INFO] 	 Parsing done (117ms). 
% 1.24/1.02  % [INFO] 	 Running in sequential loop mode. 
% 1.68/1.25  % [INFO] 	 nitpick registered as external prover. 
% 1.68/1.26  % [INFO] 	 Scanning for conjecture ... 
% 1.88/1.34  % [INFO] 	 Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ... 
% 1.93/1.36  % [INFO] 	 Axiom selection finished. Selected 8 axioms (removed 0 axioms). 
% 1.93/1.38  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.93/1.39  % [INFO] 	 Type checking passed. 
% 1.93/1.39  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 68.50/10.72  % [INFO] 	 Killing All external provers ... 
% 68.50/10.72  % Time passed: 10213ms (effective reasoning time: 9699ms)
% 68.50/10.72  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 68.50/10.73  % Axioms used in derivation (6): empty_set_defn, empty_defn, commutativity_of_union, equal_defn, union_defn, subset_defn
% 68.50/10.73  % No. of inferences in proof: 185
% 68.50/10.73  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 10213 ms resp. 9699 ms w/o parsing
% 68.50/10.78  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 68.50/10.79  % [INFO] 	 Killing All external provers ... 
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