Leo-III---1.8.0.THM-Ref.s

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SEU136+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 08:37:42 AM UTC 2026

% Result   : Theorem 179.05s 50.75s
% Output   : Refutation 180.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   53
%            Number of leaves      :   29
% Syntax   : Number of formulae    : 1284 ( 431 unt;   0 typ;   9 def)
%            Number of atoms       : 3522 (1286 equ;   0 cnn)
%            Maximal formula atoms :   26 (   2 avg)
%            Number of connectives : 13523 (2033   ~;1450   |;  59   &;9923   @)
%                                         (   6 <=>;  52  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  17 usr;   7 con; 0-3 aty)
%            Number of variables   : 3614 (  14   ^;3581   !;  10   ?;3614   :)
%                                         (   0  !>;   0  ?*;   0  @-;   9  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(set_difference_decl,type,
    set_difference: $i > $i > $i ).

thf(set_union2_decl,type,
    set_union2: $i > $i > $i ).

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

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

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

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

thf(sk1_decl,type,
    sk1: $i ).

thf(sk2_decl,type,
    sk2: $i ).

thf(sk3_decl,type,
    sk3: $i ).

thf(sk4_decl,type,
    sk4: $i ).

thf(sk5_decl,type,
    sk5: $i > $i > $i ).

thf(sk6_decl,type,
    sk6: $i > $i > $i > $o ).

thf(sk7_decl,type,
    sk7: $i > $i > $i > $i ).

thf(sk8_decl,type,
    sk8: $i > $i > $i > $i ).

thf(sk9_decl,type,
    sk9: $i > $i > $i > $o ).

thf(sk10_decl,type,
    sk10: $i > $i > $i > $i ).

thf(sk11_decl,type,
    sk11: $i > $i > $i > $i ).

thf(sk1_def,definition,
    ( sk1
    = ( @+[A: $i] :
          ~ ! [B: $i] :
              ( ( B @ ( B @ ( A @ set_union2 ) @ set_difference ) )
              = ( B @ ( A @ set_difference ) ) ) ) ) ).

thf(sk2_def,definition,
    ( sk2
    = ( @+[A: $i] :
          ( ( A @ ( A @ ( sk1 @ set_union2 ) @ set_difference ) )
         != ( A @ ( sk1 @ set_difference ) ) ) ) ) ).

thf(sk3_def,definition,
    ( sk3
    = ( @+[A: $i] : ( A @ empty ) ) ) ).

thf(sk4_def,definition,
    ( sk4
    = ( @+[A: $i] :
          ~ ( A @ empty ) ) ) ).

thf(sk5_def,definition,
    ( sk5
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ~ ( ( B @ ( C @ in ) )
           => ( A @ ( C @ in ) ) ) ) ) ).

thf(sk7_def,definition,
    ( sk7
    = ( ^ [A: $i,B: $i,C: $i] :
        @+[D: $i] :
          ~ ( ( A @ ( D @ in ) )
           => ( ( B @ ( D @ in ) )
              | ( C @ ( D @ in ) ) ) ) ) ) ).

thf(sk8_def,definition,
    ( sk8
    = ( ^ [A: $i,B: $i,C: $i] :
        @+[D: $i] :
          ~ ( ( ( B @ ( D @ in ) )
              | ( C @ ( D @ in ) ) )
           => ( A @ ( D @ in ) ) ) ) ) ).

thf(sk10_def,definition,
    ( sk10
    = ( ^ [A: $i,B: $i,C: $i] :
        @+[D: $i] :
          ~ ( ( A @ ( D @ in ) )
           => ( ~ ( B @ ( D @ in ) )
              & ( C @ ( D @ in ) ) ) ) ) ) ).

thf(sk11_def,definition,
    ( sk11
    = ( ^ [A: $i,B: $i,C: $i] :
        @+[D: $i] :
          ~ ( ( ~ ( B @ ( D @ in ) )
              & ( C @ ( D @ in ) ) )
           => ( A @ ( D @ in ) ) ) ) ) ).

thf(20,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( B @ ( A @ set_difference ) ) )
    <=> ! [D: $i] :
          ( ( C @ ( D @ in ) )
        <=> ( ~ ( B @ ( D @ in ) )
            & ( A @ ( D @ in ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).

thf(110,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ! [D: $i] :
            ( ( ( ~ ( B @ ( D @ in ) )
                & ( A @ ( D @ in ) ) )
             => ( C @ ( D @ in ) ) )
            & ( ( C @ ( D @ in ) )
             => ( ~ ( B @ ( D @ in ) )
                & ( A @ ( D @ in ) ) ) ) )
       => ( C
          = ( B @ ( A @ set_difference ) ) ) )
      & ( ( C
          = ( B @ ( A @ set_difference ) ) )
       => ! [D: $i] :
            ( ( ( ~ ( B @ ( D @ in ) )
                & ( A @ ( D @ in ) ) )
             => ( C @ ( D @ in ) ) )
            & ( ( C @ ( D @ in ) )
             => ( ~ ( B @ ( D @ in ) )
                & ( A @ ( D @ in ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(111,plain,
    ( ! [A: $i,B: $i,C: $i] :
        ( ( ! [D: $i] :
              ( ( ~ ( B @ ( D @ in ) )
                & ( A @ ( D @ in ) ) )
             => ( C @ ( D @ in ) ) )
          & ! [D: $i] :
              ( ( C @ ( D @ in ) )
             => ( ~ ( B @ ( D @ in ) )
                & ( A @ ( D @ in ) ) ) ) )
       => ( C
          = ( B @ ( A @ set_difference ) ) ) )
    & ! [A: $i,B: $i,C: $i] :
        ( ( C
          = ( B @ ( A @ set_difference ) ) )
       => ( ! [D: $i] :
              ( ( ~ ( B @ ( D @ in ) )
                & ( A @ ( D @ in ) ) )
             => ( C @ ( D @ in ) ) )
          & ! [D: $i] :
              ( ( C @ ( D @ in ) )
             => ( ~ ( B @ ( D @ in ) )
                & ( A @ ( D @ in ) ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[110]) ).

thf(112,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( H
          = ( G @ ( F @ set_difference ) ) )
        | ~ ( H @ ( F @ ( G @ ( H @ sk11 ) ) @ in ) )
        | ( H @ ( G @ ( F @ sk9 ) ) ) )
      & ( ( H
          = ( G @ ( F @ set_difference ) ) )
        | ~ ( G @ ( F @ ( G @ ( H @ sk11 ) ) @ in ) )
        | ( H @ ( G @ ( F @ sk9 ) ) ) )
      & ( ( H
          = ( G @ ( F @ set_difference ) ) )
        | ( F @ ( F @ ( G @ ( H @ sk11 ) ) @ in ) )
        | ( H @ ( G @ ( F @ sk9 ) ) ) )
      & ( ( H
          = ( G @ ( F @ set_difference ) ) )
        | ~ ( H @ ( G @ ( F @ sk9 ) ) )
        | ( G @ ( F @ ( G @ ( H @ sk10 ) ) @ in ) )
        | ~ ( F @ ( F @ ( G @ ( H @ sk10 ) ) @ in ) ) )
      & ( ( H
          = ( G @ ( F @ set_difference ) ) )
        | ~ ( H @ ( G @ ( F @ sk9 ) ) )
        | ( H @ ( F @ ( G @ ( H @ sk10 ) ) @ in ) ) )
      & ( ( C @ ( E @ in ) )
        | ( B @ ( E @ in ) )
        | ~ ( A @ ( E @ in ) )
        | ( C
         != ( B @ ( A @ set_difference ) ) ) )
      & ( ~ ( B @ ( D @ in ) )
        | ~ ( C @ ( D @ in ) )
        | ( C
         != ( B @ ( A @ set_difference ) ) ) )
      & ( ( A @ ( D @ in ) )
        | ~ ( C @ ( D @ in ) )
        | ( C
         != ( B @ ( A @ set_difference ) ) ) ) ),
    inference(cnf,[status(esa)],[111]) ).

thf(119,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( A @ set_difference ) ) )
      | ( A @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
      | ( C @ ( B @ ( A @ sk9 ) ) ) ),
    inference(cnfConj,[status(thm)],[112]) ).

thf(131,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
      | ( C @ ( B @ ( A @ sk9 ) ) )
      | ( C
        = ( B @ ( A @ set_difference ) ) ) ),
    inference(lifteq,[status(thm)],[119]) ).

thf(132,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
      | ( C @ ( B @ ( A @ sk9 ) ) )
      | ( C
        = ( B @ ( A @ set_difference ) ) ) ),
    inference(simp,[status(thm)],[131]) ).

thf(8,axiom,
    empty_set @ empty,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).

thf(48,plain,
    empty_set @ empty,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(11,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( B @ empty )
        & ( B @ ( A @ in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

thf(60,plain,
    ! [A: $i,B: $i] :
      ~ ( ( B @ empty )
        & ( B @ ( A @ in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(61,plain,
    ~ ? [A: $i,B: $i] :
        ( ( B @ empty )
        & ( B @ ( A @ in ) ) ),
    inference(miniscope,[status(thm)],[60]) ).

thf(62,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ empty )
      | ~ ( B @ ( A @ in ) ) ),
    inference(cnf,[status(esa)],[61]) ).

thf(1483,plain,
    ! [B: $i,A: $i] :
      ( ( ( empty_set @ empty )
       != ( B @ empty ) )
      | ~ $true
      | ~ ( B @ ( A @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[48,62]) ).

thf(1484,plain,
    ! [B: $i,A: $i] :
      ( ( ( empty_set @ empty )
       != ( B @ empty ) )
      | ~ ( B @ ( A @ in ) ) ),
    inference(simp,[status(thm)],[1483]) ).

thf(1485,plain,
    ! [A: $i] :
      ~ ( empty_set @ ( A @ in ) ),
    inference(pattern_uni,[status(thm)],[1484:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).

thf(1510,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
       != ( empty_set @ ( D @ in ) ) )
      | ~ $true
      | ( C @ ( B @ ( A @ sk9 ) ) )
      | ( C
        = ( B @ ( A @ set_difference ) ) ) ),
    inference(paramod_ordered,[status(thm)],[132,1485]) ).

thf(1511,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
       != ( empty_set @ ( D @ in ) ) )
      | ( C @ ( B @ ( A @ sk9 ) ) )
      | ( C
        = ( B @ ( A @ set_difference ) ) ) ),
    inference(simp,[status(thm)],[1510]) ).

thf(1512,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( empty_set @ sk9 ) ) )
      | ( A
        = ( B @ ( empty_set @ set_difference ) ) ) ),
    inference(pattern_uni,[status(thm)],[1511:[bind(A,$thf( empty_set )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( empty_set @ ( F @ ( E @ sk11 ) ) ))]]) ).

thf(1522,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( empty_set @ sk9 ) ) )
      | ( A
        = ( B @ ( empty_set @ set_difference ) ) ) ),
    inference(simp,[status(thm)],[1512]) ).

thf(15,axiom,
    ! [A: $i] :
      ( ( A @ ( empty_set @ set_difference ) )
      = empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).

thf(95,plain,
    ! [A: $i] :
      ( ( A @ ( empty_set @ set_difference ) )
      = empty_set ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(96,plain,
    ! [A: $i] :
      ( ( A @ ( empty_set @ set_difference ) )
      = empty_set ),
    inference(cnf,[status(esa)],[95]) ).

thf(97,plain,
    ! [A: $i] :
      ( ( A @ ( empty_set @ set_difference ) )
      = empty_set ),
    inference(lifteq,[status(thm)],[96]) ).

thf(1599,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( empty_set @ sk9 ) ) )
      | ( A = empty_set ) ),
    inference(rewrite,[status(thm)],[1522,97]) ).

thf(17,axiom,
    ! [A: $i] :
      ( ( empty_set @ ( A @ set_union2 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).

thf(101,plain,
    ! [A: $i] :
      ( ( empty_set @ ( A @ set_union2 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(102,plain,
    ! [A: $i] :
      ( ( empty_set @ ( A @ set_union2 ) )
      = A ),
    inference(cnf,[status(esa)],[101]) ).

thf(103,plain,
    ! [A: $i] :
      ( ( empty_set @ ( A @ set_union2 ) )
      = A ),
    inference(lifteq,[status(thm)],[102]) ).

thf(1,conjecture,
    ! [A: $i,B: $i] :
      ( ( B @ ( B @ ( A @ set_union2 ) @ set_difference ) )
      = ( B @ ( A @ set_difference ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i] :
        ( ( B @ ( B @ ( A @ set_union2 ) @ set_difference ) )
        = ( B @ ( A @ set_difference ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(22,plain,
    ~ ! [A: $i,B: $i] :
        ( ( B @ ( B @ ( A @ set_union2 ) @ set_difference ) )
        = ( B @ ( A @ set_difference ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(23,plain,
    ( ( sk2 @ ( sk2 @ ( sk1 @ set_union2 ) @ set_difference ) )
   != ( sk2 @ ( sk1 @ set_difference ) ) ),
    inference(cnf,[status(esa)],[22]) ).

thf(24,plain,
    ( ( sk2 @ ( sk2 @ ( sk1 @ set_union2 ) @ set_difference ) )
   != ( sk2 @ ( sk1 @ set_difference ) ) ),
    inference(lifteq,[status(thm)],[23]) ).

thf(155,plain,
    ! [A: $i] :
      ( ( ( empty_set @ ( A @ set_union2 ) )
       != ( sk2 @ ( sk1 @ set_union2 ) ) )
      | ( ( sk2 @ ( A @ set_difference ) )
       != ( sk2 @ ( sk1 @ set_difference ) ) ) ),
    inference(paramod_ordered,[status(thm)],[103,24]) ).

thf(160,plain,
    ! [A: $i] :
      ( ( sk2 != empty_set )
      | ( A != sk1 )
      | ( sk2 != sk2 )
      | ( A != sk1 ) ),
    inference(simp,[status(thm)],[155]) ).

thf(165,plain,
    sk2 != empty_set,
    inference(simp,[status(thm)],[160]) ).

thf(1600,plain,
    ! [B: $i,A: $i] :
      ( ( A != sk2 )
      | ( empty_set != empty_set )
      | ( A @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1599,165]) ).

thf(1601,plain,
    ! [B: $i,A: $i] :
      ( ( A != sk2 )
      | ( A @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[1600]) ).

thf(1602,plain,
    ! [A: $i] : ( sk2 @ ( A @ ( empty_set @ sk9 ) ) ),
    inference(pattern_uni,[status(thm)],[1601:[bind(A,$thf( sk2 ))]]) ).

thf(1809,plain,
    ! [A: $i] : ( sk2 @ ( A @ ( empty_set @ sk9 ) ) ),
    inference(simp,[status(thm)],[1602]) ).

thf(115,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( A @ set_difference ) ) )
      | ~ ( C @ ( B @ ( A @ sk9 ) ) )
      | ( C @ ( A @ ( B @ ( C @ sk10 ) ) @ in ) ) ),
    inference(cnfConj,[status(thm)],[112]) ).

thf(133,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ sk9 ) ) )
      | ( C @ ( A @ ( B @ ( C @ sk10 ) ) @ in ) )
      | ( C
        = ( B @ ( A @ set_difference ) ) ) ),
    inference(lifteq,[status(thm)],[115]) ).

thf(134,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ sk9 ) ) )
      | ( C @ ( A @ ( B @ ( C @ sk10 ) ) @ in ) )
      | ( C
        = ( B @ ( A @ set_difference ) ) ) ),
    inference(simp,[status(thm)],[133]) ).

thf(11661,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ ( empty_set @ sk9 ) ) )
       != ( D @ ( C @ ( B @ sk9 ) ) ) )
      | ~ $true
      | ( D @ ( B @ ( C @ ( D @ sk10 ) ) @ in ) )
      | ( D
        = ( C @ ( B @ set_difference ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1809,134]) ).

thf(11662,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ ( empty_set @ sk9 ) ) )
       != ( D @ ( C @ ( B @ sk9 ) ) ) )
      | ( D @ ( B @ ( C @ ( D @ sk10 ) ) @ in ) )
      | ( D
        = ( C @ ( B @ set_difference ) ) ) ),
    inference(simp,[status(thm)],[11661]) ).

thf(11663,plain,
    ! [A: $i] :
      ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
      | ( ( A @ ( empty_set @ set_difference ) )
        = sk2 ) ),
    inference(pattern_uni,[status(thm)],[11662:[bind(A,$thf( A )),bind(B,$thf( empty_set )),bind(C,$thf( A )),bind(D,$thf( sk2 ))]]) ).

thf(13697,plain,
    ! [A: $i] :
      ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
      | ( sk2 = empty_set ) ),
    inference(rewrite,[status(thm)],[11663,97]) ).

thf(13698,plain,
    ! [A: $i] : ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) ),
    inference(simplifyReflect,[status(thm)],[13697,165]) ).

thf(21,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ set_union2 ) )
      = ( A @ ( B @ set_union2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

thf(137,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ set_union2 ) )
      = ( A @ ( B @ set_union2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(138,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ set_union2 ) )
      = ( A @ ( B @ set_union2 ) ) ),
    inference(cnf,[status(esa)],[137]) ).

thf(139,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ set_union2 ) )
      = ( A @ ( B @ set_union2 ) ) ),
    inference(lifteq,[status(thm)],[138]) ).

thf(14,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( B @ ( A @ set_union2 ) ) )
    <=> ! [D: $i] :
          ( ( C @ ( D @ in ) )
        <=> ( ( B @ ( D @ in ) )
            | ( A @ ( D @ in ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).

thf(68,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ! [D: $i] :
            ( ( ( ( B @ ( D @ in ) )
                | ( A @ ( D @ in ) ) )
             => ( C @ ( D @ in ) ) )
            & ( ( C @ ( D @ in ) )
             => ( ( B @ ( D @ in ) )
                | ( A @ ( D @ in ) ) ) ) )
       => ( C
          = ( B @ ( A @ set_union2 ) ) ) )
      & ( ( C
          = ( B @ ( A @ set_union2 ) ) )
       => ! [D: $i] :
            ( ( ( ( B @ ( D @ in ) )
                | ( A @ ( D @ in ) ) )
             => ( C @ ( D @ in ) ) )
            & ( ( C @ ( D @ in ) )
             => ( ( B @ ( D @ in ) )
                | ( A @ ( D @ in ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(69,plain,
    ( ! [A: $i,B: $i,C: $i] :
        ( ( ! [D: $i] :
              ( ( ( B @ ( D @ in ) )
                | ( A @ ( D @ in ) ) )
             => ( C @ ( D @ in ) ) )
          & ! [D: $i] :
              ( ( C @ ( D @ in ) )
             => ( ( B @ ( D @ in ) )
                | ( A @ ( D @ in ) ) ) ) )
       => ( C
          = ( B @ ( A @ set_union2 ) ) ) )
    & ! [A: $i,B: $i,C: $i] :
        ( ( C
          = ( B @ ( A @ set_union2 ) ) )
       => ( ! [D: $i] :
              ( ( ( B @ ( D @ in ) )
                | ( A @ ( D @ in ) ) )
             => ( C @ ( D @ in ) ) )
          & ! [D: $i] :
              ( ( C @ ( D @ in ) )
             => ( ( B @ ( D @ in ) )
                | ( A @ ( D @ in ) ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[68]) ).

thf(70,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( H
          = ( G @ ( F @ set_union2 ) ) )
        | ~ ( H @ ( F @ ( G @ ( H @ sk8 ) ) @ in ) )
        | ( H @ ( G @ ( F @ sk6 ) ) ) )
      & ( ( H
          = ( G @ ( F @ set_union2 ) ) )
        | ( G @ ( F @ ( G @ ( H @ sk8 ) ) @ in ) )
        | ( F @ ( F @ ( G @ ( H @ sk8 ) ) @ in ) )
        | ( H @ ( G @ ( F @ sk6 ) ) ) )
      & ( ( H
          = ( G @ ( F @ set_union2 ) ) )
        | ~ ( H @ ( G @ ( F @ sk6 ) ) )
        | ~ ( G @ ( F @ ( G @ ( H @ sk7 ) ) @ in ) ) )
      & ( ( H
          = ( G @ ( F @ set_union2 ) ) )
        | ~ ( H @ ( G @ ( F @ sk6 ) ) )
        | ~ ( F @ ( F @ ( G @ ( H @ sk7 ) ) @ in ) ) )
      & ( ( H
          = ( G @ ( F @ set_union2 ) ) )
        | ~ ( H @ ( G @ ( F @ sk6 ) ) )
        | ( H @ ( F @ ( G @ ( H @ sk7 ) ) @ in ) ) )
      & ( ( C @ ( E @ in ) )
        | ~ ( B @ ( E @ in ) )
        | ( C
         != ( B @ ( A @ set_union2 ) ) ) )
      & ( ( C @ ( E @ in ) )
        | ~ ( A @ ( E @ in ) )
        | ( C
         != ( B @ ( A @ set_union2 ) ) ) )
      & ( ( B @ ( D @ in ) )
        | ( A @ ( D @ in ) )
        | ~ ( C @ ( D @ in ) )
        | ( C
         != ( B @ ( A @ set_union2 ) ) ) ) ),
    inference(cnf,[status(esa)],[69]) ).

thf(74,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ in ) )
      | ~ ( B @ ( D @ in ) )
      | ( C
       != ( B @ ( A @ set_union2 ) ) ) ),
    inference(cnfConj,[status(thm)],[70]) ).

thf(81,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ in ) )
      | ~ ( B @ ( D @ in ) )
      | ( C
       != ( B @ ( A @ set_union2 ) ) ) ),
    inference(lifteq,[status(thm)],[74]) ).

thf(82,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
      | ~ ( B @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[81]) ).

thf(78,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ in ) )
      | ~ ( A @ ( D @ in ) )
      | ( C
       != ( B @ ( A @ set_union2 ) ) ) ),
    inference(cnfConj,[status(thm)],[70]) ).

thf(79,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ in ) )
      | ~ ( A @ ( D @ in ) )
      | ( C
       != ( B @ ( A @ set_union2 ) ) ) ),
    inference(lifteq,[status(thm)],[78]) ).

thf(80,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
      | ~ ( A @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[79]) ).

thf(12,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ in ) )
     => ~ ( A @ ( B @ in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(63,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ in ) )
     => ~ ( A @ ( B @ in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(64,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ in ) )
      | ~ ( B @ ( A @ in ) ) ),
    inference(cnf,[status(esa)],[63]) ).

thf(1880,plain,
    ! [B: $i,A: $i] :
      ( ~ $true
      | ( ( A @ ( B @ in ) )
       != ( B @ ( A @ in ) ) )
      | ~ ( B @ ( A @ in ) ) ),
    inference(eqfactor_ordered,[status(thm)],[64]) ).

thf(1881,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ in ) ),
    inference(pattern_uni,[status(thm)],[1880:[bind(A,$thf( B ))]]) ).

thf(1884,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ in ) ),
    inference(simp,[status(thm)],[1881]) ).

thf(2157,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( D @ ( D @ in ) ) )
      | ~ $true
      | ~ ( A @ ( C @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[80,1884]) ).

thf(2158,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( D @ ( D @ in ) ) )
      | ~ ( A @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[2157]) ).

thf(2159,plain,
    ! [B: $i,A: $i] :
      ~ ( A @ ( B @ ( A @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[2158:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ set_union2 ) )),bind(D,$thf( F @ ( E @ set_union2 ) ))]]) ).

thf(2192,plain,
    ! [B: $i,A: $i] :
      ~ ( A @ ( B @ ( A @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[2159]) ).

thf(2466,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( D @ ( E @ ( D @ set_union2 ) @ in ) ) )
      | ~ $true
      | ~ ( B @ ( C @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[82,2192]) ).

thf(2467,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( D @ ( E @ ( D @ set_union2 ) @ in ) ) )
      | ~ ( B @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[2466]) ).

thf(2468,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( C @ ( A @ ( C @ ( B @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[2467:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( G @ ( I @ ( H @ set_union2 ) @ set_union2 ) )),bind(D,$thf( I @ ( H @ set_union2 ) )),bind(E,$thf( G ))]]) ).

thf(2504,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( C @ ( A @ ( C @ ( B @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[2468]) ).

thf(3740,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( E @ ( D @ set_union2 ) ) )
      | ~ ( E @ ( C @ ( A @ ( B @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[139,2504]) ).

thf(3741,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ ( C @ ( A @ ( B @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[3740:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).

thf(13806,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( C @ ( D @ ( B @ ( C @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13698,3741]) ).

thf(13807,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
     != ( C @ ( D @ ( B @ ( C @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[13806]) ).

thf(13952,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 != C )
      | ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
       != ( D @ ( B @ ( C @ set_union2 ) @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[13807]) ).

thf(13955,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
     != ( C @ ( B @ ( sk2 @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[13952]) ).

thf(9,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ subset ) )
    <=> ! [C: $i] :
          ( ( A @ ( C @ in ) )
         => ( B @ ( C @ in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

thf(49,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i] :
            ( ( A @ ( C @ in ) )
           => ( B @ ( C @ in ) ) )
       => ( B @ ( A @ subset ) ) )
      & ( ( B @ ( A @ subset ) )
       => ! [C: $i] :
            ( ( A @ ( C @ in ) )
           => ( B @ ( C @ in ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(50,plain,
    ( ! [A: $i,B: $i] :
        ( ! [C: $i] :
            ( ( A @ ( C @ in ) )
           => ( B @ ( C @ in ) ) )
       => ( B @ ( A @ subset ) ) )
    & ! [A: $i,B: $i] :
        ( ( B @ ( A @ subset ) )
       => ! [C: $i] :
            ( ( A @ ( C @ in ) )
           => ( B @ ( C @ in ) ) ) ) ),
    inference(miniscope,[status(thm)],[49]) ).

thf(51,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ subset ) )
        | ~ ( E @ ( D @ ( E @ sk5 ) @ in ) ) )
      & ( ( E @ ( D @ subset ) )
        | ( D @ ( D @ ( E @ sk5 ) @ in ) ) )
      & ( ( B @ ( C @ in ) )
        | ~ ( A @ ( C @ in ) )
        | ~ ( B @ ( A @ subset ) ) ) ),
    inference(cnf,[status(esa)],[50]) ).

thf(53,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ subset ) )
      | ( A @ ( A @ ( B @ sk5 ) @ in ) ) ),
    inference(cnfConj,[status(thm)],[51]) ).

thf(55,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ subset ) )
      | ( A @ ( A @ ( B @ sk5 ) @ in ) ) ),
    inference(simp,[status(thm)],[53]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
    <=> ( ( A @ ( B @ subset ) )
        & ( B @ ( A @ subset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).

thf(25,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A @ ( B @ subset ) )
          & ( B @ ( A @ subset ) ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( A @ ( B @ subset ) )
          & ( B @ ( A @ subset ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(26,plain,
    ( ! [A: $i,B: $i] :
        ( ( ( A @ ( B @ subset ) )
          & ( B @ ( A @ subset ) ) )
       => ( A = B ) )
    & ! [A: $i,B: $i] :
        ( ( A = B )
       => ( ( A @ ( B @ subset ) )
          & ( B @ ( A @ subset ) ) ) ) ),
    inference(miniscope,[status(thm)],[25]) ).

thf(27,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C = D )
        | ~ ( C @ ( D @ subset ) )
        | ~ ( D @ ( C @ subset ) ) )
      & ( ( A @ ( B @ subset ) )
        | ( A != B ) )
      & ( ( B @ ( A @ subset ) )
        | ( A != B ) ) ),
    inference(cnf,[status(esa)],[26]) ).

thf(28,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ subset ) )
      | ( A != B ) ),
    inference(cnfConj,[status(thm)],[27]) ).

thf(31,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ subset ) )
      | ( A != B ) ),
    inference(lifteq,[status(thm)],[28]) ).

thf(32,plain,
    ! [A: $i] : ( A @ ( A @ subset ) ),
    inference(simp,[status(thm)],[31]) ).

thf(30,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(cnfConj,[status(thm)],[27]) ).

thf(35,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[30]) ).

thf(36,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) )
      | ( A = B ) ),
    inference(simp,[status(thm)],[35]) ).

thf(1513,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ sk5 ) @ in ) )
       != ( empty_set @ ( C @ in ) ) )
      | ~ $true
      | ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[55,1485]) ).

thf(1514,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ sk5 ) @ in ) )
       != ( empty_set @ ( C @ in ) ) )
      | ( B @ ( A @ subset ) ) ),
    inference(simp,[status(thm)],[1513]) ).

thf(1515,plain,
    ! [A: $i] : ( A @ ( empty_set @ subset ) ),
    inference(pattern_uni,[status(thm)],[1514:[bind(A,$thf( empty_set )),bind(B,$thf( D )),bind(C,$thf( empty_set @ ( D @ sk5 ) ))]]) ).

thf(1524,plain,
    ! [A: $i] : ( A @ ( empty_set @ subset ) ),
    inference(simp,[status(thm)],[1515]) ).

thf(13,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( A @ set_union2 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).

thf(65,plain,
    ! [A: $i] :
      ( ( A @ ( A @ set_union2 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(66,plain,
    ! [A: $i] :
      ( ( A @ ( A @ set_union2 ) )
      = A ),
    inference(cnf,[status(esa)],[65]) ).

thf(67,plain,
    ! [A: $i] :
      ( ( A @ ( A @ set_union2 ) )
      = A ),
    inference(lifteq,[status(thm)],[66]) ).

thf(146,plain,
    ( ( sk2 != sk2 )
    | ( ( sk2 @ ( sk1 @ set_union2 ) )
     != sk1 ) ),
    inference(simp,[status(thm)],[24]) ).

thf(147,plain,
    ( ( sk2 @ ( sk1 @ set_union2 ) )
   != sk1 ),
    inference(simp,[status(thm)],[146]) ).

thf(361,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ set_union2 ) )
       != ( sk2 @ ( sk1 @ set_union2 ) ) )
      | ( A != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[67,147]) ).

thf(375,plain,
    ( ( sk2 != sk1 )
    | ( sk1 != sk1 ) ),
    inference(simp,[status(thm)],[361]) ).

thf(384,plain,
    sk2 != sk1,
    inference(simp,[status(thm)],[375]) ).

thf(388,plain,
    ! [B: $i,A: $i] :
      ( ( A != sk2 )
      | ( B != sk1 )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,384]) ).

thf(389,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ~ ( sk2 @ ( A @ subset ) )
      | ~ ( A @ ( sk2 @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[388:[bind(A,$thf( sk2 ))]]) ).

thf(392,plain,
    ( ~ ( sk2 @ ( sk1 @ subset ) )
    | ~ ( sk1 @ ( sk2 @ subset ) ) ),
    inference(simp,[status(thm)],[389]) ).

thf(2049,plain,
    ! [A: $i] :
      ( ( ( A @ ( empty_set @ subset ) )
       != ( sk2 @ ( sk1 @ subset ) ) )
      | ~ $true
      | ~ ( sk1 @ ( sk2 @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[1524,392]) ).

thf(2050,plain,
    ! [A: $i] :
      ( ( ( A @ ( empty_set @ subset ) )
       != ( sk2 @ ( sk1 @ subset ) ) )
      | ~ ( sk1 @ ( sk2 @ subset ) ) ),
    inference(simp,[status(thm)],[2049]) ).

thf(2102,plain,
    ! [A: $i] :
      ( ( A != sk2 )
      | ( sk1 != empty_set )
      | ~ ( sk1 @ ( sk2 @ subset ) ) ),
    inference(simp,[status(thm)],[2050]) ).

thf(2116,plain,
    ( ( sk1 != empty_set )
    | ~ ( sk1 @ ( sk2 @ subset ) ) ),
    inference(simp,[status(thm)],[2102]) ).

thf(2738,plain,
    ! [B: $i,A: $i] :
      ( ( A != sk1 )
      | ( B != empty_set )
      | ~ ( sk1 @ ( sk2 @ subset ) )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,2116]) ).

thf(2739,plain,
    ! [A: $i] :
      ( ( A != empty_set )
      | ~ ( sk1 @ ( sk2 @ subset ) )
      | ~ ( sk1 @ ( A @ subset ) )
      | ~ ( A @ ( sk1 @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[2738:[bind(A,$thf( sk1 ))]]) ).

thf(2753,plain,
    ( ~ ( sk1 @ ( sk2 @ subset ) )
    | ~ ( sk1 @ ( empty_set @ subset ) )
    | ~ ( empty_set @ ( sk1 @ subset ) ) ),
    inference(simp,[status(thm)],[2739]) ).

thf(48721,plain,
    ( ~ ( sk1 @ ( sk2 @ subset ) )
    | ~ $true
    | ~ ( empty_set @ ( sk1 @ subset ) ) ),
    inference(rewrite,[status(thm)],[2753,1524]) ).

thf(48722,plain,
    ( ~ ( sk1 @ ( sk2 @ subset ) )
    | ~ ( empty_set @ ( sk1 @ subset ) ) ),
    inference(simp,[status(thm)],[48721]) ).

thf(48867,plain,
    ( ~ $true
    | ( ( sk1 @ ( sk2 @ subset ) )
     != ( empty_set @ ( sk1 @ subset ) ) )
    | ~ ( empty_set @ ( sk1 @ subset ) ) ),
    inference(eqfactor_ordered,[status(thm)],[48722]) ).

thf(48873,plain,
    ( ( ( sk1 @ ( sk2 @ subset ) )
     != ( empty_set @ ( sk1 @ subset ) ) )
    | ~ ( empty_set @ ( sk1 @ subset ) ) ),
    inference(simp,[status(thm)],[48867]) ).

thf(92048,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ subset ) )
       != ( empty_set @ ( sk1 @ subset ) ) )
      | ( ( sk1 @ ( sk2 @ subset ) )
       != ( empty_set @ ( sk1 @ subset ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[32,48873]) ).

thf(92049,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ subset ) )
       != ( empty_set @ ( sk1 @ subset ) ) )
      | ( ( sk1 @ ( sk2 @ subset ) )
       != ( empty_set @ ( sk1 @ subset ) ) ) ),
    inference(simp,[status(thm)],[92048]) ).

thf(92162,plain,
    ! [A: $i] :
      ( ( A != empty_set )
      | ( A != sk1 )
      | ( ( sk1 @ ( sk2 @ subset ) )
       != ( empty_set @ ( sk1 @ subset ) ) ) ),
    inference(simp,[status(thm)],[92049]) ).

thf(92170,plain,
    ( ( sk1 != empty_set )
    | ( ( sk1 @ ( sk2 @ subset ) )
     != ( empty_set @ ( sk1 @ subset ) ) ) ),
    inference(simp,[status(thm)],[92162]) ).

thf(92231,plain,
    ( ( empty_set @ ( sk1 @ subset ) )
    | ( sk1 @ ( sk2 @ subset ) )
    | ( sk1 != empty_set ) ),
    inference(bool_ext,[status(thm)],[92170]) ).

thf(92944,plain,
    ( ( ( sk1 @ ( sk2 @ subset ) )
     != ( sk1 @ ( sk2 @ subset ) ) )
    | ( sk1 != empty_set )
    | ~ $true
    | ( empty_set @ ( sk1 @ subset ) )
    | ( sk1 != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[92231,2116]) ).

thf(92945,plain,
    ( ( ( sk1 @ ( sk2 @ subset ) )
     != ( sk1 @ ( sk2 @ subset ) ) )
    | ( empty_set @ ( sk1 @ subset ) )
    | ( sk1 != empty_set ) ),
    inference(simp,[status(thm)],[92944]) ).

thf(92946,plain,
    ( ( empty_set @ ( sk1 @ subset ) )
    | ( sk1 != empty_set ) ),
    inference(pattern_uni,[status(thm)],[92945:[]]) ).

thf(284,plain,
    ! [B: $i,A: $i] :
      ( ( B != empty_set )
      | ( A @ empty )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,48]) ).

thf(285,plain,
    ! [A: $i] :
      ( ( A @ empty )
      | ~ ( A @ ( empty_set @ subset ) )
      | ~ ( empty_set @ ( A @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[284:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).

thf(22209,plain,
    ! [A: $i] :
      ( ( A @ empty )
      | ~ $true
      | ~ ( empty_set @ ( A @ subset ) ) ),
    inference(rewrite,[status(thm)],[285,1524]) ).

thf(22210,plain,
    ! [A: $i] :
      ( ( A @ empty )
      | ~ ( empty_set @ ( A @ subset ) ) ),
    inference(simp,[status(thm)],[22209]) ).

thf(93296,plain,
    ! [A: $i] :
      ( ( ( empty_set @ ( sk1 @ subset ) )
       != ( empty_set @ ( A @ subset ) ) )
      | ( A @ empty )
      | ~ $true
      | ( sk1 != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[92946,22210]) ).

thf(93297,plain,
    ! [A: $i] :
      ( ( ( empty_set @ ( sk1 @ subset ) )
       != ( empty_set @ ( A @ subset ) ) )
      | ( A @ empty )
      | ( sk1 != empty_set ) ),
    inference(simp,[status(thm)],[93296]) ).

thf(93298,plain,
    ( ( sk1 @ empty )
    | ( sk1 != empty_set ) ),
    inference(pattern_uni,[status(thm)],[93297:[bind(A,$thf( sk1 ))]]) ).

thf(93891,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk1 @ empty )
       != ( B @ empty ) )
      | ~ $true
      | ~ ( B @ ( A @ in ) )
      | ( sk1 != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[93298,62]) ).

thf(93892,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk1 @ empty )
       != ( B @ empty ) )
      | ~ ( B @ ( A @ in ) )
      | ( sk1 != empty_set ) ),
    inference(simp,[status(thm)],[93891]) ).

thf(93893,plain,
    ! [A: $i] :
      ( ~ ( sk1 @ ( A @ in ) )
      | ( sk1 != empty_set ) ),
    inference(pattern_uni,[status(thm)],[93892:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).

thf(95118,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ sk5 ) @ in ) )
       != ( sk1 @ ( C @ in ) ) )
      | ~ $true
      | ( sk1 != empty_set )
      | ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[55,93893]) ).

thf(95119,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ sk5 ) @ in ) )
       != ( sk1 @ ( C @ in ) ) )
      | ( sk1 != empty_set )
      | ( B @ ( A @ subset ) ) ),
    inference(simp,[status(thm)],[95118]) ).

thf(95120,plain,
    ! [A: $i] :
      ( ( sk1 != empty_set )
      | ( A @ ( sk1 @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[95119:[bind(A,$thf( sk1 )),bind(B,$thf( D )),bind(C,$thf( sk1 @ ( D @ sk5 ) ))]]) ).

thf(95184,plain,
    ! [A: $i] :
      ( ( sk1 != empty_set )
      | ( A @ ( sk1 @ subset ) ) ),
    inference(simp,[status(thm)],[95120]) ).

thf(19,axiom,
    ! [A: $i] :
      ( ( empty_set @ ( A @ set_difference ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).

thf(107,plain,
    ! [A: $i] :
      ( ( empty_set @ ( A @ set_difference ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(108,plain,
    ! [A: $i] :
      ( ( empty_set @ ( A @ set_difference ) )
      = A ),
    inference(cnf,[status(esa)],[107]) ).

thf(109,plain,
    ! [A: $i] :
      ( ( empty_set @ ( A @ set_difference ) )
      = A ),
    inference(lifteq,[status(thm)],[108]) ).

thf(1610,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( empty_set @ ( C @ set_difference ) ) )
      | ( empty_set = C )
      | ( A @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1599,109]) ).

thf(1611,plain,
    ! [B: $i,A: $i] :
      ( ( empty_set = B )
      | ( empty_set @ ( B @ set_difference ) @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1610:[bind(A,$thf( empty_set @ ( D @ set_difference ) )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).

thf(1814,plain,
    ! [B: $i,A: $i] :
      ( ( empty_set = B )
      | ( empty_set @ ( B @ set_difference ) @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[1611]) ).

thf(7213,plain,
    ! [B: $i,A: $i] :
      ( ( empty_set = B )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(rewrite,[status(thm)],[1814,109]) ).

thf(2099,plain,
    ( ~ $true
    | ( ( sk1 @ ( sk2 @ subset ) )
     != ( sk2 @ ( sk1 @ subset ) ) )
    | ~ ( sk2 @ ( sk1 @ subset ) ) ),
    inference(eqfactor_ordered,[status(thm)],[392]) ).

thf(2103,plain,
    ( ( ( sk1 @ ( sk2 @ subset ) )
     != ( sk2 @ ( sk1 @ subset ) ) )
    | ~ ( sk2 @ ( sk1 @ subset ) ) ),
    inference(simp,[status(thm)],[2099]) ).

thf(35693,plain,
    ! [A: $i] :
      ( ( ( A @ ( empty_set @ subset ) )
       != ( sk2 @ ( sk1 @ subset ) ) )
      | ( ( sk1 @ ( sk2 @ subset ) )
       != ( sk2 @ ( sk1 @ subset ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1524,2103]) ).

thf(35694,plain,
    ! [A: $i] :
      ( ( ( A @ ( empty_set @ subset ) )
       != ( sk2 @ ( sk1 @ subset ) ) )
      | ( ( sk1 @ ( sk2 @ subset ) )
       != ( sk2 @ ( sk1 @ subset ) ) ) ),
    inference(simp,[status(thm)],[35693]) ).

thf(35732,plain,
    ! [A: $i] :
      ( ( A != sk2 )
      | ( sk1 != empty_set )
      | ( ( sk1 @ ( sk2 @ subset ) )
       != ( sk2 @ ( sk1 @ subset ) ) ) ),
    inference(simp,[status(thm)],[35694]) ).

thf(35744,plain,
    ( ( sk1 != empty_set )
    | ( ( sk1 @ ( sk2 @ subset ) )
     != ( sk2 @ ( sk1 @ subset ) ) ) ),
    inference(simp,[status(thm)],[35732]) ).

thf(36082,plain,
    ( ( sk2 @ ( sk1 @ subset ) )
    | ( sk1 @ ( sk2 @ subset ) )
    | ( sk1 != empty_set ) ),
    inference(bool_ext,[status(thm)],[35744]) ).

thf(37038,plain,
    ( ( ( sk1 @ ( sk2 @ subset ) )
     != ( sk1 @ ( sk2 @ subset ) ) )
    | ( sk1 != empty_set )
    | ~ $true
    | ( sk2 @ ( sk1 @ subset ) )
    | ( sk1 != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[36082,2116]) ).

thf(37039,plain,
    ( ( ( sk1 @ ( sk2 @ subset ) )
     != ( sk1 @ ( sk2 @ subset ) ) )
    | ( sk2 @ ( sk1 @ subset ) )
    | ( sk1 != empty_set ) ),
    inference(simp,[status(thm)],[37038]) ).

thf(37040,plain,
    ( ( sk2 @ ( sk1 @ subset ) )
    | ( sk1 != empty_set ) ),
    inference(pattern_uni,[status(thm)],[37039:[]]) ).

thf(37218,plain,
    ! [B: $i,A: $i] :
      ( ( B != sk1 )
      | ( sk2 @ ( sk1 @ subset ) )
      | ( empty_set != empty_set )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7213,37040]) ).

thf(37219,plain,
    ! [B: $i,A: $i] :
      ( ( B != sk1 )
      | ( sk2 @ ( sk1 @ subset ) )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[37218]) ).

thf(37220,plain,
    ! [A: $i] :
      ( ( sk2 @ ( sk1 @ subset ) )
      | ( sk1 @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[37219:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).

thf(13710,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( C @ ( D @ in ) ) )
      | ( C @ ( B @ set_union2 ) @ ( D @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13698,82]) ).

thf(13711,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( C @ ( D @ in ) ) )
      | ( C @ ( B @ set_union2 ) @ ( D @ in ) ) ),
    inference(simp,[status(thm)],[13710]) ).

thf(13712,plain,
    ! [B: $i,A: $i] : ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) ),
    inference(pattern_uni,[status(thm)],[13711:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( sk2 )),bind(D,$thf( empty_set @ ( F @ ( sk2 @ sk10 ) ) ))]]) ).

thf(13960,plain,
    ! [B: $i,A: $i] : ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) ),
    inference(simp,[status(thm)],[13712]) ).

thf(15030,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( empty_set @ ( C @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13960,1485]) ).

thf(15031,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
     != ( empty_set @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[15030]) ).

thf(15140,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) )
       != empty_set )
      | ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
       != C ) ),
    inference(simp,[status(thm)],[15031]) ).

thf(15192,plain,
    ! [A: $i] :
      ( ( sk2 @ ( A @ set_union2 ) )
     != empty_set ),
    inference(simp,[status(thm)],[15140]) ).

thf(15315,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk2 @ ( C @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) )
       != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[139,15192]) ).

thf(15316,plain,
    ! [A: $i] :
      ( ( A @ ( sk2 @ set_union2 ) )
     != empty_set ),
    inference(pattern_uni,[status(thm)],[15315:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).

thf(16065,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
       != ( C @ ( sk2 @ set_union2 ) ) )
      | ( empty_set != empty_set )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7213,15316]) ).

thf(16066,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
       != ( C @ ( sk2 @ set_union2 ) ) )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[16065]) ).

thf(16067,plain,
    ! [B: $i,A: $i] : ( B @ ( sk2 @ set_union2 ) @ ( A @ ( empty_set @ sk9 ) ) ),
    inference(pattern_uni,[status(thm)],[16066:[bind(A,$thf( A )),bind(B,$thf( E @ ( sk2 @ set_union2 ) )),bind(C,$thf( E ))]]) ).

thf(16124,plain,
    ! [B: $i,A: $i] : ( B @ ( sk2 @ set_union2 ) @ ( A @ ( empty_set @ sk9 ) ) ),
    inference(simp,[status(thm)],[16067]) ).

thf(7,axiom,
    ? [A: $i] :
      ~ ( A @ empty ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(45,plain,
    ? [A: $i] :
      ~ ( A @ empty ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(46,plain,
    ~ ! [A: $i] : ( A @ empty ),
    inference(miniscope,[status(thm)],[45]) ).

thf(47,plain,
    ~ ( sk4 @ empty ),
    inference(cnf,[status(esa)],[46]) ).

thf(143,plain,
    ( ( ( sk4 @ empty )
     != ( empty_set @ empty ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[48,47]) ).

thf(144,plain,
    ( ( sk4 @ empty )
   != ( empty_set @ empty ) ),
    inference(simp,[status(thm)],[143]) ).

thf(145,plain,
    sk4 != empty_set,
    inference(simp,[status(thm)],[144]) ).

thf(258,plain,
    ! [B: $i,A: $i] :
      ( ( A != sk4 )
      | ( B != empty_set )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,145]) ).

thf(259,plain,
    ! [A: $i] :
      ( ( A != empty_set )
      | ~ ( sk4 @ ( A @ subset ) )
      | ~ ( A @ ( sk4 @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[258:[bind(A,$thf( sk4 ))]]) ).

thf(313,plain,
    ( ~ ( sk4 @ ( empty_set @ subset ) )
    | ~ ( empty_set @ ( sk4 @ subset ) ) ),
    inference(simp,[status(thm)],[259]) ).

thf(1990,plain,
    ( ~ $true
    | ~ ( empty_set @ ( sk4 @ subset ) ) ),
    inference(rewrite,[status(thm)],[313,1524]) ).

thf(1991,plain,
    ~ ( empty_set @ ( sk4 @ subset ) ),
    inference(simp,[status(thm)],[1990]) ).

thf(93442,plain,
    ( ( ( empty_set @ ( sk4 @ subset ) )
     != ( empty_set @ ( sk1 @ subset ) ) )
    | ~ $true
    | ( sk1 != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[92946,1991]) ).

thf(93443,plain,
    ( ( ( empty_set @ ( sk4 @ subset ) )
     != ( empty_set @ ( sk1 @ subset ) ) )
    | ( sk1 != empty_set ) ),
    inference(simp,[status(thm)],[93442]) ).

thf(93630,plain,
    ( ( empty_set != empty_set )
    | ( sk4 != sk1 )
    | ( sk1 != empty_set ) ),
    inference(simp,[status(thm)],[93443]) ).

thf(93716,plain,
    ( ( sk4 != sk1 )
    | ( sk1 != empty_set ) ),
    inference(simp,[status(thm)],[93630]) ).

thf(94081,plain,
    ! [B: $i,A: $i] :
      ( ( B != sk1 )
      | ( sk4 != sk1 )
      | ( empty_set != empty_set )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7213,93716]) ).

thf(94082,plain,
    ! [B: $i,A: $i] :
      ( ( B != sk1 )
      | ( sk4 != sk1 )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[94081]) ).

thf(94083,plain,
    ! [A: $i] :
      ( ( sk4 != sk1 )
      | ( sk1 @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[94082:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).

thf(71,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( A @ set_union2 ) ) )
      | ~ ( C @ ( B @ ( A @ sk6 ) ) )
      | ( C @ ( A @ ( B @ ( C @ sk7 ) ) @ in ) ) ),
    inference(cnfConj,[status(thm)],[70]) ).

thf(87,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ sk6 ) ) )
      | ( C @ ( A @ ( B @ ( C @ sk7 ) ) @ in ) )
      | ( C
        = ( B @ ( A @ set_union2 ) ) ) ),
    inference(lifteq,[status(thm)],[71]) ).

thf(88,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ sk6 ) ) )
      | ( C @ ( A @ ( B @ ( C @ sk7 ) ) @ in ) )
      | ( C
        = ( B @ ( A @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[87]) ).

thf(1648,plain,
    ! [B: $i,A: $i] :
      ( ( A != sk4 )
      | ( empty_set != empty_set )
      | ( A @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1599,145]) ).

thf(1649,plain,
    ! [B: $i,A: $i] :
      ( ( A != sk4 )
      | ( A @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[1648]) ).

thf(1650,plain,
    ! [A: $i] : ( sk4 @ ( A @ ( empty_set @ sk9 ) ) ),
    inference(pattern_uni,[status(thm)],[1649:[bind(A,$thf( sk4 ))]]) ).

thf(1845,plain,
    ! [A: $i] : ( sk4 @ ( A @ ( empty_set @ sk9 ) ) ),
    inference(simp,[status(thm)],[1650]) ).

thf(11667,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( A @ ( empty_set @ sk9 ) ) )
       != ( D @ ( C @ ( B @ sk9 ) ) ) )
      | ~ $true
      | ( D @ ( B @ ( C @ ( D @ sk10 ) ) @ in ) )
      | ( D
        = ( C @ ( B @ set_difference ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1845,134]) ).

thf(11668,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( A @ ( empty_set @ sk9 ) ) )
       != ( D @ ( C @ ( B @ sk9 ) ) ) )
      | ( D @ ( B @ ( C @ ( D @ sk10 ) ) @ in ) )
      | ( D
        = ( C @ ( B @ set_difference ) ) ) ),
    inference(simp,[status(thm)],[11667]) ).

thf(11669,plain,
    ! [A: $i] :
      ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
      | ( ( A @ ( empty_set @ set_difference ) )
        = sk4 ) ),
    inference(pattern_uni,[status(thm)],[11668:[bind(A,$thf( A )),bind(B,$thf( empty_set )),bind(C,$thf( A )),bind(D,$thf( sk4 ))]]) ).

thf(19906,plain,
    ! [A: $i] :
      ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
      | ( sk4 = empty_set ) ),
    inference(rewrite,[status(thm)],[11669,97]) ).

thf(19907,plain,
    ! [A: $i] : ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) ),
    inference(simplifyReflect,[status(thm)],[19906,145]) ).

thf(2237,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ set_union2 ) )
       != ( D @ ( C @ set_union2 ) ) )
      | ~ ( C @ ( B @ ( A @ set_union2 ) @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[139,2192]) ).

thf(2238,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( B @ ( A @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[2237:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).

thf(2432,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( E @ ( E @ ( D @ set_union2 ) @ in ) ) )
      | ~ $true
      | ~ ( B @ ( C @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[82,2238]) ).

thf(2433,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( E @ ( E @ ( D @ set_union2 ) @ in ) ) )
      | ~ ( B @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[2432]) ).

thf(2434,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( C @ ( C @ ( B @ set_union2 ) @ ( A @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[2433:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( I @ ( H @ set_union2 ) @ ( F @ set_union2 ) )),bind(D,$thf( F )),bind(E,$thf( I @ ( H @ set_union2 ) ))]]) ).

thf(2492,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( C @ ( C @ ( B @ set_union2 ) @ ( A @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[2434]) ).

thf(3230,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ set_union2 ) )
       != ( E @ ( D @ set_union2 ) ) )
      | ~ ( E @ ( B @ ( A @ set_union2 ) @ ( C @ set_union2 ) @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[139,2492]) ).

thf(3231,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( A @ ( B @ ( A @ set_union2 ) @ ( C @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[3230:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( A ))]]) ).

thf(19950,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( B @ ( C @ ( B @ set_union2 ) @ ( D @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19907,3231]) ).

thf(19951,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
     != ( B @ ( C @ ( B @ set_union2 ) @ ( D @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[19950]) ).

thf(20137,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 != B )
      | ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
       != ( C @ ( B @ set_union2 ) @ ( D @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[19951]) ).

thf(20194,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
     != ( B @ ( sk4 @ set_union2 ) @ ( C @ set_union2 ) ) ),
    inference(simp,[status(thm)],[20137]) ).

thf(20012,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( C @ ( B @ in ) ) )
      | ~ ( B @ ( C @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19907,64]) ).

thf(20013,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( C @ ( B @ in ) ) )
      | ~ ( B @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[20012]) ).

thf(20014,plain,
    ! [A: $i] :
      ~ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ ( sk4 @ in ) ),
    inference(pattern_uni,[status(thm)],[20013:[bind(A,$thf( E )),bind(B,$thf( empty_set @ ( E @ ( sk4 @ sk10 ) ) )),bind(C,$thf( sk4 ))]]) ).

thf(20200,plain,
    ! [A: $i] :
      ~ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ ( sk4 @ in ) ),
    inference(simp,[status(thm)],[20014]) ).

thf(3219,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( F @ ( F @ ( E @ set_union2 ) @ ( D @ set_union2 ) @ in ) ) )
      | ~ $true
      | ~ ( A @ ( C @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[80,2492]) ).

thf(3220,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( F @ ( F @ ( E @ set_union2 ) @ ( D @ set_union2 ) @ in ) ) )
      | ~ ( A @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[3219]) ).

thf(3221,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( C @ ( D @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ ( A @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[3220:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( L @ ( K @ set_union2 ) @ ( I @ set_union2 ) @ ( G @ set_union2 ) )),bind(D,$thf( G )),bind(E,$thf( I )),bind(F,$thf( L @ ( K @ set_union2 ) ))]]) ).

thf(3253,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( C @ ( D @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ ( A @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[3221]) ).

thf(11172,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( empty_set @ ( A @ set_union2 ) )
       != ( E @ ( D @ set_union2 ) ) )
      | ~ ( D @ ( A @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[103,3253]) ).

thf(11173,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( A @ ( A @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[11172:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( empty_set ))]]) ).

thf(20045,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( B @ ( B @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19907,11173]) ).

thf(20046,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
     != ( B @ ( B @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[20045]) ).

thf(20138,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 != B )
      | ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
       != ( B @ ( D @ set_union2 ) @ ( C @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[20046]) ).

thf(20196,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
     != ( sk4 @ ( C @ set_union2 ) @ ( B @ set_union2 ) ) ),
    inference(simp,[status(thm)],[20138]) ).

thf(31256,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk4 @ ( E @ set_union2 ) @ ( D @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) )
       != ( empty_set @ ( C @ ( sk4 @ sk10 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,20196]) ).

thf(31257,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( sk4 @ ( C @ set_union2 ) @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk4 @ sk10 ) ) ) ),
    inference(pattern_uni,[status(thm)],[31256:[bind(A,$thf( A )),bind(B,$thf( sk4 @ ( F @ set_union2 ) )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( F ))]]) ).

thf(31340,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( sk4 @ ( C @ set_union2 ) @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk4 @ sk10 ) ) ) ),
    inference(simp,[status(thm)],[31257]) ).

thf(40875,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk4 @ ( E @ set_union2 ) ) )
      | ( ( C @ ( A @ ( B @ set_union2 ) @ set_union2 ) )
       != ( empty_set @ ( D @ ( sk4 @ sk10 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,31340]) ).

thf(40876,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( sk4 @ set_union2 ) @ set_union2 ) )
     != ( empty_set @ ( C @ ( sk4 @ sk10 ) ) ) ),
    inference(pattern_uni,[status(thm)],[40875:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A ))]]) ).

thf(41015,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( sk4 @ set_union2 ) @ set_union2 ) )
     != ( empty_set @ ( C @ ( sk4 @ sk10 ) ) ) ),
    inference(simp,[status(thm)],[40876]) ).

thf(13842,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( B @ ( D @ in ) ) )
      | ( C @ ( B @ set_union2 ) @ ( D @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13698,80]) ).

thf(13843,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( B @ ( D @ in ) ) )
      | ( C @ ( B @ set_union2 ) @ ( D @ in ) ) ),
    inference(simp,[status(thm)],[13842]) ).

thf(13844,plain,
    ! [B: $i,A: $i] : ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) ),
    inference(pattern_uni,[status(thm)],[13843:[bind(A,$thf( F )),bind(B,$thf( sk2 )),bind(C,$thf( C )),bind(D,$thf( empty_set @ ( F @ ( sk2 @ sk10 ) ) ))]]) ).

thf(13962,plain,
    ! [B: $i,A: $i] : ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) ),
    inference(simp,[status(thm)],[13844]) ).

thf(2235,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( D @ ( C @ set_union2 ) ) )
      | ~ ( C @ ( A @ ( B @ set_union2 ) @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[139,2192]) ).

thf(2236,plain,
    ! [B: $i,A: $i] :
      ~ ( A @ ( A @ ( B @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[2235:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).

thf(2286,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( C @ ( D @ set_union2 ) ) )
      | ~ ( C @ ( A @ ( B @ set_union2 ) @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[139,2236]) ).

thf(2287,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( A @ ( B @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[2286:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).

thf(18328,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( C @ ( D @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13962,2287]) ).

thf(18329,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
     != ( D @ ( C @ ( D @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[18328]) ).

thf(18407,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) )
       != D )
      | ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
       != ( C @ ( D @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[18329]) ).

thf(18514,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
     != ( C @ ( A @ ( sk2 @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[18407]) ).

thf(216,plain,
    ! [B: $i,A: $i] :
      ( ( B != sk1 )
      | ( ( sk2 @ ( A @ set_union2 ) )
       != sk1 )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,147]) ).

thf(217,plain,
    ! [A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) )
       != sk1 )
      | ~ ( A @ ( sk1 @ subset ) )
      | ~ ( sk1 @ ( A @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[216:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).

thf(20130,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( C @ ( C @ ( B @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19907,2238]) ).

thf(20131,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
     != ( C @ ( C @ ( B @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[20130]) ).

thf(20134,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sk4 != C )
      | ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
       != ( C @ ( B @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[20131]) ).

thf(20191,plain,
    ! [B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
     != ( sk4 @ ( B @ set_union2 ) ) ),
    inference(simp,[status(thm)],[20134]) ).

thf(20712,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk4 @ ( D @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) )
       != ( empty_set @ ( C @ ( sk4 @ sk10 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,20191]) ).

thf(20713,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( sk4 @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk4 @ sk10 ) ) ) ),
    inference(pattern_uni,[status(thm)],[20712:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).

thf(20813,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( sk4 @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk4 @ sk10 ) ) ) ),
    inference(simp,[status(thm)],[20713]) ).

thf(14849,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( E @ in ) ) )
      | ( D @ ( C @ set_union2 ) @ ( E @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13960,82]) ).

thf(14850,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( E @ in ) ) )
      | ( D @ ( C @ set_union2 ) @ ( E @ in ) ) ),
    inference(simp,[status(thm)],[14849]) ).

thf(14851,plain,
    ! [C: $i,B: $i,A: $i] : ( sk2 @ ( C @ set_union2 ) @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) ),
    inference(pattern_uni,[status(thm)],[14850:[bind(A,$thf( I )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( sk2 @ ( I @ set_union2 ) )),bind(E,$thf( empty_set @ ( G @ ( sk2 @ sk10 ) ) ))]]) ).

thf(15148,plain,
    ! [C: $i,B: $i,A: $i] : ( sk2 @ ( C @ set_union2 ) @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) ),
    inference(simp,[status(thm)],[14851]) ).

thf(57328,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( C @ set_union2 ) @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( E @ ( D @ in ) ) )
      | ~ ( E @ empty )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[15148,62]) ).

thf(57329,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( C @ set_union2 ) @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( E @ ( D @ in ) ) )
      | ~ ( E @ empty ) ),
    inference(simp,[status(thm)],[57328]) ).

thf(57330,plain,
    ! [B: $i,A: $i] :
      ~ ( sk2 @ ( B @ set_union2 ) @ ( A @ set_union2 ) @ empty ),
    inference(pattern_uni,[status(thm)],[57329:[bind(A,$thf( I )),bind(B,$thf( G )),bind(C,$thf( K )),bind(D,$thf( empty_set @ ( G @ ( sk2 @ sk10 ) ) )),bind(E,$thf( sk2 @ ( K @ set_union2 ) @ ( I @ set_union2 ) ))]]) ).

thf(57561,plain,
    ! [B: $i,A: $i] :
      ~ ( sk2 @ ( B @ set_union2 ) @ ( A @ set_union2 ) @ empty ),
    inference(simp,[status(thm)],[57330]) ).

thf(57934,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk2 @ ( D @ set_union2 ) @ ( C @ set_union2 ) ) )
      | ~ ( A @ ( B @ set_union2 ) @ empty ) ),
    inference(paramod_ordered,[status(thm)],[139,57561]) ).

thf(57935,plain,
    ! [B: $i,A: $i] :
      ~ ( A @ ( sk2 @ ( B @ set_union2 ) @ set_union2 ) @ empty ),
    inference(pattern_uni,[status(thm)],[57934:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( E @ set_union2 ) )),bind(C,$thf( A )),bind(D,$thf( E ))]]) ).

thf(58019,plain,
    ! [B: $i,A: $i] :
      ~ ( A @ ( sk2 @ ( B @ set_union2 ) @ set_union2 ) @ empty ),
    inference(simp,[status(thm)],[57935]) ).

thf(58679,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk2 @ ( D @ set_union2 ) ) )
      | ~ ( C @ ( A @ ( B @ set_union2 ) @ set_union2 ) @ empty ) ),
    inference(paramod_ordered,[status(thm)],[139,58019]) ).

thf(58680,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( A @ ( sk2 @ set_union2 ) @ set_union2 ) @ empty ),
    inference(pattern_uni,[status(thm)],[58679:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).

thf(58750,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( A @ ( sk2 @ set_union2 ) @ set_union2 ) @ empty ),
    inference(simp,[status(thm)],[58680]) ).

thf(20054,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( B @ ( D @ in ) ) )
      | ( C @ ( B @ set_union2 ) @ ( D @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19907,80]) ).

thf(20055,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( B @ ( D @ in ) ) )
      | ( C @ ( B @ set_union2 ) @ ( D @ in ) ) ),
    inference(simp,[status(thm)],[20054]) ).

thf(20056,plain,
    ! [B: $i,A: $i] : ( A @ ( sk4 @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) ),
    inference(pattern_uni,[status(thm)],[20055:[bind(A,$thf( F )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( empty_set @ ( F @ ( sk4 @ sk10 ) ) ))]]) ).

thf(20241,plain,
    ! [B: $i,A: $i] : ( A @ ( sk4 @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) ),
    inference(simp,[status(thm)],[20056]) ).

thf(21015,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk4 @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( C @ ( E @ in ) ) )
      | ( D @ ( C @ set_union2 ) @ ( E @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[20241,80]) ).

thf(21016,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk4 @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( C @ ( E @ in ) ) )
      | ( D @ ( C @ set_union2 ) @ ( E @ in ) ) ),
    inference(simp,[status(thm)],[21015]) ).

thf(21017,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( sk4 @ set_union2 ) @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) ),
    inference(pattern_uni,[status(thm)],[21016:[bind(A,$thf( J )),bind(B,$thf( G )),bind(C,$thf( J @ ( sk4 @ set_union2 ) )),bind(D,$thf( D )),bind(E,$thf( empty_set @ ( G @ ( sk4 @ sk10 ) ) ))]]) ).

thf(21163,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( sk4 @ set_union2 ) @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) ),
    inference(simp,[status(thm)],[21017]) ).

thf(66725,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( sk4 @ set_union2 ) @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( E @ ( D @ in ) ) )
      | ~ ( E @ empty )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[21163,62]) ).

thf(66726,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( sk4 @ set_union2 ) @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( E @ ( D @ in ) ) )
      | ~ ( E @ empty ) ),
    inference(simp,[status(thm)],[66725]) ).

thf(66727,plain,
    ! [B: $i,A: $i] :
      ~ ( A @ ( B @ ( sk4 @ set_union2 ) @ set_union2 ) @ empty ),
    inference(pattern_uni,[status(thm)],[66726:[bind(A,$thf( J )),bind(B,$thf( G )),bind(C,$thf( L )),bind(D,$thf( empty_set @ ( G @ ( sk4 @ sk10 ) ) )),bind(E,$thf( J @ ( L @ ( sk4 @ set_union2 ) @ set_union2 ) ))]]) ).

thf(66895,plain,
    ! [B: $i,A: $i] :
      ~ ( A @ ( B @ ( sk4 @ set_union2 ) @ set_union2 ) @ empty ),
    inference(simp,[status(thm)],[66727]) ).

thf(57156,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( C @ set_union2 ) @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( E @ ( D @ in ) ) )
      | ~ ( D @ ( E @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[15148,64]) ).

thf(57157,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( C @ set_union2 ) @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( E @ ( D @ in ) ) )
      | ~ ( D @ ( E @ in ) ) ),
    inference(simp,[status(thm)],[57156]) ).

thf(57158,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ ( sk2 @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[57157:[bind(A,$thf( I )),bind(B,$thf( G )),bind(C,$thf( K )),bind(D,$thf( empty_set @ ( G @ ( sk2 @ sk10 ) ) )),bind(E,$thf( sk2 @ ( K @ set_union2 ) @ ( I @ set_union2 ) ))]]) ).

thf(57471,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ ( sk2 @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[57158]) ).

thf(37780,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( A @ ( empty_set @ sk9 ) ) )
       != ( D @ ( C @ ( B @ sk9 ) ) ) )
      | ~ $true
      | ( D @ ( B @ ( C @ ( D @ sk10 ) ) @ in ) )
      | ( D
        = ( C @ ( B @ set_difference ) ) )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[37220,134]) ).

thf(37781,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( A @ ( empty_set @ sk9 ) ) )
       != ( D @ ( C @ ( B @ sk9 ) ) ) )
      | ( D @ ( B @ ( C @ ( D @ sk10 ) ) @ in ) )
      | ( D
        = ( C @ ( B @ set_difference ) ) )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(simp,[status(thm)],[37780]) ).

thf(37782,plain,
    ! [A: $i] :
      ( ( sk1 @ ( empty_set @ ( A @ ( sk1 @ sk10 ) ) @ in ) )
      | ( ( A @ ( empty_set @ set_difference ) )
        = sk1 )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[37781:[bind(A,$thf( A )),bind(B,$thf( empty_set )),bind(C,$thf( A )),bind(D,$thf( sk1 ))]]) ).

thf(42358,plain,
    ! [A: $i] :
      ( ( sk1 @ ( empty_set @ ( A @ ( sk1 @ sk10 ) ) @ in ) )
      | ( sk1 = empty_set )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(rewrite,[status(thm)],[37782,97]) ).

thf(42385,plain,
    ! [A: $i] :
      ( ( sk1 != sk1 )
      | ( sk2 @ ( sk1 @ subset ) )
      | ( empty_set != empty_set )
      | ( sk1 @ ( empty_set @ ( A @ ( sk1 @ sk10 ) ) @ in ) )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[42358,37040]) ).

thf(42386,plain,
    ! [A: $i] :
      ( ( sk1 != sk1 )
      | ( sk1 @ ( empty_set @ ( A @ ( sk1 @ sk10 ) ) @ in ) )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(simp,[status(thm)],[42385]) ).

thf(42387,plain,
    ! [A: $i] :
      ( ( sk1 @ ( empty_set @ ( A @ ( sk1 @ sk10 ) ) @ in ) )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[42386:[]]) ).

thf(208,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( sk2 @ ( sk1 @ set_union2 ) ) )
      | ( B != sk1 )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,147]) ).

thf(209,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ~ ( sk2 @ ( sk1 @ set_union2 ) @ ( A @ subset ) )
      | ~ ( A @ ( sk2 @ ( sk1 @ set_union2 ) @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[208:[bind(A,$thf( sk2 @ ( sk1 @ set_union2 ) )),bind(B,$thf( B ))]]) ).

thf(340,plain,
    ( ~ ( sk2 @ ( sk1 @ set_union2 ) @ ( sk1 @ subset ) )
    | ~ ( sk1 @ ( sk2 @ ( sk1 @ set_union2 ) @ subset ) ) ),
    inference(simp,[status(thm)],[209]) ).

thf(37597,plain,
    ! [A: $i] :
      ( ( ( A @ ( empty_set @ subset ) )
       != ( sk2 @ ( sk1 @ set_union2 ) @ ( sk1 @ subset ) ) )
      | ~ $true
      | ~ ( sk1 @ ( sk2 @ ( sk1 @ set_union2 ) @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[1524,340]) ).

thf(37598,plain,
    ! [A: $i] :
      ( ( ( A @ ( empty_set @ subset ) )
       != ( sk2 @ ( sk1 @ set_union2 ) @ ( sk1 @ subset ) ) )
      | ~ ( sk1 @ ( sk2 @ ( sk1 @ set_union2 ) @ subset ) ) ),
    inference(simp,[status(thm)],[37597]) ).

thf(37700,plain,
    ! [A: $i] :
      ( ( A
       != ( sk2 @ ( sk1 @ set_union2 ) ) )
      | ( sk1 != empty_set )
      | ~ ( sk1 @ ( sk2 @ ( sk1 @ set_union2 ) @ subset ) ) ),
    inference(simp,[status(thm)],[37598]) ).

thf(37719,plain,
    ( ( sk1 != empty_set )
    | ~ ( sk1 @ ( sk2 @ ( sk1 @ set_union2 ) @ subset ) ) ),
    inference(simp,[status(thm)],[37700]) ).

thf(67094,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( D @ ( sk4 @ set_union2 ) ) )
      | ~ ( C @ ( A @ ( B @ set_union2 ) @ set_union2 ) @ empty ) ),
    inference(paramod_ordered,[status(thm)],[139,66895]) ).

thf(67095,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( sk4 @ ( A @ set_union2 ) @ set_union2 ) @ empty ),
    inference(pattern_uni,[status(thm)],[67094:[bind(A,$thf( sk4 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).

thf(67150,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( sk4 @ ( A @ set_union2 ) @ set_union2 ) @ empty ),
    inference(simp,[status(thm)],[67095]) ).

thf(20073,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( C @ ( D @ in ) ) )
      | ( C @ ( B @ set_union2 ) @ ( D @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19907,82]) ).

thf(20074,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( C @ ( D @ in ) ) )
      | ( C @ ( B @ set_union2 ) @ ( D @ in ) ) ),
    inference(simp,[status(thm)],[20073]) ).

thf(20075,plain,
    ! [B: $i,A: $i] : ( sk4 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) ),
    inference(pattern_uni,[status(thm)],[20074:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( sk4 )),bind(D,$thf( empty_set @ ( F @ ( sk4 @ sk10 ) ) ))]]) ).

thf(20250,plain,
    ! [B: $i,A: $i] : ( sk4 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) ),
    inference(simp,[status(thm)],[20075]) ).

thf(22872,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( D @ ( C @ ( D @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[20250,2287]) ).

thf(22873,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
     != ( D @ ( C @ ( D @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[22872]) ).

thf(22960,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( A @ set_union2 ) )
       != D )
      | ( ( empty_set @ ( B @ ( sk4 @ sk10 ) ) )
       != ( C @ ( D @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[22873]) ).

thf(23056,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk4 @ sk10 ) ) )
     != ( C @ ( sk4 @ ( A @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[22960]) ).

thf(10,axiom,
    ! [A: $i] :
      ( ( A @ empty )
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

thf(57,plain,
    ! [A: $i] :
      ( ( A @ empty )
     => ( A = empty_set ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

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

thf(59,plain,
    ! [A: $i] :
      ( ~ ( A @ empty )
      | ( A = empty_set ) ),
    inference(lifteq,[status(thm)],[58]) ).

thf(94113,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( sk4 != sk1 )
      | ( empty_set != empty_set )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[59,93716]) ).

thf(94114,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( sk4 != sk1 )
      | ~ ( A @ empty ) ),
    inference(simp,[status(thm)],[94113]) ).

thf(94115,plain,
    ( ( sk4 != sk1 )
    | ~ ( sk1 @ empty ) ),
    inference(pattern_uni,[status(thm)],[94114:[bind(A,$thf( sk1 ))]]) ).

thf(2281,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( D @ ( D @ ( E @ set_union2 ) @ in ) ) )
      | ~ $true
      | ~ ( A @ ( C @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[80,2236]) ).

thf(2282,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( D @ ( D @ ( E @ set_union2 ) @ in ) ) )
      | ~ ( A @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[2281]) ).

thf(2283,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ ( C @ ( B @ set_union2 ) @ ( A @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[2282:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( I @ ( H @ set_union2 ) @ ( F @ set_union2 ) )),bind(D,$thf( I @ ( H @ set_union2 ) )),bind(E,$thf( F ))]]) ).

thf(2298,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ ( C @ ( B @ set_union2 ) @ ( A @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[2283]) ).

thf(2624,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( E @ ( F @ ( E @ set_union2 ) @ ( D @ set_union2 ) @ in ) ) )
      | ~ $true
      | ~ ( B @ ( C @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[82,2298]) ).

thf(2625,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( E @ ( F @ ( E @ set_union2 ) @ ( D @ set_union2 ) @ in ) ) )
      | ~ ( B @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[2624]) ).

thf(2626,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( D @ ( B @ ( D @ ( C @ set_union2 ) @ set_union2 ) @ ( A @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[2625:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( J @ ( L @ ( K @ set_union2 ) @ set_union2 ) @ ( G @ set_union2 ) )),bind(D,$thf( G )),bind(E,$thf( L @ ( K @ set_union2 ) )),bind(F,$thf( J ))]]) ).

thf(2676,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( D @ ( B @ ( D @ ( C @ set_union2 ) @ set_union2 ) @ ( A @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[2626]) ).

thf(398,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( empty_set @ ( C @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) )
        = C ) ),
    inference(paramod_ordered,[status(thm)],[139,103]) ).

thf(399,plain,
    ! [A: $i] :
      ( ( A @ ( empty_set @ set_union2 ) )
      = A ),
    inference(pattern_uni,[status(thm)],[398:[bind(A,$thf( A )),bind(B,$thf( empty_set )),bind(C,$thf( A ))]]) ).

thf(712,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != empty_set )
      | ( ( C @ ( B @ set_union2 ) )
        = C )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,399]) ).

thf(713,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
        = B )
      | ~ ( empty_set @ ( A @ subset ) )
      | ~ ( A @ ( empty_set @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[712:[bind(A,$thf( empty_set ))]]) ).

thf(739,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
        = B )
      | ~ ( empty_set @ ( A @ subset ) )
      | ~ ( A @ ( empty_set @ subset ) ) ),
    inference(simp,[status(thm)],[713]) ).

thf(95260,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
        = B )
      | ~ ( empty_set @ ( A @ subset ) )
      | ~ $true ),
    inference(rewrite,[status(thm)],[739,1524]) ).

thf(95261,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
        = B )
      | ~ ( empty_set @ ( A @ subset ) ) ),
    inference(simp,[status(thm)],[95260]) ).

thf(3693,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( F @ ( D @ ( F @ ( E @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true
      | ~ ( B @ ( C @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[82,2504]) ).

thf(3694,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( F @ ( D @ ( F @ ( E @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ ( B @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[3693]) ).

thf(3695,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( D @ ( A @ ( D @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[3694:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( H @ ( L @ ( K @ set_union2 ) @ ( I @ set_union2 ) @ set_union2 ) )),bind(D,$thf( H )),bind(E,$thf( I )),bind(F,$thf( L @ ( K @ set_union2 ) ))]]) ).

thf(3784,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( D @ ( A @ ( D @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[3695]) ).

thf(13708,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( E @ ( B @ ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13698,3784]) ).

thf(13709,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
     != ( E @ ( B @ ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[13708]) ).

thf(13923,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 != E )
      | ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
       != ( B @ ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[13709]) ).

thf(14004,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
     != ( B @ ( sk2 @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[13923]) ).

thf(97668,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( D @ ( sk2 @ ( F @ set_union2 ) @ ( E @ set_union2 ) @ set_union2 ) ) )
      | ( B
       != ( empty_set @ ( C @ ( sk2 @ sk10 ) ) ) )
      | ~ ( empty_set @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[95261,14004]) ).

thf(97669,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( empty_set @ ( B @ ( sk2 @ sk10 ) ) ) )
      | ~ ( empty_set @ ( sk2 @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[97668:[bind(A,$thf( sk2 @ ( I @ set_union2 ) @ ( G @ set_union2 ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( G )),bind(F,$thf( I ))]]) ).

thf(97900,plain,
    ! [B: $i,A: $i] :
      ~ ( empty_set @ ( sk2 @ ( B @ set_union2 ) @ ( A @ set_union2 ) @ subset ) ),
    inference(simp,[status(thm)],[97669]) ).

thf(98188,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk2 @ ( D @ set_union2 ) @ ( C @ set_union2 ) ) )
      | ~ ( empty_set @ ( A @ ( B @ set_union2 ) @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[139,97900]) ).

thf(98189,plain,
    ! [B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk2 @ ( B @ set_union2 ) @ set_union2 ) @ subset ) ),
    inference(pattern_uni,[status(thm)],[98188:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( E @ set_union2 ) )),bind(C,$thf( A )),bind(D,$thf( E ))]]) ).

thf(98332,plain,
    ! [B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk2 @ ( B @ set_union2 ) @ set_union2 ) @ subset ) ),
    inference(simp,[status(thm)],[98189]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( B @ empty )
        & ( A != B )
        & ( A @ empty ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).

thf(39,plain,
    ! [A: $i,B: $i] :
      ~ ( ( B @ empty )
        & ( A != B )
        & ( A @ empty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(40,plain,
    ~ ? [A: $i] :
        ( ? [B: $i] :
            ( ( B @ empty )
            & ( A != B ) )
        & ( A @ empty ) ),
    inference(miniscope,[status(thm)],[39]) ).

thf(41,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ empty )
      | ( A = B )
      | ~ ( A @ empty ) ),
    inference(cnf,[status(esa)],[40]) ).

thf(42,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ empty )
      | ~ ( A @ empty )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[41]) ).

thf(498,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != empty_set )
      | ( ( C @ ( B @ set_difference ) )
        = empty_set )
      | ~ ( B @ empty )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[42,97]) ).

thf(499,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ set_difference ) )
        = empty_set )
      | ~ ( A @ empty )
      | ~ ( empty_set @ empty ) ),
    inference(pattern_uni,[status(thm)],[498:[bind(A,$thf( empty_set ))]]) ).

thf(682,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ set_difference ) )
        = empty_set )
      | ~ ( A @ empty )
      | ~ ( empty_set @ empty ) ),
    inference(simp,[status(thm)],[499]) ).

thf(92579,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ set_difference ) )
        = empty_set )
      | ~ ( A @ empty )
      | ~ $true ),
    inference(rewrite,[status(thm)],[682,48]) ).

thf(92580,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ set_difference ) )
        = empty_set )
      | ~ ( A @ empty ) ),
    inference(simp,[status(thm)],[92579]) ).

thf(3744,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ set_union2 ) )
       != ( E @ ( D @ set_union2 ) ) )
      | ~ ( E @ ( C @ ( B @ ( A @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[139,2504]) ).

thf(3745,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( A @ ( C @ ( B @ ( A @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[3744:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( A ))]]) ).

thf(2649,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( E @ ( F @ ( E @ set_union2 ) @ ( D @ set_union2 ) @ in ) ) )
      | ~ $true
      | ~ ( A @ ( C @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[80,2298]) ).

thf(2650,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( E @ ( F @ ( E @ set_union2 ) @ ( D @ set_union2 ) @ in ) ) )
      | ~ ( A @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[2649]) ).

thf(2651,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( C @ ( B @ ( D @ ( C @ set_union2 ) @ set_union2 ) @ ( A @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[2650:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( J @ ( L @ ( K @ set_union2 ) @ set_union2 ) @ ( G @ set_union2 ) )),bind(D,$thf( G )),bind(E,$thf( L @ ( K @ set_union2 ) )),bind(F,$thf( J ))]]) ).

thf(2686,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( C @ ( B @ ( D @ ( C @ set_union2 ) @ set_union2 ) @ ( A @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[2651]) ).

thf(2230,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( D @ ( E @ ( D @ set_union2 ) @ in ) ) )
      | ~ $true
      | ~ ( A @ ( C @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[80,2192]) ).

thf(2231,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( D @ ( E @ ( D @ set_union2 ) @ in ) ) )
      | ~ ( A @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[2230]) ).

thf(2232,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ ( A @ ( C @ ( B @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[2231:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( G @ ( I @ ( H @ set_union2 ) @ set_union2 ) )),bind(D,$thf( I @ ( H @ set_union2 ) )),bind(E,$thf( G ))]]) ).

thf(2254,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ ( A @ ( C @ ( B @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[2232]) ).

thf(2533,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( E @ ( D @ ( F @ ( E @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true
      | ~ ( B @ ( C @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[82,2254]) ).

thf(2534,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( E @ ( D @ ( F @ ( E @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ ( B @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[2533]) ).

thf(2535,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( D @ ( A @ ( B @ ( D @ ( C @ set_union2 ) @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[2534:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( H @ ( J @ ( L @ ( K @ set_union2 ) @ set_union2 ) @ set_union2 ) )),bind(D,$thf( H )),bind(E,$thf( L @ ( K @ set_union2 ) )),bind(F,$thf( J ))]]) ).

thf(2599,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( D @ ( A @ ( B @ ( D @ ( C @ set_union2 ) @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[2535]) ).

thf(8068,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( empty_set @ set_union2 ) )
       != ( E @ ( D @ set_union2 ) ) )
      | ~ ( E @ ( B @ ( C @ ( A @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[399,2599]) ).

thf(8069,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( A @ ( B @ ( C @ ( A @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[8068:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( empty_set )),bind(E,$thf( A ))]]) ).

thf(13740,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( B @ ( C @ ( D @ ( B @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13698,8069]) ).

thf(13741,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
     != ( B @ ( C @ ( D @ ( B @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[13740]) ).

thf(13931,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 != B )
      | ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
       != ( C @ ( D @ ( B @ set_union2 ) @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[13741]) ).

thf(14014,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
     != ( B @ ( C @ ( sk2 @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[13931]) ).

thf(116,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ in ) )
      | ~ ( C @ ( D @ in ) )
      | ( C
       != ( B @ ( A @ set_difference ) ) ) ),
    inference(cnfConj,[status(thm)],[112]) ).

thf(121,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ in ) )
      | ~ ( C @ ( D @ in ) )
      | ( C
       != ( B @ ( A @ set_difference ) ) ) ),
    inference(lifteq,[status(thm)],[116]) ).

thf(122,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ in ) )
      | ~ ( B @ ( A @ set_difference ) @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[121]) ).

thf(21104,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk4 @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( D @ ( E @ in ) ) )
      | ~ $true
      | ~ ( D @ ( C @ set_difference ) @ ( E @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[20241,122]) ).

thf(21105,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk4 @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( D @ ( E @ in ) ) )
      | ~ ( D @ ( C @ set_difference ) @ ( E @ in ) ) ),
    inference(simp,[status(thm)],[21104]) ).

thf(21106,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( C @ ( sk4 @ set_union2 ) @ ( A @ set_difference ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) ),
    inference(pattern_uni,[status(thm)],[21105:[bind(A,$thf( J )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( J @ ( sk4 @ set_union2 ) )),bind(E,$thf( empty_set @ ( G @ ( sk4 @ sk10 ) ) ))]]) ).

thf(21192,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( C @ ( sk4 @ set_union2 ) @ ( A @ set_difference ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) ),
    inference(simp,[status(thm)],[21106]) ).

thf(18219,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( E @ ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13962,2504]) ).

thf(18220,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
     != ( E @ ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[18219]) ).

thf(18433,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) )
       != E )
      | ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
       != ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[18220]) ).

thf(18438,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
     != ( C @ ( A @ ( sk2 @ set_union2 ) @ ( D @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[18433]) ).

thf(22792,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( D @ ( C @ in ) ) )
      | ~ ( C @ ( D @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[20250,64]) ).

thf(22793,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( D @ ( C @ in ) ) )
      | ~ ( C @ ( D @ in ) ) ),
    inference(simp,[status(thm)],[22792]) ).

thf(22794,plain,
    ! [B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ ( sk4 @ ( B @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[22793:[bind(A,$thf( H )),bind(B,$thf( F )),bind(C,$thf( empty_set @ ( F @ ( sk4 @ sk10 ) ) )),bind(D,$thf( sk4 @ ( H @ set_union2 ) ))]]) ).

thf(22989,plain,
    ! [B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ ( sk4 @ ( B @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[22794]) ).

thf(93775,plain,
    ! [B: $i,A: $i] :
      ( ( B != sk1 )
      | ( sk1 @ empty )
      | ( empty_set != empty_set )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7213,93298]) ).

thf(93776,plain,
    ! [B: $i,A: $i] :
      ( ( B != sk1 )
      | ( sk1 @ empty )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[93775]) ).

thf(93777,plain,
    ! [A: $i] :
      ( ( sk1 @ empty )
      | ( sk1 @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[93776:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).

thf(14964,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( E @ ( C @ ( D @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13960,3741]) ).

thf(14965,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
     != ( D @ ( E @ ( C @ ( D @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[14964]) ).

thf(15127,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) )
       != D )
      | ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
       != ( E @ ( C @ ( D @ set_union2 ) @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[14965]) ).

thf(15175,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
     != ( D @ ( C @ ( sk2 @ ( A @ set_union2 ) @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[15127]) ).

thf(22844,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( C @ ( E @ in ) ) )
      | ( D @ ( C @ set_union2 ) @ ( E @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[20250,80]) ).

thf(22845,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( C @ ( E @ in ) ) )
      | ( D @ ( C @ set_union2 ) @ ( E @ in ) ) ),
    inference(simp,[status(thm)],[22844]) ).

thf(22846,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( sk4 @ ( C @ set_union2 ) @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) ),
    inference(pattern_uni,[status(thm)],[22845:[bind(A,$thf( I )),bind(B,$thf( G )),bind(C,$thf( sk4 @ ( I @ set_union2 ) )),bind(D,$thf( D )),bind(E,$thf( empty_set @ ( G @ ( sk4 @ sk10 ) ) ))]]) ).

thf(23002,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( sk4 @ ( C @ set_union2 ) @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) ),
    inference(simp,[status(thm)],[22846]) ).

thf(13855,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( E @ ( B @ ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13698,2599]) ).

thf(13856,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
     != ( E @ ( B @ ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[13855]) ).

thf(13941,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 != E )
      | ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
       != ( B @ ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[13856]) ).

thf(14025,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
     != ( B @ ( C @ ( sk2 @ ( D @ set_union2 ) @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[13941]) ).

thf(54,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ subset ) )
      | ~ ( B @ ( A @ ( B @ sk5 ) @ in ) ) ),
    inference(cnfConj,[status(thm)],[51]) ).

thf(56,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ subset ) )
      | ~ ( B @ ( A @ ( B @ sk5 ) @ in ) ) ),
    inference(simp,[status(thm)],[54]) ).

thf(726,plain,
    ! [A: $i] :
      ( ( ( A @ ( empty_set @ set_union2 ) )
       != ( sk2 @ ( sk1 @ set_union2 ) ) )
      | ( ( sk2 @ ( A @ set_difference ) )
       != ( sk2 @ ( sk1 @ set_difference ) ) ) ),
    inference(paramod_ordered,[status(thm)],[399,24]) ).

thf(731,plain,
    ! [A: $i] :
      ( ( A != sk2 )
      | ( sk1 != empty_set )
      | ( ( sk2 @ ( A @ set_difference ) )
       != ( sk2 @ ( sk1 @ set_difference ) ) ) ),
    inference(simp,[status(thm)],[726]) ).

thf(747,plain,
    ( ( sk1 != empty_set )
    | ( ( sk2 @ ( sk2 @ set_difference ) )
     != ( sk2 @ ( sk1 @ set_difference ) ) ) ),
    inference(simp,[status(thm)],[731]) ).

thf(43096,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( empty_set @ ( A @ ( sk1 @ sk10 ) ) @ in ) )
       != ( C @ ( D @ in ) ) )
      | ( C @ ( B @ set_union2 ) @ ( D @ in ) )
      | ~ $true
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[42387,82]) ).

thf(43097,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( empty_set @ ( A @ ( sk1 @ sk10 ) ) @ in ) )
       != ( C @ ( D @ in ) ) )
      | ( C @ ( B @ set_union2 ) @ ( D @ in ) )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(simp,[status(thm)],[43096]) ).

thf(43098,plain,
    ! [B: $i,A: $i] :
      ( ( sk1 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk1 @ sk10 ) ) @ in ) )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[43097:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( sk1 )),bind(D,$thf( empty_set @ ( F @ ( sk1 @ sk10 ) ) ))]]) ).

thf(43218,plain,
    ! [B: $i,A: $i] :
      ( ( sk1 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk1 @ sk10 ) ) @ in ) )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(simp,[status(thm)],[43098]) ).

thf(44045,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk1 @ sk10 ) ) @ in ) )
       != ( D @ ( C @ in ) ) )
      | ~ ( D @ empty )
      | ~ $true
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[43218,62]) ).

thf(44046,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk1 @ sk10 ) ) @ in ) )
       != ( D @ ( C @ in ) ) )
      | ~ ( D @ empty )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(simp,[status(thm)],[44045]) ).

thf(44047,plain,
    ! [A: $i] :
      ( ~ ( sk1 @ ( A @ set_union2 ) @ empty )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[44046:[bind(A,$thf( H )),bind(B,$thf( F )),bind(C,$thf( empty_set @ ( F @ ( sk1 @ sk10 ) ) )),bind(D,$thf( sk1 @ ( H @ set_union2 ) ))]]) ).

thf(44123,plain,
    ! [A: $i] :
      ( ~ ( sk1 @ ( A @ set_union2 ) @ empty )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(simp,[status(thm)],[44047]) ).

thf(93444,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( empty_set @ ( sk1 @ subset ) )
      | ( empty_set != empty_set )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[59,92946]) ).

thf(93445,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( empty_set @ ( sk1 @ subset ) )
      | ~ ( A @ empty ) ),
    inference(simp,[status(thm)],[93444]) ).

thf(93446,plain,
    ( ( empty_set @ ( sk1 @ subset ) )
    | ~ ( sk1 @ empty ) ),
    inference(pattern_uni,[status(thm)],[93445:[bind(A,$thf( sk1 ))]]) ).

thf(2568,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ set_union2 ) )
       != ( E @ ( D @ set_union2 ) ) )
      | ~ ( D @ ( C @ ( B @ ( A @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[139,2254]) ).

thf(2569,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ ( C @ ( B @ ( A @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[2568:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( A ))]]) ).

thf(20069,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( C @ ( D @ ( C @ ( B @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19907,2569]) ).

thf(20070,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
     != ( C @ ( D @ ( C @ ( B @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[20069]) ).

thf(20142,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 != C )
      | ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
       != ( D @ ( C @ ( B @ set_union2 ) @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[20070]) ).

thf(20201,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
     != ( C @ ( sk4 @ ( B @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[20142]) ).

thf(31898,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( E @ ( sk4 @ ( D @ set_union2 ) @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) )
       != ( empty_set @ ( C @ ( sk4 @ sk10 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,20201]) ).

thf(31899,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sk4 @ ( C @ set_union2 ) @ ( A @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk4 @ sk10 ) ) ) ),
    inference(pattern_uni,[status(thm)],[31898:[bind(A,$thf( sk4 @ ( F @ set_union2 ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F )),bind(E,$thf( B ))]]) ).

thf(32032,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sk4 @ ( C @ set_union2 ) @ ( A @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk4 @ sk10 ) ) ) ),
    inference(simp,[status(thm)],[31899]) ).

thf(13833,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( B @ ( B @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13698,11173]) ).

thf(13834,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
     != ( B @ ( B @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[13833]) ).

thf(13917,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 != B )
      | ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
       != ( B @ ( D @ set_union2 ) @ ( C @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[13834]) ).

thf(13997,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
     != ( sk2 @ ( C @ set_union2 ) @ ( B @ set_union2 ) ) ),
    inference(simp,[status(thm)],[13917]) ).

thf(77,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( A @ set_union2 ) ) )
      | ( B @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) )
      | ( A @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) )
      | ( C @ ( B @ ( A @ sk6 ) ) ) ),
    inference(cnfConj,[status(thm)],[70]) ).

thf(83,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) )
      | ( A @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) )
      | ( C @ ( B @ ( A @ sk6 ) ) )
      | ( C
        = ( B @ ( A @ set_union2 ) ) ) ),
    inference(lifteq,[status(thm)],[77]) ).

thf(84,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) )
      | ( A @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) )
      | ( C @ ( B @ ( A @ sk6 ) ) )
      | ( C
        = ( B @ ( A @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[83]) ).

thf(2874,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk2 @ ( sk1 @ set_union2 ) ) )
      | ( C != sk1 )
      | ( B @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) )
      | ( A @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) )
      | ( C @ ( B @ ( A @ sk6 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[84,147]) ).

thf(2875,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( sk2 @ ( sk1 @ ( sk2 @ ( A @ sk8 ) ) @ in ) )
      | ( sk1 @ ( sk1 @ ( sk2 @ ( A @ sk8 ) ) @ in ) )
      | ( A @ ( sk2 @ ( sk1 @ sk6 ) ) ) ),
    inference(pattern_uni,[status(thm)],[2874:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(3088,plain,
    ( ( sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) )
    | ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) )
    | ( sk1 @ ( sk2 @ ( sk1 @ sk6 ) ) ) ),
    inference(simp,[status(thm)],[2875]) ).

thf(20889,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk4 @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( C @ ( C @ ( D @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[20241,2236]) ).

thf(20890,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( sk4 @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
     != ( C @ ( C @ ( D @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[20889]) ).

thf(21121,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk4 @ set_union2 ) )
       != C )
      | ( ( empty_set @ ( B @ ( sk4 @ sk10 ) ) )
       != ( C @ ( D @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[20890]) ).

thf(21203,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk4 @ sk10 ) ) )
     != ( A @ ( sk4 @ set_union2 ) @ ( C @ set_union2 ) ) ),
    inference(simp,[status(thm)],[21121]) ).

thf(67092,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( C @ ( D @ ( sk4 @ set_union2 ) @ set_union2 ) ) )
      | ~ ( A @ ( B @ set_union2 ) @ empty ) ),
    inference(paramod_ordered,[status(thm)],[139,66895]) ).

thf(67093,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( sk4 @ set_union2 ) @ ( A @ set_union2 ) @ empty ),
    inference(pattern_uni,[status(thm)],[67092:[bind(A,$thf( F @ ( sk4 @ set_union2 ) )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( F ))]]) ).

thf(67149,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( sk4 @ set_union2 ) @ ( A @ set_union2 ) @ empty ),
    inference(simp,[status(thm)],[67093]) ).

thf(67583,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( D @ ( sk4 @ set_union2 ) ) )
      | ~ ( A @ ( B @ set_union2 ) @ ( C @ set_union2 ) @ empty ) ),
    inference(paramod_ordered,[status(thm)],[139,67149]) ).

thf(67584,plain,
    ! [B: $i,A: $i] :
      ~ ( sk4 @ ( A @ set_union2 ) @ ( B @ set_union2 ) @ empty ),
    inference(pattern_uni,[status(thm)],[67583:[bind(A,$thf( sk4 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).

thf(67631,plain,
    ! [B: $i,A: $i] :
      ~ ( sk4 @ ( A @ set_union2 ) @ ( B @ set_union2 ) @ empty ),
    inference(simp,[status(thm)],[67584]) ).

thf(220,plain,
    ! [B: $i,A: $i] :
      ( ( A != sk2 )
      | ( B != empty_set )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,165]) ).

thf(221,plain,
    ! [A: $i] :
      ( ( A != empty_set )
      | ~ ( sk2 @ ( A @ subset ) )
      | ~ ( A @ ( sk2 @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[220:[bind(A,$thf( sk2 ))]]) ).

thf(344,plain,
    ( ~ ( sk2 @ ( empty_set @ subset ) )
    | ~ ( empty_set @ ( sk2 @ subset ) ) ),
    inference(simp,[status(thm)],[221]) ).

thf(1528,plain,
    ( ~ $true
    | ~ ( empty_set @ ( sk2 @ subset ) ) ),
    inference(rewrite,[status(thm)],[344,1524]) ).

thf(1529,plain,
    ~ ( empty_set @ ( sk2 @ subset ) ),
    inference(simp,[status(thm)],[1528]) ).

thf(22933,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( D @ ( E @ in ) ) )
      | ~ $true
      | ~ ( D @ ( C @ set_difference ) @ ( E @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[20250,122]) ).

thf(22934,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( D @ ( E @ in ) ) )
      | ~ ( D @ ( C @ set_difference ) @ ( E @ in ) ) ),
    inference(simp,[status(thm)],[22933]) ).

thf(22935,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( sk4 @ ( C @ set_union2 ) @ ( A @ set_difference ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) ),
    inference(pattern_uni,[status(thm)],[22934:[bind(A,$thf( I )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( sk4 @ ( I @ set_union2 ) )),bind(E,$thf( empty_set @ ( G @ ( sk4 @ sk10 ) ) ))]]) ).

thf(23030,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( sk4 @ ( C @ set_union2 ) @ ( A @ set_difference ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) ),
    inference(simp,[status(thm)],[22935]) ).

thf(4,axiom,
    ! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(37,plain,
    ! [A: $i] : ( A @ ( A @ subset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(19917,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( E @ ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) @ ( B @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19907,2676]) ).

thf(19918,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
     != ( E @ ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) @ ( B @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[19917]) ).

thf(20149,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 != E )
      | ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
       != ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) @ ( B @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[19918]) ).

thf(20209,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
     != ( C @ ( sk4 @ ( D @ set_union2 ) @ set_union2 ) @ ( B @ set_union2 ) ) ),
    inference(simp,[status(thm)],[20149]) ).

thf(43770,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk1 @ sk10 ) ) @ in ) )
       != ( empty_set @ ( C @ in ) ) )
      | ~ $true
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[43218,1485]) ).

thf(43771,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk1 @ sk10 ) ) @ in ) )
       != ( empty_set @ ( C @ in ) ) )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(simp,[status(thm)],[43770]) ).

thf(44109,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( A @ set_union2 ) )
       != empty_set )
      | ( ( empty_set @ ( B @ ( sk1 @ sk10 ) ) )
       != C )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(simp,[status(thm)],[43771]) ).

thf(44179,plain,
    ! [A: $i] :
      ( ( ( sk1 @ ( A @ set_union2 ) )
       != empty_set )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(simp,[status(thm)],[44109]) ).

thf(446,plain,
    ! [B: $i,A: $i] :
      ( ( B != empty_set )
      | ~ ( sk2 @ ( empty_set @ subset ) )
      | ~ ( A @ ( sk2 @ subset ) )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,344]) ).

thf(447,plain,
    ! [A: $i] :
      ( ~ ( sk2 @ ( empty_set @ subset ) )
      | ~ ( A @ ( sk2 @ subset ) )
      | ~ ( A @ ( empty_set @ subset ) )
      | ~ ( empty_set @ ( A @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[446:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).

thf(56594,plain,
    ! [A: $i] :
      ( ~ $true
      | ~ ( A @ ( sk2 @ subset ) )
      | ~ $true
      | ~ ( empty_set @ ( A @ subset ) ) ),
    inference(rewrite,[status(thm)],[447,1524]) ).

thf(56595,plain,
    ! [A: $i] :
      ( ~ ( A @ ( sk2 @ subset ) )
      | ~ ( empty_set @ ( A @ subset ) ) ),
    inference(simp,[status(thm)],[56594]) ).

thf(94003,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( A @ ( empty_set @ sk9 ) ) )
       != ( D @ ( C @ ( B @ sk9 ) ) ) )
      | ~ $true
      | ( D @ ( B @ ( C @ ( D @ sk10 ) ) @ in ) )
      | ( D
        = ( C @ ( B @ set_difference ) ) )
      | ( sk1 @ empty ) ),
    inference(paramod_ordered,[status(thm)],[93777,134]) ).

thf(94004,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( A @ ( empty_set @ sk9 ) ) )
       != ( D @ ( C @ ( B @ sk9 ) ) ) )
      | ( D @ ( B @ ( C @ ( D @ sk10 ) ) @ in ) )
      | ( D
        = ( C @ ( B @ set_difference ) ) )
      | ( sk1 @ empty ) ),
    inference(simp,[status(thm)],[94003]) ).

thf(94005,plain,
    ! [A: $i] :
      ( ( sk1 @ ( empty_set @ ( A @ ( sk1 @ sk10 ) ) @ in ) )
      | ( ( A @ ( empty_set @ set_difference ) )
        = sk1 )
      | ( sk1 @ empty ) ),
    inference(pattern_uni,[status(thm)],[94004:[bind(A,$thf( A )),bind(B,$thf( empty_set )),bind(C,$thf( A )),bind(D,$thf( sk1 ))]]) ).

thf(102580,plain,
    ! [A: $i] :
      ( ( sk1 @ ( empty_set @ ( A @ ( sk1 @ sk10 ) ) @ in ) )
      | ( sk1 = empty_set )
      | ( sk1 @ empty ) ),
    inference(rewrite,[status(thm)],[94005,97]) ).

thf(102950,plain,
    ! [A: $i] :
      ( ( sk1 != sk1 )
      | ( sk1 @ empty )
      | ( empty_set != empty_set )
      | ( sk1 @ ( empty_set @ ( A @ ( sk1 @ sk10 ) ) @ in ) )
      | ( sk1 @ empty ) ),
    inference(paramod_ordered,[status(thm)],[102580,93298]) ).

thf(102951,plain,
    ! [A: $i] :
      ( ( sk1 != sk1 )
      | ( sk1 @ ( empty_set @ ( A @ ( sk1 @ sk10 ) ) @ in ) )
      | ( sk1 @ empty ) ),
    inference(simp,[status(thm)],[102950]) ).

thf(102952,plain,
    ! [A: $i] :
      ( ( sk1 @ ( empty_set @ ( A @ ( sk1 @ sk10 ) ) @ in ) )
      | ( sk1 @ empty ) ),
    inference(pattern_uni,[status(thm)],[102951:[]]) ).

thf(18309,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13962,2298]) ).

thf(18310,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
     != ( D @ ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[18309]) ).

thf(18432,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) )
       != D )
      | ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
       != ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[18310]) ).

thf(18437,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
     != ( D @ ( A @ ( sk2 @ set_union2 ) @ set_union2 ) @ ( C @ set_union2 ) ) ),
    inference(simp,[status(thm)],[18432]) ).

thf(52,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ in ) )
      | ~ ( A @ ( C @ in ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(cnfConj,[status(thm)],[51]) ).

thf(56963,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( C @ set_union2 ) @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( empty_set @ ( D @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[15148,1485]) ).

thf(56964,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( C @ set_union2 ) @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
     != ( empty_set @ ( D @ in ) ) ),
    inference(simp,[status(thm)],[56963]) ).

thf(57366,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( C @ set_union2 ) @ ( A @ set_union2 ) )
       != empty_set )
      | ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
       != D ) ),
    inference(simp,[status(thm)],[56964]) ).

thf(57425,plain,
    ! [B: $i,A: $i] :
      ( ( sk2 @ ( B @ set_union2 ) @ ( A @ set_union2 ) )
     != empty_set ),
    inference(simp,[status(thm)],[57366]) ).

thf(57691,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk2 @ ( D @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) @ ( C @ set_union2 ) )
       != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[139,57425]) ).

thf(57692,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( sk2 @ set_union2 ) @ ( B @ set_union2 ) )
     != empty_set ),
    inference(pattern_uni,[status(thm)],[57691:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).

thf(57786,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( sk2 @ set_union2 ) @ ( B @ set_union2 ) )
     != empty_set ),
    inference(simp,[status(thm)],[57692]) ).

thf(58428,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( C @ ( sk2 @ set_union2 ) @ ( D @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) )
       != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[139,57786]) ).

thf(58429,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( sk2 @ set_union2 ) @ set_union2 ) )
     != empty_set ),
    inference(pattern_uni,[status(thm)],[58428:[bind(A,$thf( A )),bind(B,$thf( F @ ( sk2 @ set_union2 ) )),bind(C,$thf( F )),bind(D,$thf( A ))]]) ).

thf(58504,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( sk2 @ set_union2 ) @ set_union2 ) )
     != empty_set ),
    inference(simp,[status(thm)],[58429]) ).

thf(43075,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( empty_set @ ( A @ ( sk1 @ sk10 ) ) @ in ) )
       != ( B @ ( D @ in ) ) )
      | ( C @ ( B @ set_union2 ) @ ( D @ in ) )
      | ~ $true
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[42387,80]) ).

thf(43076,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( empty_set @ ( A @ ( sk1 @ sk10 ) ) @ in ) )
       != ( B @ ( D @ in ) ) )
      | ( C @ ( B @ set_union2 ) @ ( D @ in ) )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(simp,[status(thm)],[43075]) ).

thf(43077,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( sk1 @ set_union2 ) @ ( empty_set @ ( B @ ( sk1 @ sk10 ) ) @ in ) )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[43076:[bind(A,$thf( F )),bind(B,$thf( sk1 )),bind(C,$thf( C )),bind(D,$thf( empty_set @ ( F @ ( sk1 @ sk10 ) ) ))]]) ).

thf(43217,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( sk1 @ set_union2 ) @ ( empty_set @ ( B @ ( sk1 @ sk10 ) ) @ in ) )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(simp,[status(thm)],[43077]) ).

thf(43296,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk1 @ set_union2 ) @ ( empty_set @ ( B @ ( sk1 @ sk10 ) ) @ in ) )
       != ( empty_set @ ( C @ in ) ) )
      | ~ $true
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[43217,1485]) ).

thf(43297,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk1 @ set_union2 ) @ ( empty_set @ ( B @ ( sk1 @ sk10 ) ) @ in ) )
       != ( empty_set @ ( C @ in ) ) )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(simp,[status(thm)],[43296]) ).

thf(43629,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk1 @ set_union2 ) )
       != empty_set )
      | ( ( empty_set @ ( B @ ( sk1 @ sk10 ) ) )
       != C )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(simp,[status(thm)],[43297]) ).

thf(43716,plain,
    ! [A: $i] :
      ( ( ( A @ ( sk1 @ set_union2 ) )
       != empty_set )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(simp,[status(thm)],[43629]) ).

thf(52775,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ ( sk1 @ set_union2 ) ) )
      | ( empty_set != empty_set )
      | ( sk2 @ ( sk1 @ subset ) )
      | ( A @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1599,43716]) ).

thf(52776,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ ( sk1 @ set_union2 ) ) )
      | ( sk2 @ ( sk1 @ subset ) )
      | ( A @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[52775]) ).

thf(52777,plain,
    ! [B: $i,A: $i] :
      ( ( sk2 @ ( sk1 @ subset ) )
      | ( B @ ( sk1 @ set_union2 ) @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[52776:[bind(A,$thf( E @ ( sk1 @ set_union2 ) )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).

thf(52988,plain,
    ! [B: $i,A: $i] :
      ( ( sk2 @ ( sk1 @ subset ) )
      | ( B @ ( sk1 @ set_union2 ) @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[52777]) ).

thf(53584,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( D @ ( sk1 @ set_union2 ) ) )
      | ( sk2 @ ( sk1 @ subset ) )
      | ( A @ ( B @ set_union2 ) @ ( C @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,52988]) ).

thf(53585,plain,
    ! [B: $i,A: $i] :
      ( ( sk2 @ ( sk1 @ subset ) )
      | ( sk1 @ ( A @ set_union2 ) @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[53584:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).

thf(53651,plain,
    ! [B: $i,A: $i] :
      ( ( sk2 @ ( sk1 @ subset ) )
      | ( sk1 @ ( A @ set_union2 ) @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[53585]) ).

thf(20837,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk4 @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( empty_set @ ( C @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[20241,1485]) ).

thf(20838,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( sk4 @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
     != ( empty_set @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[20837]) ).

thf(21150,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk4 @ set_union2 ) )
       != empty_set )
      | ( ( empty_set @ ( B @ ( sk4 @ sk10 ) ) )
       != C ) ),
    inference(simp,[status(thm)],[20838]) ).

thf(21236,plain,
    ! [A: $i] :
      ( ( A @ ( sk4 @ set_union2 ) )
     != empty_set ),
    inference(simp,[status(thm)],[21150]) ).

thf(21639,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
       != ( C @ ( sk4 @ set_union2 ) ) )
      | ( empty_set != empty_set )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7213,21236]) ).

thf(21640,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
       != ( C @ ( sk4 @ set_union2 ) ) )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[21639]) ).

thf(21641,plain,
    ! [B: $i,A: $i] : ( B @ ( sk4 @ set_union2 ) @ ( A @ ( empty_set @ sk9 ) ) ),
    inference(pattern_uni,[status(thm)],[21640:[bind(A,$thf( A )),bind(B,$thf( E @ ( sk4 @ set_union2 ) )),bind(C,$thf( E ))]]) ).

thf(21703,plain,
    ! [B: $i,A: $i] : ( B @ ( sk4 @ set_union2 ) @ ( A @ ( empty_set @ sk9 ) ) ),
    inference(simp,[status(thm)],[21641]) ).

thf(21926,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( D @ ( sk4 @ set_union2 ) ) )
      | ( A @ ( B @ set_union2 ) @ ( C @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,21703]) ).

thf(21927,plain,
    ! [B: $i,A: $i] : ( sk4 @ ( A @ set_union2 ) @ ( B @ ( empty_set @ sk9 ) ) ),
    inference(pattern_uni,[status(thm)],[21926:[bind(A,$thf( sk4 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).

thf(21985,plain,
    ! [B: $i,A: $i] : ( sk4 @ ( A @ set_union2 ) @ ( B @ ( empty_set @ sk9 ) ) ),
    inference(simp,[status(thm)],[21927]) ).

thf(22869,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( D @ ( E @ in ) ) )
      | ( D @ ( C @ set_union2 ) @ ( E @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[20250,82]) ).

thf(22870,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( D @ ( E @ in ) ) )
      | ( D @ ( C @ set_union2 ) @ ( E @ in ) ) ),
    inference(simp,[status(thm)],[22869]) ).

thf(22871,plain,
    ! [C: $i,B: $i,A: $i] : ( sk4 @ ( C @ set_union2 ) @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) ),
    inference(pattern_uni,[status(thm)],[22870:[bind(A,$thf( I )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( sk4 @ ( I @ set_union2 ) )),bind(E,$thf( empty_set @ ( G @ ( sk4 @ sk10 ) ) ))]]) ).

thf(23006,plain,
    ! [C: $i,B: $i,A: $i] : ( sk4 @ ( C @ set_union2 ) @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) ),
    inference(simp,[status(thm)],[22871]) ).

thf(799,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ in ) )
       != ( D @ ( F @ in ) ) )
      | ( E @ ( F @ in ) )
      | ~ $true
      | ~ ( E @ ( D @ subset ) )
      | ~ ( A @ ( C @ in ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[52,52]) ).

thf(800,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ in ) )
       != ( D @ ( F @ in ) ) )
      | ( E @ ( F @ in ) )
      | ~ ( E @ ( D @ subset ) )
      | ~ ( A @ ( C @ in ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(simp,[status(thm)],[799]) ).

thf(801,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ in ) )
      | ~ ( D @ ( B @ subset ) )
      | ~ ( A @ ( C @ in ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[800:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( E )),bind(F,$thf( C ))]]) ).

thf(802,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ in ) )
      | ~ ( D @ ( B @ subset ) )
      | ~ ( A @ ( C @ in ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(simp,[status(thm)],[801]) ).

thf(26757,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk2 @ ( E @ set_union2 ) @ ( D @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) )
       != ( empty_set @ ( C @ ( sk2 @ sk10 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,13997]) ).

thf(26758,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( sk2 @ ( C @ set_union2 ) @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk2 @ sk10 ) ) ) ),
    inference(pattern_uni,[status(thm)],[26757:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( F @ set_union2 ) )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( F ))]]) ).

thf(26884,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( sk2 @ ( C @ set_union2 ) @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk2 @ sk10 ) ) ) ),
    inference(simp,[status(thm)],[26758]) ).

thf(66647,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( sk4 @ set_union2 ) @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( empty_set @ ( D @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[21163,1485]) ).

thf(66648,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( sk4 @ set_union2 ) @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
     != ( empty_set @ ( D @ in ) ) ),
    inference(simp,[status(thm)],[66647]) ).

thf(66757,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( sk4 @ set_union2 ) @ set_union2 ) )
       != empty_set )
      | ( ( empty_set @ ( B @ ( sk4 @ sk10 ) ) )
       != D ) ),
    inference(simp,[status(thm)],[66648]) ).

thf(66916,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( sk4 @ set_union2 ) @ set_union2 ) )
     != empty_set ),
    inference(simp,[status(thm)],[66757]) ).

thf(67255,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
       != ( C @ ( D @ ( sk4 @ set_union2 ) @ set_union2 ) ) )
      | ( empty_set != empty_set )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7213,66916]) ).

thf(67256,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
       != ( C @ ( D @ ( sk4 @ set_union2 ) @ set_union2 ) ) )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[67255]) ).

thf(67257,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( sk4 @ set_union2 ) @ set_union2 ) @ ( A @ ( empty_set @ sk9 ) ) ),
    inference(pattern_uni,[status(thm)],[67256:[bind(A,$thf( A )),bind(B,$thf( F @ ( H @ ( sk4 @ set_union2 ) @ set_union2 ) )),bind(C,$thf( F )),bind(D,$thf( H ))]]) ).

thf(67430,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( sk4 @ set_union2 ) @ set_union2 ) @ ( A @ ( empty_set @ sk9 ) ) ),
    inference(simp,[status(thm)],[67257]) ).

thf(68991,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( E @ ( sk4 @ set_union2 ) ) )
      | ( D @ ( A @ ( B @ set_union2 ) @ set_union2 ) @ ( C @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,67430]) ).

thf(68992,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( sk4 @ ( A @ set_union2 ) @ set_union2 ) @ ( B @ ( empty_set @ sk9 ) ) ),
    inference(pattern_uni,[status(thm)],[68991:[bind(A,$thf( sk4 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B ))]]) ).

thf(69049,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( sk4 @ ( A @ set_union2 ) @ set_union2 ) @ ( B @ ( empty_set @ sk9 ) ) ),
    inference(simp,[status(thm)],[68992]) ).

thf(2660,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ set_union2 ) )
       != ( E @ ( D @ set_union2 ) ) )
      | ~ ( D @ ( B @ ( A @ set_union2 ) @ ( C @ set_union2 ) @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[139,2298]) ).

thf(2661,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ ( B @ ( A @ set_union2 ) @ ( C @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[2660:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( A ))]]) ).

thf(13847,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( C @ ( C @ ( B @ set_union2 ) @ ( D @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13698,2661]) ).

thf(13848,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
     != ( C @ ( C @ ( B @ set_union2 ) @ ( D @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[13847]) ).

thf(13921,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 != C )
      | ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
       != ( C @ ( B @ set_union2 ) @ ( D @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[13848]) ).

thf(14002,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
     != ( sk2 @ ( B @ set_union2 ) @ ( C @ set_union2 ) ) ),
    inference(simp,[status(thm)],[13921]) ).

thf(57689,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk2 @ ( D @ set_union2 ) @ ( C @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) )
       != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[139,57425]) ).

thf(57690,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( sk2 @ ( B @ set_union2 ) @ set_union2 ) )
     != empty_set ),
    inference(pattern_uni,[status(thm)],[57689:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( E @ set_union2 ) )),bind(C,$thf( A )),bind(D,$thf( E ))]]) ).

thf(57785,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( sk2 @ ( B @ set_union2 ) @ set_union2 ) )
     != empty_set ),
    inference(simp,[status(thm)],[57690]) ).

thf(58185,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk2 @ ( D @ set_union2 ) ) )
      | ( ( C @ ( A @ ( B @ set_union2 ) @ set_union2 ) )
       != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[139,57785]) ).

thf(58186,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( sk2 @ set_union2 ) @ set_union2 ) )
     != empty_set ),
    inference(pattern_uni,[status(thm)],[58185:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).

thf(58265,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( sk2 @ set_union2 ) @ set_union2 ) )
     != empty_set ),
    inference(simp,[status(thm)],[58186]) ).

thf(59430,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( C @ ( sk2 @ set_union2 ) ) )
      | ( ( D @ ( A @ ( B @ set_union2 ) @ set_union2 ) )
       != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[139,58265]) ).

thf(59431,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( sk2 @ ( A @ set_union2 ) @ set_union2 ) )
     != empty_set ),
    inference(pattern_uni,[status(thm)],[59430:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).

thf(59495,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( sk2 @ ( A @ set_union2 ) @ set_union2 ) )
     != empty_set ),
    inference(simp,[status(thm)],[59431]) ).

thf(3733,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( F @ ( D @ ( F @ ( E @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true
      | ~ ( A @ ( C @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[80,2504]) ).

thf(3734,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( F @ ( D @ ( F @ ( E @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ ( A @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[3733]) ).

thf(3735,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( C @ ( A @ ( D @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[3734:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( H @ ( L @ ( K @ set_union2 ) @ ( I @ set_union2 ) @ set_union2 ) )),bind(D,$thf( H )),bind(E,$thf( I )),bind(F,$thf( L @ ( K @ set_union2 ) ))]]) ).

thf(3768,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( C @ ( A @ ( D @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[3735]) ).

thf(20020,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( D @ ( B @ ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19907,3768]) ).

thf(20021,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
     != ( D @ ( B @ ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[20020]) ).

thf(20144,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 != D )
      | ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
       != ( B @ ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[20021]) ).

thf(20203,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
     != ( B @ ( D @ ( sk4 @ set_union2 ) @ ( C @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[20144]) ).

thf(15022,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( C @ ( D @ ( C @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13960,2192]) ).

thf(15023,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
     != ( C @ ( D @ ( C @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[15022]) ).

thf(15118,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) )
       != C )
      | ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
       != ( D @ ( C @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[15023]) ).

thf(15161,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
     != ( C @ ( sk2 @ ( A @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[15118]) ).

thf(13808,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( B @ ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13698,3768]) ).

thf(13809,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
     != ( D @ ( B @ ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[13808]) ).

thf(13935,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 != D )
      | ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
       != ( B @ ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[13809]) ).

thf(14019,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
     != ( B @ ( D @ ( sk2 @ set_union2 ) @ ( C @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[13935]) ).

thf(18174,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( C @ ( D @ ( E @ ( C @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13962,8069]) ).

thf(18175,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
     != ( C @ ( D @ ( E @ ( C @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[18174]) ).

thf(18404,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) )
       != C )
      | ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
       != ( D @ ( E @ ( C @ set_union2 ) @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[18175]) ).

thf(18511,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
     != ( C @ ( D @ ( A @ ( sk2 @ set_union2 ) @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[18404]) ).

thf(13908,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( C @ ( D @ in ) ) )
      | ~ $true
      | ~ ( C @ ( B @ set_difference ) @ ( D @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[13698,122]) ).

thf(13909,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( C @ ( D @ in ) ) )
      | ~ ( C @ ( B @ set_difference ) @ ( D @ in ) ) ),
    inference(simp,[status(thm)],[13908]) ).

thf(13910,plain,
    ! [B: $i,A: $i] :
      ~ ( sk2 @ ( A @ set_difference ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) ),
    inference(pattern_uni,[status(thm)],[13909:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( sk2 )),bind(D,$thf( empty_set @ ( F @ ( sk2 @ sk10 ) ) ))]]) ).

thf(13992,plain,
    ! [B: $i,A: $i] :
      ~ ( sk2 @ ( A @ set_difference ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) ),
    inference(simp,[status(thm)],[13910]) ).

thf(18288,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( C @ ( C @ ( E @ set_union2 ) @ ( D @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13962,11173]) ).

thf(18289,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
     != ( C @ ( C @ ( E @ set_union2 ) @ ( D @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[18288]) ).

thf(18416,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) )
       != C )
      | ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
       != ( C @ ( E @ set_union2 ) @ ( D @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[18289]) ).

thf(18528,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
     != ( A @ ( sk2 @ set_union2 ) @ ( D @ set_union2 ) @ ( C @ set_union2 ) ) ),
    inference(simp,[status(thm)],[18416]) ).

thf(54174,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
       != ( sk1 @ ( C @ set_union2 ) ) )
      | ( empty_set != empty_set )
      | ( sk2 @ ( sk1 @ subset ) )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7213,44179]) ).

thf(54175,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
       != ( sk1 @ ( C @ set_union2 ) ) )
      | ( sk2 @ ( sk1 @ subset ) )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[54174]) ).

thf(54176,plain,
    ! [B: $i,A: $i] :
      ( ( sk2 @ ( sk1 @ subset ) )
      | ( sk1 @ ( B @ set_union2 ) @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[54175:[bind(A,$thf( A )),bind(B,$thf( sk1 @ ( D @ set_union2 ) )),bind(C,$thf( D ))]]) ).

thf(54521,plain,
    ! [B: $i,A: $i] :
      ( ( sk2 @ ( sk1 @ subset ) )
      | ( sk1 @ ( B @ set_union2 ) @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[54176]) ).

thf(13706,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( B @ ( C @ ( B @ set_union2 ) @ ( D @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13698,3231]) ).

thf(13707,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
     != ( B @ ( C @ ( B @ set_union2 ) @ ( D @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[13706]) ).

thf(13918,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 != B )
      | ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
       != ( C @ ( B @ set_union2 ) @ ( D @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[13707]) ).

thf(13998,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
     != ( B @ ( sk2 @ set_union2 ) @ ( C @ set_union2 ) ) ),
    inference(simp,[status(thm)],[13918]) ).

thf(27396,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( D @ ( sk2 @ set_union2 ) @ ( E @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) )
       != ( empty_set @ ( C @ ( sk2 @ sk10 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,13998]) ).

thf(27397,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( sk2 @ set_union2 ) @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk2 @ sk10 ) ) ) ),
    inference(pattern_uni,[status(thm)],[27396:[bind(A,$thf( A )),bind(B,$thf( G @ ( sk2 @ set_union2 ) )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( A ))]]) ).

thf(27470,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( sk2 @ set_union2 ) @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk2 @ sk10 ) ) ) ),
    inference(simp,[status(thm)],[27397]) ).

thf(36652,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( E @ ( sk2 @ set_union2 ) ) )
      | ( ( C @ ( A @ ( B @ set_union2 ) @ set_union2 ) )
       != ( empty_set @ ( D @ ( sk2 @ sk10 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,27470]) ).

thf(36653,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( sk2 @ ( A @ set_union2 ) @ set_union2 ) )
     != ( empty_set @ ( C @ ( sk2 @ sk10 ) ) ) ),
    inference(pattern_uni,[status(thm)],[36652:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B ))]]) ).

thf(36743,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( sk2 @ ( A @ set_union2 ) @ set_union2 ) )
     != ( empty_set @ ( C @ ( sk2 @ sk10 ) ) ) ),
    inference(simp,[status(thm)],[36653]) ).

thf(13853,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( C @ ( D @ ( C @ ( B @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13698,2569]) ).

thf(13854,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
     != ( C @ ( D @ ( C @ ( B @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[13853]) ).

thf(13916,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 != C )
      | ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
       != ( D @ ( C @ ( B @ set_union2 ) @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[13854]) ).

thf(13996,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
     != ( C @ ( sk2 @ ( B @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[13916]) ).

thf(26435,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( E @ ( sk2 @ ( D @ set_union2 ) @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) )
       != ( empty_set @ ( C @ ( sk2 @ sk10 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,13996]) ).

thf(26436,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( C @ set_union2 ) @ ( A @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk2 @ sk10 ) ) ) ),
    inference(pattern_uni,[status(thm)],[26435:[bind(A,$thf( sk2 @ ( F @ set_union2 ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F )),bind(E,$thf( B ))]]) ).

thf(26534,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( C @ set_union2 ) @ ( A @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk2 @ sk10 ) ) ) ),
    inference(simp,[status(thm)],[26436]) ).

thf(590,plain,
    ! [B: $i,A: $i] :
      ( ( B != sk1 )
      | ( ( sk2 @ ( sk2 @ ( A @ set_union2 ) @ set_difference ) )
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ~ ( B @ empty )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[42,24]) ).

thf(591,plain,
    ! [A: $i] :
      ( ( ( sk2 @ ( sk2 @ ( A @ set_union2 ) @ set_difference ) )
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ~ ( sk1 @ empty )
      | ~ ( A @ empty ) ),
    inference(pattern_uni,[status(thm)],[590:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).

thf(18,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( A @ empty )
     => ~ ( A @ ( B @ set_union2 ) @ empty ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).

thf(104,plain,
    ! [A: $i,B: $i] :
      ( ~ ( A @ empty )
     => ~ ( A @ ( B @ set_union2 ) @ empty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(105,plain,
    ! [A: $i] :
      ( ~ ( A @ empty )
     => ~ ? [B: $i] : ( A @ ( B @ set_union2 ) @ empty ) ),
    inference(miniscope,[status(thm)],[104]) ).

thf(106,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ set_union2 ) @ empty )
      | ( A @ empty ) ),
    inference(cnf,[status(esa)],[105]) ).

thf(43009,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( empty_set @ ( C @ ( sk1 @ sk10 ) ) ) )
      | ( sk1 @ ( empty_set @ in ) )
      | ( sk2 @ ( sk1 @ subset ) )
      | ( A @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1599,42387]) ).

thf(43010,plain,
    ! [B: $i,A: $i] :
      ( ( sk1 @ ( empty_set @ in ) )
      | ( sk2 @ ( sk1 @ subset ) )
      | ( empty_set @ ( B @ ( sk1 @ sk10 ) ) @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[43009:[bind(A,$thf( empty_set @ ( E @ ( sk1 @ sk10 ) ) )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).

thf(43203,plain,
    ! [B: $i,A: $i] :
      ( ( sk1 @ ( empty_set @ in ) )
      | ( sk2 @ ( sk1 @ subset ) )
      | ( empty_set @ ( B @ ( sk1 @ sk10 ) ) @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[43010]) ).

thf(936,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
       != ( sk2 @ ( sk2 @ ( sk1 @ set_union2 ) @ set_difference ) ) )
      | ( ( B @ ( A @ set_difference ) )
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ( A @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
      | ( C @ ( B @ ( A @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[132,24]) ).

thf(937,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ set_difference ) )
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ( A @ ( A @ ( B @ ( sk2 @ ( sk2 @ ( sk1 @ set_union2 ) @ set_difference ) @ sk11 ) ) @ in ) )
      | ( sk2 @ ( sk2 @ ( sk1 @ set_union2 ) @ set_difference ) @ ( B @ ( A @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[936:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk2 @ ( sk2 @ ( sk1 @ set_union2 ) @ set_difference ) ))]]) ).

thf(35913,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk2 @ ( E @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) @ ( C @ set_union2 ) )
       != ( empty_set @ ( D @ ( sk2 @ sk10 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,26534]) ).

thf(35914,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( sk2 @ set_union2 ) @ ( B @ set_union2 ) )
     != ( empty_set @ ( C @ ( sk2 @ sk10 ) ) ) ),
    inference(pattern_uni,[status(thm)],[35913:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A ))]]) ).

thf(36013,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( sk2 @ set_union2 ) @ ( B @ set_union2 ) )
     != ( empty_set @ ( C @ ( sk2 @ sk10 ) ) ) ),
    inference(simp,[status(thm)],[35914]) ).

thf(14924,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( E @ ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13960,2492]) ).

thf(14925,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
     != ( E @ ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[14924]) ).

thf(15135,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) )
       != E )
      | ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
       != ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[14925]) ).

thf(15186,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
     != ( sk2 @ ( A @ set_union2 ) @ ( D @ set_union2 ) @ ( C @ set_union2 ) ) ),
    inference(simp,[status(thm)],[15135]) ).

thf(866,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ ( D @ sk5 ) ) )
      | ( D @ ( C @ subset ) )
      | ~ ( D @ ( B @ in ) )
      | ~ ( B @ empty )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[42,56]) ).

thf(867,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ subset ) )
      | ~ ( B @ ( A @ in ) )
      | ~ ( A @ empty )
      | ~ ( C @ ( B @ sk5 ) @ empty ) ),
    inference(pattern_uni,[status(thm)],[866:[bind(A,$thf( F @ ( E @ sk5 ) )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( E ))]]) ).

thf(877,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ subset ) )
      | ~ ( B @ ( A @ in ) )
      | ~ ( A @ empty )
      | ~ ( C @ ( B @ sk5 ) @ empty ) ),
    inference(simp,[status(thm)],[867]) ).

thf(37275,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( sk2 @ ( sk1 @ subset ) )
      | ( empty_set != empty_set )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[59,37040]) ).

thf(37276,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( sk2 @ ( sk1 @ subset ) )
      | ~ ( A @ empty ) ),
    inference(simp,[status(thm)],[37275]) ).

thf(37277,plain,
    ( ( sk2 @ ( sk1 @ subset ) )
    | ~ ( sk1 @ empty ) ),
    inference(pattern_uni,[status(thm)],[37276:[bind(A,$thf( sk1 ))]]) ).

thf(30613,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( D @ ( sk4 @ set_union2 ) @ ( E @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) )
       != ( empty_set @ ( C @ ( sk4 @ sk10 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,20194]) ).

thf(30614,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( sk4 @ set_union2 ) @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk4 @ sk10 ) ) ) ),
    inference(pattern_uni,[status(thm)],[30613:[bind(A,$thf( A )),bind(B,$thf( G @ ( sk4 @ set_union2 ) )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( A ))]]) ).

thf(30748,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( sk4 @ set_union2 ) @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk4 @ sk10 ) ) ) ),
    inference(simp,[status(thm)],[30614]) ).

thf(40528,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( E @ ( sk4 @ set_union2 ) ) )
      | ( ( C @ ( A @ ( B @ set_union2 ) @ set_union2 ) )
       != ( empty_set @ ( D @ ( sk4 @ sk10 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,30748]) ).

thf(40529,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( sk4 @ ( A @ set_union2 ) @ set_union2 ) )
     != ( empty_set @ ( C @ ( sk4 @ sk10 ) ) ) ),
    inference(pattern_uni,[status(thm)],[40528:[bind(A,$thf( sk4 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B ))]]) ).

thf(40632,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( sk4 @ ( A @ set_union2 ) @ set_union2 ) )
     != ( empty_set @ ( C @ ( sk4 @ sk10 ) ) ) ),
    inference(simp,[status(thm)],[40529]) ).

thf(12965,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( empty_set @ ( A @ set_union2 ) )
       != ( E @ ( D @ set_union2 ) ) )
      | ~ ( D @ ( B @ ( A @ ( C @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[103,3768]) ).

thf(12966,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( A @ ( B @ ( A @ ( C @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[12965:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( empty_set ))]]) ).

thf(3226,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( E @ ( D @ set_union2 ) ) )
      | ~ ( E @ ( A @ ( B @ set_union2 ) @ ( C @ set_union2 ) @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[139,2492]) ).

thf(3227,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ ( A @ ( B @ set_union2 ) @ ( C @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[3226:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).

thf(18392,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( C @ ( D @ set_union2 ) @ ( E @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13962,3227]) ).

thf(18393,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
     != ( D @ ( C @ ( D @ set_union2 ) @ ( E @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[18392]) ).

thf(18399,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) )
       != D )
      | ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
       != ( C @ ( D @ set_union2 ) @ ( E @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[18393]) ).

thf(18507,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
     != ( C @ ( A @ ( sk2 @ set_union2 ) @ set_union2 ) @ ( D @ set_union2 ) ) ),
    inference(simp,[status(thm)],[18399]) ).

thf(100036,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk2 @ ( D @ set_union2 ) ) )
      | ~ ( empty_set @ ( C @ ( A @ ( B @ set_union2 ) @ set_union2 ) @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[139,98332]) ).

thf(100037,plain,
    ! [B: $i,A: $i] :
      ~ ( empty_set @ ( B @ ( A @ ( sk2 @ set_union2 ) @ set_union2 ) @ subset ) ),
    inference(pattern_uni,[status(thm)],[100036:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).

thf(100212,plain,
    ! [B: $i,A: $i] :
      ~ ( empty_set @ ( B @ ( A @ ( sk2 @ set_union2 ) @ set_union2 ) @ subset ) ),
    inference(simp,[status(thm)],[100037]) ).

thf(256,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B != empty_set )
      | ( ( A @ ( C @ set_union2 ) )
        = C )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,103]) ).

thf(257,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ set_union2 ) )
        = B )
      | ~ ( A @ ( empty_set @ subset ) )
      | ~ ( empty_set @ ( A @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[256:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).

thf(312,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ set_union2 ) )
        = B )
      | ~ ( A @ ( empty_set @ subset ) )
      | ~ ( empty_set @ ( A @ subset ) ) ),
    inference(simp,[status(thm)],[257]) ).

thf(24050,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ set_union2 ) )
        = B )
      | ~ $true
      | ~ ( empty_set @ ( A @ subset ) ) ),
    inference(rewrite,[status(thm)],[312,1524]) ).

thf(24051,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ set_union2 ) )
        = B )
      | ~ ( empty_set @ ( A @ subset ) ) ),
    inference(simp,[status(thm)],[24050]) ).

thf(26789,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ set_union2 ) )
       != ( sk2 @ ( E @ set_union2 ) @ ( D @ set_union2 ) ) )
      | ( B
       != ( empty_set @ ( C @ ( sk2 @ sk10 ) ) ) )
      | ~ ( empty_set @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[24051,13997]) ).

thf(26790,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( empty_set @ ( B @ ( sk2 @ sk10 ) ) ) )
      | ~ ( empty_set @ ( sk2 @ ( C @ set_union2 ) @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[26789:[bind(A,$thf( sk2 @ ( F @ set_union2 ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( F ))]]) ).

thf(26900,plain,
    ! [A: $i] :
      ~ ( empty_set @ ( sk2 @ ( A @ set_union2 ) @ subset ) ),
    inference(simp,[status(thm)],[26790]) ).

thf(27003,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk2 @ ( C @ set_union2 ) ) )
      | ~ ( empty_set @ ( A @ ( B @ set_union2 ) @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[139,26900]) ).

thf(27004,plain,
    ! [A: $i] :
      ~ ( empty_set @ ( A @ ( sk2 @ set_union2 ) @ subset ) ),
    inference(pattern_uni,[status(thm)],[27003:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).

thf(93478,plain,
    ! [A: $i] :
      ( ( ( empty_set @ ( A @ ( sk2 @ set_union2 ) @ subset ) )
       != ( empty_set @ ( sk1 @ subset ) ) )
      | ~ $true
      | ( sk1 != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[92946,27004]) ).

thf(93479,plain,
    ! [A: $i] :
      ( ( ( empty_set @ ( A @ ( sk2 @ set_union2 ) @ subset ) )
       != ( empty_set @ ( sk1 @ subset ) ) )
      | ( sk1 != empty_set ) ),
    inference(simp,[status(thm)],[93478]) ).

thf(93616,plain,
    ! [A: $i] :
      ( ( empty_set != empty_set )
      | ( ( A @ ( sk2 @ set_union2 ) )
       != sk1 )
      | ( sk1 != empty_set ) ),
    inference(simp,[status(thm)],[93479]) ).

thf(93701,plain,
    ! [A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) )
       != sk1 )
      | ( sk1 != empty_set ) ),
    inference(simp,[status(thm)],[93616]) ).

thf(13742,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( B @ ( B @ ( C @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13698,2236]) ).

thf(13743,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
     != ( B @ ( B @ ( C @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[13742]) ).

thf(13954,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sk2 != B )
      | ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
       != ( B @ ( C @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[13743]) ).

thf(13957,plain,
    ! [B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
     != ( sk2 @ ( B @ set_union2 ) ) ),
    inference(simp,[status(thm)],[13954]) ).

thf(14480,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk2 @ ( D @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) )
       != ( empty_set @ ( C @ ( sk2 @ sk10 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,13957]) ).

thf(14481,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( sk2 @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk2 @ sk10 ) ) ) ),
    inference(pattern_uni,[status(thm)],[14480:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).

thf(14537,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( sk2 @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk2 @ sk10 ) ) ) ),
    inference(simp,[status(thm)],[14481]) ).

thf(18176,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( C @ ( C @ ( D @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13962,2236]) ).

thf(18177,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
     != ( C @ ( C @ ( D @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[18176]) ).

thf(18411,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) )
       != C )
      | ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
       != ( C @ ( D @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[18177]) ).

thf(18520,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
     != ( A @ ( sk2 @ set_union2 ) @ ( C @ set_union2 ) ) ),
    inference(simp,[status(thm)],[18411]) ).

thf(224,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ ( empty_set @ set_difference ) ) )
      | ( B = empty_set )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,97]) ).

thf(225,plain,
    ! [B: $i,A: $i] :
      ( ( A = empty_set )
      | ~ ( B @ ( empty_set @ set_difference ) @ ( A @ subset ) )
      | ~ ( A @ ( B @ ( empty_set @ set_difference ) @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[224:[bind(A,$thf( E @ ( empty_set @ set_difference ) )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).

thf(346,plain,
    ! [B: $i,A: $i] :
      ( ( A = empty_set )
      | ~ ( B @ ( empty_set @ set_difference ) @ ( A @ subset ) )
      | ~ ( A @ ( B @ ( empty_set @ set_difference ) @ subset ) ) ),
    inference(simp,[status(thm)],[225]) ).

thf(38090,plain,
    ! [A: $i] :
      ( ( A = empty_set )
      | ~ ( empty_set @ ( A @ subset ) )
      | ~ ( A @ ( empty_set @ subset ) ) ),
    inference(rewrite,[status(thm)],[346,97]) ).

thf(94642,plain,
    ! [A: $i] :
      ( ( ( empty_set @ ( sk1 @ subset ) )
       != ( empty_set @ ( A @ subset ) ) )
      | ( A = empty_set )
      | ~ $true
      | ~ ( A @ ( empty_set @ subset ) )
      | ~ ( sk1 @ empty ) ),
    inference(paramod_ordered,[status(thm)],[93446,38090]) ).

thf(94643,plain,
    ! [A: $i] :
      ( ( ( empty_set @ ( sk1 @ subset ) )
       != ( empty_set @ ( A @ subset ) ) )
      | ( A = empty_set )
      | ~ ( A @ ( empty_set @ subset ) )
      | ~ ( sk1 @ empty ) ),
    inference(simp,[status(thm)],[94642]) ).

thf(94644,plain,
    ( ( sk1 = empty_set )
    | ~ ( sk1 @ ( empty_set @ subset ) )
    | ~ ( sk1 @ empty ) ),
    inference(pattern_uni,[status(thm)],[94643:[bind(A,$thf( sk1 ))]]) ).

thf(133764,plain,
    ( ( sk1 = empty_set )
    | ~ $true
    | ~ ( sk1 @ empty ) ),
    inference(rewrite,[status(thm)],[94644,1524]) ).

thf(133765,plain,
    ( ( sk1 = empty_set )
    | ~ ( sk1 @ empty ) ),
    inference(simp,[status(thm)],[133764]) ).

thf(200,plain,
    ! [B: $i,A: $i] :
      ( ( B
       != ( sk2 @ ( sk1 @ set_union2 ) ) )
      | ( ( sk2 @ ( A @ set_difference ) )
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,24]) ).

thf(201,plain,
    ! [A: $i] :
      ( ( ( sk2 @ ( A @ set_difference ) )
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ~ ( A @ ( sk2 @ ( sk1 @ set_union2 ) @ subset ) )
      | ~ ( sk2 @ ( sk1 @ set_union2 ) @ ( A @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[200:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ set_union2 ) ))]]) ).

thf(367,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ ( C @ set_union2 ) ) )
      | ( B = C )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,67]) ).

thf(368,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( B @ ( B @ set_union2 ) @ ( A @ subset ) )
      | ~ ( A @ ( B @ ( B @ set_union2 ) @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[367:[bind(A,$thf( E @ ( E @ set_union2 ) )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).

thf(381,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( B @ ( B @ set_union2 ) @ ( A @ subset ) )
      | ~ ( A @ ( B @ ( B @ set_union2 ) @ subset ) ) ),
    inference(simp,[status(thm)],[368]) ).

thf(30645,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ set_union2 ) )
       != ( D @ ( sk4 @ set_union2 ) @ ( E @ set_union2 ) ) )
      | ( B
       != ( empty_set @ ( C @ ( sk4 @ sk10 ) ) ) )
      | ~ ( empty_set @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[24051,20194]) ).

thf(30646,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( empty_set @ ( B @ ( sk4 @ sk10 ) ) ) )
      | ~ ( empty_set @ ( C @ ( sk4 @ set_union2 ) @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[30645:[bind(A,$thf( G @ ( sk4 @ set_union2 ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( B ))]]) ).

thf(30764,plain,
    ! [A: $i] :
      ~ ( empty_set @ ( A @ ( sk4 @ set_union2 ) @ subset ) ),
    inference(simp,[status(thm)],[30646]) ).

thf(93471,plain,
    ! [A: $i] :
      ( ( ( empty_set @ ( A @ ( sk4 @ set_union2 ) @ subset ) )
       != ( empty_set @ ( sk1 @ subset ) ) )
      | ~ $true
      | ( sk1 != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[92946,30764]) ).

thf(93472,plain,
    ! [A: $i] :
      ( ( ( empty_set @ ( A @ ( sk4 @ set_union2 ) @ subset ) )
       != ( empty_set @ ( sk1 @ subset ) ) )
      | ( sk1 != empty_set ) ),
    inference(simp,[status(thm)],[93471]) ).

thf(93606,plain,
    ! [A: $i] :
      ( ( empty_set != empty_set )
      | ( ( A @ ( sk4 @ set_union2 ) )
       != sk1 )
      | ( sk1 != empty_set ) ),
    inference(simp,[status(thm)],[93472]) ).

thf(93692,plain,
    ! [A: $i] :
      ( ( ( A @ ( sk4 @ set_union2 ) )
       != sk1 )
      | ( sk1 != empty_set ) ),
    inference(simp,[status(thm)],[93606]) ).

thf(36129,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( empty_set != empty_set )
      | ( ( sk1 @ ( sk2 @ subset ) )
       != ( sk2 @ ( sk1 @ subset ) ) )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[59,35744]) ).

thf(36130,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( ( sk1 @ ( sk2 @ subset ) )
       != ( sk2 @ ( sk1 @ subset ) ) )
      | ~ ( A @ empty ) ),
    inference(simp,[status(thm)],[36129]) ).

thf(36131,plain,
    ( ( ( sk1 @ ( sk2 @ subset ) )
     != ( sk2 @ ( sk1 @ subset ) ) )
    | ~ ( sk1 @ empty ) ),
    inference(pattern_uni,[status(thm)],[36130:[bind(A,$thf( sk1 ))]]) ).

thf(188,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( sk2 @ ( sk2 @ ( sk1 @ set_union2 ) @ set_difference ) ) )
      | ( B
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,24]) ).

thf(189,plain,
    ! [A: $i] :
      ( ( A
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ~ ( sk2 @ ( sk2 @ ( sk1 @ set_union2 ) @ set_difference ) @ ( A @ subset ) )
      | ~ ( A @ ( sk2 @ ( sk2 @ ( sk1 @ set_union2 ) @ set_difference ) @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[188:[bind(A,$thf( sk2 @ ( sk2 @ ( sk1 @ set_union2 ) @ set_difference ) )),bind(B,$thf( B ))]]) ).

thf(334,plain,
    ( ~ ( sk2 @ ( sk2 @ ( sk1 @ set_union2 ) @ set_difference ) @ ( sk2 @ ( sk1 @ set_difference ) @ subset ) )
    | ~ ( sk2 @ ( sk1 @ set_difference ) @ ( sk2 @ ( sk2 @ ( sk1 @ set_union2 ) @ set_difference ) @ subset ) ) ),
    inference(simp,[status(thm)],[189]) ).

thf(952,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
       != ( sk2 @ ( sk1 @ set_union2 ) ) )
      | ( ( B @ ( A @ set_difference ) )
       != sk1 )
      | ( A @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
      | ( C @ ( B @ ( A @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[132,147]) ).

thf(953,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ set_difference ) )
       != sk1 )
      | ( A @ ( A @ ( B @ ( sk2 @ ( sk1 @ set_union2 ) @ sk11 ) ) @ in ) )
      | ( sk2 @ ( sk1 @ set_union2 ) @ ( B @ ( A @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[952:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk2 @ ( sk1 @ set_union2 ) ))]]) ).

thf(130378,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( empty_set @ ( A @ set_difference ) )
       != ( C @ ( B @ set_difference ) ) )
      | ( A != sk1 )
      | ( B @ ( B @ ( C @ ( sk2 @ ( sk1 @ set_union2 ) @ sk11 ) ) @ in ) )
      | ( sk2 @ ( sk1 @ set_union2 ) @ ( C @ ( B @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,953]) ).

thf(130379,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( A @ ( A @ ( empty_set @ ( sk2 @ ( sk1 @ set_union2 ) @ sk11 ) ) @ in ) )
      | ( sk2 @ ( sk1 @ set_union2 ) @ ( empty_set @ ( A @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[130378:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( empty_set ))]]) ).

thf(131021,plain,
    ( ( sk1 @ ( sk1 @ ( empty_set @ ( sk2 @ ( sk1 @ set_union2 ) @ sk11 ) ) @ in ) )
    | ( sk2 @ ( sk1 @ set_union2 ) @ ( empty_set @ ( sk1 @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[130379]) ).

thf(83427,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk4 @ ( C @ set_union2 ) @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( E @ ( D @ in ) ) )
      | ~ ( D @ ( E @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[23002,64]) ).

thf(83428,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk4 @ ( C @ set_union2 ) @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( E @ ( D @ in ) ) )
      | ~ ( D @ ( E @ in ) ) ),
    inference(simp,[status(thm)],[83427]) ).

thf(83429,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ ( B @ ( sk4 @ ( C @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[83428:[bind(A,$thf( J )),bind(B,$thf( G )),bind(C,$thf( K )),bind(D,$thf( empty_set @ ( G @ ( sk4 @ sk10 ) ) )),bind(E,$thf( J @ ( sk4 @ ( K @ set_union2 ) @ set_union2 ) ))]]) ).

thf(83890,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ ( B @ ( sk4 @ ( C @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[83429]) ).

thf(122927,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( D @ ( F @ ( sk4 @ set_union2 ) @ ( E @ set_union2 ) @ set_union2 ) ) )
      | ( B
       != ( empty_set @ ( C @ ( sk4 @ sk10 ) ) ) )
      | ~ ( empty_set @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[95261,20203]) ).

thf(122928,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( empty_set @ ( B @ ( sk4 @ sk10 ) ) ) )
      | ~ ( empty_set @ ( D @ ( sk4 @ set_union2 ) @ ( C @ set_union2 ) @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[122927:[bind(A,$thf( J @ ( sk4 @ set_union2 ) @ ( G @ set_union2 ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( G )),bind(F,$thf( J ))]]) ).

thf(123101,plain,
    ! [B: $i,A: $i] :
      ~ ( empty_set @ ( B @ ( sk4 @ set_union2 ) @ ( A @ set_union2 ) @ subset ) ),
    inference(simp,[status(thm)],[122928]) ).

thf(67336,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( C @ ( D @ ( sk4 @ set_union2 ) @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) )
       != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[139,66916]) ).

thf(67337,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( sk4 @ set_union2 ) @ ( A @ set_union2 ) )
     != empty_set ),
    inference(pattern_uni,[status(thm)],[67336:[bind(A,$thf( F @ ( sk4 @ set_union2 ) )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( F ))]]) ).

thf(67390,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( sk4 @ set_union2 ) @ ( A @ set_union2 ) )
     != empty_set ),
    inference(simp,[status(thm)],[67337]) ).

thf(68392,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
       != ( D @ ( sk4 @ set_union2 ) @ ( C @ set_union2 ) ) )
      | ( empty_set != empty_set )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7213,67390]) ).

thf(68393,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
       != ( D @ ( sk4 @ set_union2 ) @ ( C @ set_union2 ) ) )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[68392]) ).

thf(68394,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( sk4 @ set_union2 ) @ ( B @ set_union2 ) @ ( A @ ( empty_set @ sk9 ) ) ),
    inference(pattern_uni,[status(thm)],[68393:[bind(A,$thf( A )),bind(B,$thf( H @ ( sk4 @ set_union2 ) @ ( E @ set_union2 ) )),bind(C,$thf( E )),bind(D,$thf( H ))]]) ).

thf(68562,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( sk4 @ set_union2 ) @ ( B @ set_union2 ) @ ( A @ ( empty_set @ sk9 ) ) ),
    inference(simp,[status(thm)],[68394]) ).

thf(69962,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( E @ ( sk4 @ set_union2 ) ) )
      | ( A @ ( B @ set_union2 ) @ ( D @ set_union2 ) @ ( C @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,68562]) ).

thf(69963,plain,
    ! [C: $i,B: $i,A: $i] : ( sk4 @ ( A @ set_union2 ) @ ( C @ set_union2 ) @ ( B @ ( empty_set @ sk9 ) ) ),
    inference(pattern_uni,[status(thm)],[69962:[bind(A,$thf( sk4 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B ))]]) ).

thf(70061,plain,
    ! [C: $i,B: $i,A: $i] : ( sk4 @ ( A @ set_union2 ) @ ( C @ set_union2 ) @ ( B @ ( empty_set @ sk9 ) ) ),
    inference(simp,[status(thm)],[69963]) ).

thf(26113,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ set_union2 ) )
       != ( E @ ( D @ ( sk2 @ set_union2 ) @ set_union2 ) ) )
      | ( ( B @ ( A @ set_union2 ) )
       != ( empty_set @ ( C @ ( sk2 @ sk10 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,13955]) ).

thf(26114,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( sk2 @ set_union2 ) @ ( A @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk2 @ sk10 ) ) ) ),
    inference(pattern_uni,[status(thm)],[26113:[bind(A,$thf( A )),bind(B,$thf( G @ ( sk2 @ set_union2 ) )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( A ))]]) ).

thf(26182,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( sk2 @ set_union2 ) @ ( A @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk2 @ sk10 ) ) ) ),
    inference(simp,[status(thm)],[26114]) ).

thf(13810,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( B @ ( B @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13698,1884]) ).

thf(13811,plain,
    ! [B: $i,A: $i] :
      ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
     != ( B @ ( B @ in ) ) ),
    inference(simp,[status(thm)],[13810]) ).

thf(13919,plain,
    ! [B: $i,A: $i] :
      ( ( sk2 != B )
      | ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
       != B ) ),
    inference(simp,[status(thm)],[13811]) ).

thf(14000,plain,
    ! [A: $i] :
      ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
     != sk2 ),
    inference(simp,[status(thm)],[13919]) ).

thf(30863,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ set_union2 ) )
       != ( C @ ( sk4 @ set_union2 ) ) )
      | ~ ( empty_set @ ( B @ ( A @ set_union2 ) @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[139,30764]) ).

thf(30864,plain,
    ! [A: $i] :
      ~ ( empty_set @ ( sk4 @ ( A @ set_union2 ) @ subset ) ),
    inference(pattern_uni,[status(thm)],[30863:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( A ))]]) ).

thf(9925,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( empty_set @ set_union2 ) )
       != ( E @ ( D @ set_union2 ) ) )
      | ~ ( E @ ( C @ ( A @ set_union2 ) @ ( B @ set_union2 ) @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[399,2676]) ).

thf(9926,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( A @ ( C @ ( A @ set_union2 ) @ ( B @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[9925:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( empty_set )),bind(E,$thf( A ))]]) ).

thf(15016,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( C @ ( E @ ( C @ set_union2 ) @ ( D @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13960,9926]) ).

thf(15017,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
     != ( C @ ( E @ ( C @ set_union2 ) @ ( D @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[15016]) ).

thf(15123,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) )
       != C )
      | ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
       != ( E @ ( C @ set_union2 ) @ ( D @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[15017]) ).

thf(15169,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
     != ( D @ ( sk2 @ ( A @ set_union2 ) @ set_union2 ) @ ( C @ set_union2 ) ) ),
    inference(simp,[status(thm)],[15123]) ).

thf(20123,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( C @ ( D @ in ) ) )
      | ~ $true
      | ~ ( C @ ( B @ set_difference ) @ ( D @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[19907,122]) ).

thf(20124,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( C @ ( D @ in ) ) )
      | ~ ( C @ ( B @ set_difference ) @ ( D @ in ) ) ),
    inference(simp,[status(thm)],[20123]) ).

thf(20125,plain,
    ! [B: $i,A: $i] :
      ~ ( sk4 @ ( A @ set_difference ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) ),
    inference(pattern_uni,[status(thm)],[20124:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( sk4 )),bind(D,$thf( empty_set @ ( F @ ( sk4 @ sk10 ) ) ))]]) ).

thf(20188,plain,
    ! [B: $i,A: $i] :
      ~ ( sk4 @ ( A @ set_difference ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) ),
    inference(simp,[status(thm)],[20125]) ).

thf(148,plain,
    ! [A: $i] :
      ( ( ( A @ ( empty_set @ set_difference ) )
       != ( sk2 @ ( sk2 @ ( sk1 @ set_union2 ) @ set_difference ) ) )
      | ( ( sk2 @ ( sk1 @ set_difference ) )
       != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[97,24]) ).

thf(149,plain,
    ! [A: $i] :
      ( ( A != sk2 )
      | ( ( sk2 @ ( sk1 @ set_union2 ) )
       != empty_set )
      | ( ( sk2 @ ( sk1 @ set_difference ) )
       != empty_set ) ),
    inference(simp,[status(thm)],[148]) ).

thf(150,plain,
    ( ( ( sk2 @ ( sk1 @ set_union2 ) )
     != empty_set )
    | ( ( sk2 @ ( sk1 @ set_difference ) )
     != empty_set ) ),
    inference(simp,[status(thm)],[149]) ).

thf(151,plain,
    ! [A: $i] :
      ( ( ( A @ ( empty_set @ set_difference ) )
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ( ( sk2 @ ( sk1 @ set_union2 ) )
       != empty_set )
      | ( empty_set != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[97,150]) ).

thf(152,plain,
    ! [A: $i] :
      ( ( ( A @ ( empty_set @ set_difference ) )
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ( ( sk2 @ ( sk1 @ set_union2 ) )
       != empty_set ) ),
    inference(simp,[status(thm)],[151]) ).

thf(153,plain,
    ! [A: $i] :
      ( ( A != sk2 )
      | ( sk1 != empty_set )
      | ( ( sk2 @ ( sk1 @ set_union2 ) )
       != empty_set ) ),
    inference(simp,[status(thm)],[152]) ).

thf(154,plain,
    ( ( sk1 != empty_set )
    | ( ( sk2 @ ( sk1 @ set_union2 ) )
     != empty_set ) ),
    inference(simp,[status(thm)],[153]) ).

thf(274,plain,
    ! [B: $i,A: $i] :
      ( ( B != sk2 )
      | ( sk1 != empty_set )
      | ( ( A @ ( sk1 @ set_union2 ) )
       != empty_set )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,154]) ).

thf(275,plain,
    ! [A: $i] :
      ( ( sk1 != empty_set )
      | ( ( A @ ( sk1 @ set_union2 ) )
       != empty_set )
      | ~ ( A @ ( sk2 @ subset ) )
      | ~ ( sk2 @ ( A @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[274:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).

thf(72,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ in ) )
      | ( A @ ( D @ in ) )
      | ~ ( C @ ( D @ in ) )
      | ( C
       != ( B @ ( A @ set_union2 ) ) ) ),
    inference(cnfConj,[status(thm)],[70]) ).

thf(91,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ in ) )
      | ( A @ ( D @ in ) )
      | ~ ( C @ ( D @ in ) )
      | ( C
       != ( B @ ( A @ set_union2 ) ) ) ),
    inference(lifteq,[status(thm)],[72]) ).

thf(92,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ in ) )
      | ( A @ ( C @ in ) )
      | ~ ( B @ ( A @ set_union2 ) @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[91]) ).

thf(840,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ sk5 ) @ in ) )
       != ( C @ ( E @ in ) ) )
      | ( D @ ( E @ in ) )
      | ~ $true
      | ~ ( D @ ( C @ subset ) )
      | ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[55,52]) ).

thf(841,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ sk5 ) @ in ) )
       != ( C @ ( E @ in ) ) )
      | ( D @ ( E @ in ) )
      | ~ ( D @ ( C @ subset ) )
      | ( B @ ( A @ subset ) ) ),
    inference(simp,[status(thm)],[840]) ).

thf(842,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ sk5 ) @ in ) )
      | ~ ( A @ ( C @ subset ) )
      | ( B @ ( C @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[841:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( G @ ( F @ sk5 ) ))]]) ).

thf(847,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ sk5 ) @ in ) )
      | ~ ( A @ ( C @ subset ) )
      | ( B @ ( C @ subset ) ) ),
    inference(simp,[status(thm)],[842]) ).

thf(18143,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( C @ ( E @ ( D @ ( C @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13962,3745]) ).

thf(18144,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
     != ( C @ ( E @ ( D @ ( C @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[18143]) ).

thf(18421,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) )
       != C )
      | ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
       != ( E @ ( D @ ( C @ set_union2 ) @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[18144]) ).

thf(18535,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
     != ( D @ ( C @ ( A @ ( sk2 @ set_union2 ) @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[18421]) ).

thf(20018,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( C @ ( D @ ( B @ ( C @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19907,3741]) ).

thf(20019,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
     != ( C @ ( D @ ( B @ ( C @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[20018]) ).

thf(20159,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 != C )
      | ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
       != ( D @ ( B @ ( C @ set_union2 ) @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[20019]) ).

thf(20220,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
     != ( C @ ( B @ ( sk4 @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[20159]) ).

thf(20065,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( B @ ( C @ ( B @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19907,2192]) ).

thf(20066,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
     != ( B @ ( C @ ( B @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[20065]) ).

thf(20139,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sk4 != B )
      | ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
       != ( C @ ( B @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[20066]) ).

thf(20197,plain,
    ! [B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
     != ( B @ ( sk4 @ set_union2 ) ) ),
    inference(simp,[status(thm)],[20139]) ).

thf(234,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != empty_set )
      | ( ( B @ ( C @ set_difference ) )
        = C )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,109]) ).

thf(235,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ set_difference ) )
        = B )
      | ~ ( empty_set @ ( A @ subset ) )
      | ~ ( A @ ( empty_set @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[234:[bind(A,$thf( empty_set ))]]) ).

thf(351,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ set_difference ) )
        = B )
      | ~ ( empty_set @ ( A @ subset ) )
      | ~ ( A @ ( empty_set @ subset ) ) ),
    inference(simp,[status(thm)],[235]) ).

thf(41597,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ set_difference ) )
        = B )
      | ~ ( empty_set @ ( A @ subset ) )
      | ~ $true ),
    inference(rewrite,[status(thm)],[351,1524]) ).

thf(41598,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ set_difference ) )
        = B )
      | ~ ( empty_set @ ( A @ subset ) ) ),
    inference(simp,[status(thm)],[41597]) ).

thf(15281,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
       != ( sk2 @ ( C @ set_union2 ) ) )
      | ( empty_set != empty_set )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7213,15192]) ).

thf(15282,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
       != ( sk2 @ ( C @ set_union2 ) ) )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[15281]) ).

thf(15283,plain,
    ! [B: $i,A: $i] : ( sk2 @ ( B @ set_union2 ) @ ( A @ ( empty_set @ sk9 ) ) ),
    inference(pattern_uni,[status(thm)],[15282:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( D @ set_union2 ) )),bind(C,$thf( D ))]]) ).

thf(15368,plain,
    ! [B: $i,A: $i] : ( sk2 @ ( B @ set_union2 ) @ ( A @ ( empty_set @ sk9 ) ) ),
    inference(simp,[status(thm)],[15283]) ).

thf(2564,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( E @ ( D @ set_union2 ) ) )
      | ~ ( D @ ( C @ ( A @ ( B @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[139,2254]) ).

thf(2565,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( A @ ( C @ ( A @ ( B @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[2564:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).

thf(870,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ in ) )
       != ( E @ ( D @ ( E @ sk5 ) @ in ) ) )
      | ( E @ ( D @ subset ) )
      | ~ $true
      | ~ ( A @ ( C @ in ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[52,56]) ).

thf(871,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ in ) )
       != ( E @ ( D @ ( E @ sk5 ) @ in ) ) )
      | ( E @ ( D @ subset ) )
      | ~ ( A @ ( C @ in ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(simp,[status(thm)],[870]) ).

thf(872,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ subset ) )
      | ~ ( A @ ( C @ ( B @ sk5 ) @ in ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[871:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( G @ ( B @ sk5 ) )),bind(D,$thf( G )),bind(E,$thf( B ))]]) ).

thf(879,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ subset ) )
      | ~ ( A @ ( C @ ( B @ sk5 ) @ in ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(simp,[status(thm)],[872]) ).

thf(13717,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13698,3253]) ).

thf(13718,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
     != ( D @ ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[13717]) ).

thf(13929,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 != D )
      | ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
       != ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ ( B @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[13718]) ).

thf(14011,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
     != ( D @ ( sk2 @ set_union2 ) @ ( C @ set_union2 ) @ ( B @ set_union2 ) ) ),
    inference(simp,[status(thm)],[13929]) ).

thf(226,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != empty_set )
      | ( ( C @ ( B @ set_difference ) )
        = empty_set )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,97]) ).

thf(227,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ set_difference ) )
        = empty_set )
      | ~ ( empty_set @ ( A @ subset ) )
      | ~ ( A @ ( empty_set @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[226:[bind(A,$thf( empty_set ))]]) ).

thf(347,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ set_difference ) )
        = empty_set )
      | ~ ( empty_set @ ( A @ subset ) )
      | ~ ( A @ ( empty_set @ subset ) ) ),
    inference(simp,[status(thm)],[227]) ).

thf(40160,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ set_difference ) )
        = empty_set )
      | ~ ( empty_set @ ( A @ subset ) )
      | ~ $true ),
    inference(rewrite,[status(thm)],[347,1524]) ).

thf(40161,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ set_difference ) )
        = empty_set )
      | ~ ( empty_set @ ( A @ subset ) ) ),
    inference(simp,[status(thm)],[40160]) ).

thf(93504,plain,
    ! [B: $i,A: $i] :
      ( ( ( empty_set @ ( sk1 @ subset ) )
       != ( empty_set @ ( A @ subset ) ) )
      | ( ( B @ ( A @ set_difference ) )
        = empty_set )
      | ~ $true
      | ( sk1 != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[92946,40161]) ).

thf(93505,plain,
    ! [B: $i,A: $i] :
      ( ( ( empty_set @ ( sk1 @ subset ) )
       != ( empty_set @ ( A @ subset ) ) )
      | ( ( B @ ( A @ set_difference ) )
        = empty_set )
      | ( sk1 != empty_set ) ),
    inference(simp,[status(thm)],[93504]) ).

thf(93506,plain,
    ! [A: $i] :
      ( ( ( A @ ( sk1 @ set_difference ) )
        = empty_set )
      | ( sk1 != empty_set ) ),
    inference(pattern_uni,[status(thm)],[93505:[bind(A,$thf( sk1 ))]]) ).

thf(93634,plain,
    ! [A: $i] :
      ( ( ( A @ ( sk1 @ set_difference ) )
        = empty_set )
      | ( sk1 != empty_set ) ),
    inference(simp,[status(thm)],[93506]) ).

thf(43571,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk1 @ set_union2 ) @ ( empty_set @ ( B @ ( sk1 @ sk10 ) ) @ in ) )
       != ( D @ ( C @ in ) ) )
      | ~ ( D @ empty )
      | ~ $true
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[43217,62]) ).

thf(43572,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk1 @ set_union2 ) @ ( empty_set @ ( B @ ( sk1 @ sk10 ) ) @ in ) )
       != ( D @ ( C @ in ) ) )
      | ~ ( D @ empty )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(simp,[status(thm)],[43571]) ).

thf(43573,plain,
    ! [A: $i] :
      ( ~ ( A @ ( sk1 @ set_union2 ) @ empty )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[43572:[bind(A,$thf( I )),bind(B,$thf( F )),bind(C,$thf( empty_set @ ( F @ ( sk1 @ sk10 ) ) )),bind(D,$thf( I @ ( sk1 @ set_union2 ) ))]]) ).

thf(43665,plain,
    ! [A: $i] :
      ( ~ ( A @ ( sk1 @ set_union2 ) @ empty )
      | ( sk2 @ ( sk1 @ subset ) ) ),
    inference(simp,[status(thm)],[43573]) ).

thf(52319,plain,
    ! [A: $i] :
      ( ( ( sk2 @ ( sk1 @ subset ) )
       != ( sk2 @ ( sk1 @ subset ) ) )
      | ~ $true
      | ~ ( sk1 @ ( sk2 @ subset ) )
      | ~ ( A @ ( sk1 @ set_union2 ) @ empty ) ),
    inference(paramod_ordered,[status(thm)],[43665,392]) ).

thf(52320,plain,
    ! [A: $i] :
      ( ( ( sk2 @ ( sk1 @ subset ) )
       != ( sk2 @ ( sk1 @ subset ) ) )
      | ~ ( sk1 @ ( sk2 @ subset ) )
      | ~ ( A @ ( sk1 @ set_union2 ) @ empty ) ),
    inference(simp,[status(thm)],[52319]) ).

thf(52321,plain,
    ! [A: $i] :
      ( ~ ( sk1 @ ( sk2 @ subset ) )
      | ~ ( A @ ( sk1 @ set_union2 ) @ empty ) ),
    inference(pattern_uni,[status(thm)],[52320:[]]) ).

thf(96549,plain,
    ! [B: $i,A: $i] :
      ( ( A != sk1 )
      | ( empty_set != empty_set )
      | ( B @ ( sk1 @ subset ) )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[59,95184]) ).

thf(96550,plain,
    ! [B: $i,A: $i] :
      ( ( A != sk1 )
      | ( B @ ( sk1 @ subset ) )
      | ~ ( A @ empty ) ),
    inference(simp,[status(thm)],[96549]) ).

thf(96551,plain,
    ! [A: $i] :
      ( ( A @ ( sk1 @ subset ) )
      | ~ ( sk1 @ empty ) ),
    inference(pattern_uni,[status(thm)],[96550:[bind(A,$thf( sk1 ))]]) ).

thf(96708,plain,
    ! [A: $i] :
      ( ( A @ ( sk1 @ subset ) )
      | ~ ( sk1 @ empty ) ),
    inference(simp,[status(thm)],[96551]) ).

thf(280,plain,
    ! [B: $i,A: $i] :
      ( ( B != sk4 )
      | ~ ( A @ empty )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,47]) ).

thf(281,plain,
    ! [A: $i] :
      ( ~ ( A @ empty )
      | ~ ( A @ ( sk4 @ subset ) )
      | ~ ( sk4 @ ( A @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[280:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).

thf(98522,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( sk1 @ subset ) )
       != ( sk4 @ ( B @ subset ) ) )
      | ~ ( B @ empty )
      | ~ ( B @ ( sk4 @ subset ) )
      | ~ $true
      | ~ ( sk1 @ empty ) ),
    inference(paramod_ordered,[status(thm)],[96708,281]) ).

thf(98523,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( sk1 @ subset ) )
       != ( sk4 @ ( B @ subset ) ) )
      | ~ ( B @ empty )
      | ~ ( B @ ( sk4 @ subset ) )
      | ~ ( sk1 @ empty ) ),
    inference(simp,[status(thm)],[98522]) ).

thf(98524,plain,
    ( ~ ( sk1 @ empty )
    | ~ ( sk1 @ ( sk4 @ subset ) )
    | ~ ( sk1 @ empty ) ),
    inference(pattern_uni,[status(thm)],[98523:[bind(A,$thf( sk4 )),bind(B,$thf( sk1 ))]]) ).

thf(98760,plain,
    ( ~ ( sk1 @ ( sk4 @ subset ) )
    | ~ ( sk1 @ empty ) ),
    inference(simp,[status(thm)],[98524]) ).

thf(100720,plain,
    ( ( ( sk1 @ empty )
     != ( sk1 @ empty ) )
    | ~ ( sk1 @ ( sk4 @ subset ) )
    | ~ $true
    | ( sk1 != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[93298,98760]) ).

thf(100721,plain,
    ( ( ( sk1 @ empty )
     != ( sk1 @ empty ) )
    | ~ ( sk1 @ ( sk4 @ subset ) )
    | ( sk1 != empty_set ) ),
    inference(simp,[status(thm)],[100720]) ).

thf(100722,plain,
    ( ~ ( sk1 @ ( sk4 @ subset ) )
    | ( sk1 != empty_set ) ),
    inference(pattern_uni,[status(thm)],[100721:[]]) ).

thf(117,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ in ) )
      | ~ ( C @ ( D @ in ) )
      | ( C
       != ( B @ ( A @ set_difference ) ) ) ),
    inference(cnfConj,[status(thm)],[112]) ).

thf(123,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ in ) )
      | ~ ( C @ ( D @ in ) )
      | ( C
       != ( B @ ( A @ set_difference ) ) ) ),
    inference(lifteq,[status(thm)],[117]) ).

thf(124,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ in ) )
      | ~ ( B @ ( A @ set_difference ) @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[123]) ).

thf(56248,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk1 @ ( C @ set_union2 ) ) )
      | ( sk2 @ ( sk1 @ subset ) )
      | ( A @ ( B @ set_union2 ) @ ( D @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,53651]) ).

thf(56249,plain,
    ! [B: $i,A: $i] :
      ( ( sk2 @ ( sk1 @ subset ) )
      | ( A @ ( sk1 @ set_union2 ) @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[56248:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).

thf(56306,plain,
    ! [B: $i,A: $i] :
      ( ( sk2 @ ( sk1 @ subset ) )
      | ( A @ ( sk1 @ set_union2 ) @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[56249]) ).

thf(125835,plain,
    ( ( sk2 @ ( sk2 @ ( sk1 @ set_union2 ) @ set_difference ) @ ( sk2 @ ( sk1 @ sk9 ) ) )
    | ( sk1 @ ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk1 @ set_union2 ) @ set_difference ) @ sk11 ) ) @ in ) ) ),
    inference(pattern_uni,[status(thm)],[937:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(92306,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( empty_set != empty_set )
      | ( ( sk1 @ ( sk2 @ subset ) )
       != ( empty_set @ ( sk1 @ subset ) ) )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[59,92170]) ).

thf(92307,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( ( sk1 @ ( sk2 @ subset ) )
       != ( empty_set @ ( sk1 @ subset ) ) )
      | ~ ( A @ empty ) ),
    inference(simp,[status(thm)],[92306]) ).

thf(92308,plain,
    ( ( ( sk1 @ ( sk2 @ subset ) )
     != ( empty_set @ ( sk1 @ subset ) ) )
    | ~ ( sk1 @ empty ) ),
    inference(pattern_uni,[status(thm)],[92307:[bind(A,$thf( sk1 ))]]) ).

thf(114443,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != sk1 )
      | ( ( C @ ( sk1 @ set_difference ) )
        = empty_set )
      | ( empty_set != empty_set )
      | ( A @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1599,93634]) ).

thf(114444,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != sk1 )
      | ( ( C @ ( sk1 @ set_difference ) )
        = empty_set )
      | ( A @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[114443]) ).

thf(114445,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( sk1 @ set_difference ) )
        = empty_set )
      | ( sk1 @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[114444:[bind(A,$thf( sk1 ))]]) ).

thf(114585,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( sk1 @ set_difference ) )
        = empty_set )
      | ( sk1 @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[114445]) ).

thf(19954,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( C @ ( B @ ( D @ ( C @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19907,2254]) ).

thf(19955,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
     != ( C @ ( B @ ( D @ ( C @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[19954]) ).

thf(20141,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 != C )
      | ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
       != ( B @ ( D @ ( C @ set_union2 ) @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[19955]) ).

thf(20199,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
     != ( B @ ( C @ ( sk4 @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[20141]) ).

thf(31576,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( D @ ( E @ ( sk4 @ set_union2 ) @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) )
       != ( empty_set @ ( C @ ( sk4 @ sk10 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,20199]) ).

thf(31577,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( sk4 @ set_union2 ) @ ( A @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk4 @ sk10 ) ) ) ),
    inference(pattern_uni,[status(thm)],[31576:[bind(A,$thf( G @ ( sk4 @ set_union2 ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( G ))]]) ).

thf(31685,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( sk4 @ set_union2 ) @ ( A @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk4 @ sk10 ) ) ) ),
    inference(simp,[status(thm)],[31577]) ).

thf(488,plain,
    ! [B: $i,A: $i] :
      ( ( B != sk1 )
      | ( ( sk2 @ ( A @ set_union2 ) )
       != sk1 )
      | ~ ( B @ empty )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[42,147]) ).

thf(489,plain,
    ! [A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) )
       != sk1 )
      | ~ ( sk1 @ empty )
      | ~ ( A @ empty ) ),
    inference(pattern_uni,[status(thm)],[488:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).

thf(554,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( D @ ( C @ set_union2 ) ) )
      | ( B
        = ( C @ ( D @ set_union2 ) ) )
      | ~ ( B @ empty )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[42,139]) ).

thf(555,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( C @ set_union2 ) ) )
      | ~ ( A @ empty )
      | ~ ( C @ ( B @ set_union2 ) @ empty ) ),
    inference(pattern_uni,[status(thm)],[554:[bind(A,$thf( F @ ( E @ set_union2 ) )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).

thf(647,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( C @ set_union2 ) ) )
      | ~ ( A @ empty )
      | ~ ( C @ ( B @ set_union2 ) @ empty ) ),
    inference(simp,[status(thm)],[555]) ).

thf(18300,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( C @ ( E @ in ) ) )
      | ( D @ ( C @ set_union2 ) @ ( E @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13962,80]) ).

thf(18301,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( C @ ( E @ in ) ) )
      | ( D @ ( C @ set_union2 ) @ ( E @ in ) ) ),
    inference(simp,[status(thm)],[18300]) ).

thf(18302,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( sk2 @ set_union2 ) @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) ),
    inference(pattern_uni,[status(thm)],[18301:[bind(A,$thf( J )),bind(B,$thf( G )),bind(C,$thf( J @ ( sk2 @ set_union2 ) )),bind(D,$thf( D )),bind(E,$thf( empty_set @ ( G @ ( sk2 @ sk10 ) ) ))]]) ).

thf(18474,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( sk2 @ set_union2 ) @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) ),
    inference(simp,[status(thm)],[18302]) ).

thf(64843,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( sk2 @ set_union2 ) @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( E @ ( D @ in ) ) )
      | ~ ( D @ ( E @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[18474,64]) ).

thf(64844,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( sk2 @ set_union2 ) @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( E @ ( D @ in ) ) )
      | ~ ( D @ ( E @ in ) ) ),
    inference(simp,[status(thm)],[64843]) ).

thf(64845,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ ( B @ ( C @ ( sk2 @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[64844:[bind(A,$thf( J )),bind(B,$thf( G )),bind(C,$thf( L )),bind(D,$thf( empty_set @ ( G @ ( sk2 @ sk10 ) ) )),bind(E,$thf( J @ ( L @ ( sk2 @ set_union2 ) @ set_union2 ) ))]]) ).

thf(65170,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ ( B @ ( C @ ( sk2 @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[64845]) ).

thf(15011,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( C @ ( E @ in ) ) )
      | ( D @ ( C @ set_union2 ) @ ( E @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13960,80]) ).

thf(15012,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( C @ ( E @ in ) ) )
      | ( D @ ( C @ set_union2 ) @ ( E @ in ) ) ),
    inference(simp,[status(thm)],[15011]) ).

thf(15013,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( sk2 @ ( C @ set_union2 ) @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) ),
    inference(pattern_uni,[status(thm)],[15012:[bind(A,$thf( I )),bind(B,$thf( G )),bind(C,$thf( sk2 @ ( I @ set_union2 ) )),bind(D,$thf( D )),bind(E,$thf( empty_set @ ( G @ ( sk2 @ sk10 ) ) ))]]) ).

thf(15232,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( sk2 @ ( C @ set_union2 ) @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) ),
    inference(simp,[status(thm)],[15013]) ).

thf(68481,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ set_union2 ) )
       != ( D @ ( sk4 @ set_union2 ) ) )
      | ( ( B @ ( A @ set_union2 ) @ ( C @ set_union2 ) )
       != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[139,67390]) ).

thf(68482,plain,
    ! [B: $i,A: $i] :
      ( ( sk4 @ ( A @ set_union2 ) @ ( B @ set_union2 ) )
     != empty_set ),
    inference(pattern_uni,[status(thm)],[68481:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).

thf(68526,plain,
    ! [B: $i,A: $i] :
      ( ( sk4 @ ( A @ set_union2 ) @ ( B @ set_union2 ) )
     != empty_set ),
    inference(simp,[status(thm)],[68482]) ).

thf(15083,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( C @ in ) ) )
      | ~ ( D @ empty )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13960,62]) ).

thf(15084,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( C @ in ) ) )
      | ~ ( D @ empty ) ),
    inference(simp,[status(thm)],[15083]) ).

thf(15085,plain,
    ! [A: $i] :
      ~ ( sk2 @ ( A @ set_union2 ) @ empty ),
    inference(pattern_uni,[status(thm)],[15084:[bind(A,$thf( H )),bind(B,$thf( F )),bind(C,$thf( empty_set @ ( F @ ( sk2 @ sk10 ) ) )),bind(D,$thf( sk2 @ ( H @ set_union2 ) ))]]) ).

thf(15252,plain,
    ! [A: $i] :
      ~ ( sk2 @ ( A @ set_union2 ) @ empty ),
    inference(simp,[status(thm)],[15085]) ).

thf(15430,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk2 @ ( C @ set_union2 ) ) )
      | ~ ( A @ ( B @ set_union2 ) @ empty ) ),
    inference(paramod_ordered,[status(thm)],[139,15252]) ).

thf(15431,plain,
    ! [A: $i] :
      ~ ( A @ ( sk2 @ set_union2 ) @ empty ),
    inference(pattern_uni,[status(thm)],[15430:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).

thf(58126,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ ( sk2 @ ( D @ set_union2 ) @ set_union2 ) ) )
      | ( empty_set != empty_set )
      | ( A @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1599,57785]) ).

thf(58127,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ ( sk2 @ ( D @ set_union2 ) @ set_union2 ) ) )
      | ( A @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[58126]) ).

thf(58128,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( sk2 @ ( C @ set_union2 ) @ set_union2 ) @ ( A @ ( empty_set @ sk9 ) ) ),
    inference(pattern_uni,[status(thm)],[58127:[bind(A,$thf( F @ ( sk2 @ ( G @ set_union2 ) @ set_union2 ) )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( G ))]]) ).

thf(58240,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( sk2 @ ( C @ set_union2 ) @ set_union2 ) @ ( A @ ( empty_set @ sk9 ) ) ),
    inference(simp,[status(thm)],[58128]) ).

thf(204,plain,
    ! [B: $i,A: $i] :
      ( ( B != sk2 )
      | ( ( sk2 @ ( A @ ( sk1 @ set_union2 ) @ set_difference ) )
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,24]) ).

thf(205,plain,
    ! [A: $i] :
      ( ( ( sk2 @ ( A @ ( sk1 @ set_union2 ) @ set_difference ) )
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ~ ( A @ ( sk2 @ subset ) )
      | ~ ( sk2 @ ( A @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[204:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).

thf(2557,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( E @ ( D @ ( F @ ( E @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true
      | ~ ( A @ ( C @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[80,2254]) ).

thf(2558,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( E @ ( D @ ( F @ ( E @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ ( A @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[2557]) ).

thf(2559,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( C @ ( A @ ( B @ ( D @ ( C @ set_union2 ) @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[2558:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( H @ ( J @ ( L @ ( K @ set_union2 ) @ set_union2 ) @ set_union2 ) )),bind(D,$thf( H )),bind(E,$thf( L @ ( K @ set_union2 ) )),bind(F,$thf( J ))]]) ).

thf(2608,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( C @ ( A @ ( B @ ( D @ ( C @ set_union2 ) @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[2559]) ).

thf(13859,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( B @ ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13698,2608]) ).

thf(13860,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
     != ( D @ ( B @ ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[13859]) ).

thf(13926,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 != D )
      | ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
       != ( B @ ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[13860]) ).

thf(14008,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
     != ( B @ ( C @ ( D @ ( sk2 @ set_union2 ) @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[13926]) ).

thf(1562,plain,
    ! [A: $i] :
      ( ( empty_set != empty_set )
      | ~ ( A @ ( sk2 @ subset ) )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[59,1529]) ).

thf(1563,plain,
    ! [A: $i] :
      ( ~ ( A @ ( sk2 @ subset ) )
      | ~ ( A @ empty ) ),
    inference(pattern_uni,[status(thm)],[1562:[]]) ).

thf(21026,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk4 @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( C @ ( D @ ( C @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[20241,2192]) ).

thf(21027,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( sk4 @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
     != ( C @ ( D @ ( C @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[21026]) ).

thf(21139,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk4 @ set_union2 ) )
       != C )
      | ( ( empty_set @ ( B @ ( sk4 @ sk10 ) ) )
       != ( D @ ( C @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[21027]) ).

thf(21226,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk4 @ sk10 ) ) )
     != ( C @ ( A @ ( sk4 @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[21139]) ).

thf(113,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( A @ set_difference ) ) )
      | ~ ( B @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
      | ( C @ ( B @ ( A @ sk9 ) ) ) ),
    inference(cnfConj,[status(thm)],[112]) ).

thf(127,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
      | ( C @ ( B @ ( A @ sk9 ) ) )
      | ( C
        = ( B @ ( A @ set_difference ) ) ) ),
    inference(lifteq,[status(thm)],[113]) ).

thf(128,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
      | ( C @ ( B @ ( A @ sk9 ) ) )
      | ( C
        = ( B @ ( A @ set_difference ) ) ) ),
    inference(simp,[status(thm)],[127]) ).

thf(18249,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( C @ in ) ) )
      | ~ ( C @ ( D @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13962,64]) ).

thf(18250,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( C @ in ) ) )
      | ~ ( C @ ( D @ in ) ) ),
    inference(simp,[status(thm)],[18249]) ).

thf(18251,plain,
    ! [B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ ( B @ ( sk2 @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[18250:[bind(A,$thf( I )),bind(B,$thf( F )),bind(C,$thf( empty_set @ ( F @ ( sk2 @ sk10 ) ) )),bind(D,$thf( I @ ( sk2 @ set_union2 ) ))]]) ).

thf(18462,plain,
    ! [B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ ( B @ ( sk2 @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[18251]) ).

thf(104799,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( empty_set @ ( A @ ( sk1 @ sk10 ) ) @ in ) )
       != ( C @ ( D @ in ) ) )
      | ( C @ ( B @ set_union2 ) @ ( D @ in ) )
      | ~ $true
      | ( sk1 @ empty ) ),
    inference(paramod_ordered,[status(thm)],[102952,82]) ).

thf(104800,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( empty_set @ ( A @ ( sk1 @ sk10 ) ) @ in ) )
       != ( C @ ( D @ in ) ) )
      | ( C @ ( B @ set_union2 ) @ ( D @ in ) )
      | ( sk1 @ empty ) ),
    inference(simp,[status(thm)],[104799]) ).

thf(104801,plain,
    ! [B: $i,A: $i] :
      ( ( sk1 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk1 @ sk10 ) ) @ in ) )
      | ( sk1 @ empty ) ),
    inference(pattern_uni,[status(thm)],[104800:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( sk1 )),bind(D,$thf( empty_set @ ( F @ ( sk1 @ sk10 ) ) ))]]) ).

thf(104948,plain,
    ! [B: $i,A: $i] :
      ( ( sk1 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk1 @ sk10 ) ) @ in ) )
      | ( sk1 @ empty ) ),
    inference(simp,[status(thm)],[104801]) ).

thf(13766,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( B @ ( C @ ( B @ ( D @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13698,12966]) ).

thf(13767,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
     != ( B @ ( C @ ( B @ ( D @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[13766]) ).

thf(13922,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 != B )
      | ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
       != ( C @ ( B @ ( D @ set_union2 ) @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[13767]) ).

thf(14003,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
     != ( B @ ( sk2 @ ( C @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[13922]) ).

thf(20022,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( B @ ( B @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19907,1884]) ).

thf(20023,plain,
    ! [B: $i,A: $i] :
      ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
     != ( B @ ( B @ in ) ) ),
    inference(simp,[status(thm)],[20022]) ).

thf(20164,plain,
    ! [B: $i,A: $i] :
      ( ( sk4 != B )
      | ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
       != B ) ),
    inference(simp,[status(thm)],[20023]) ).

thf(20226,plain,
    ! [A: $i] :
      ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
     != sk4 ),
    inference(simp,[status(thm)],[20164]) ).

thf(41420,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( E @ ( sk4 @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) @ ( C @ set_union2 ) )
       != ( empty_set @ ( D @ ( sk4 @ sk10 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,31685]) ).

thf(41421,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sk4 @ ( A @ set_union2 ) @ ( B @ set_union2 ) )
     != ( empty_set @ ( C @ ( sk4 @ sk10 ) ) ) ),
    inference(pattern_uni,[status(thm)],[41420:[bind(A,$thf( sk4 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B ))]]) ).

thf(41569,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sk4 @ ( A @ set_union2 ) @ ( B @ set_union2 ) )
     != ( empty_set @ ( C @ ( sk4 @ sk10 ) ) ) ),
    inference(simp,[status(thm)],[41421]) ).

thf(15018,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( D @ ( C @ set_union2 ) @ ( E @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13960,2661]) ).

thf(15019,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
     != ( D @ ( D @ ( C @ set_union2 ) @ ( E @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[15018]) ).

thf(15106,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) )
       != D )
      | ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
       != ( D @ ( C @ set_union2 ) @ ( E @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[15019]) ).

thf(15147,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
     != ( sk2 @ ( A @ set_union2 ) @ ( C @ set_union2 ) @ ( D @ set_union2 ) ) ),
    inference(simp,[status(thm)],[15106]) ).

thf(41961,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk4 @ ( E @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) @ ( C @ set_union2 ) )
       != ( empty_set @ ( D @ ( sk4 @ sk10 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,32032]) ).

thf(41962,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( sk4 @ set_union2 ) @ ( B @ set_union2 ) )
     != ( empty_set @ ( C @ ( sk4 @ sk10 ) ) ) ),
    inference(pattern_uni,[status(thm)],[41961:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A ))]]) ).

thf(42125,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( sk4 @ set_union2 ) @ ( B @ set_union2 ) )
     != ( empty_set @ ( C @ ( sk4 @ sk10 ) ) ) ),
    inference(simp,[status(thm)],[41962]) ).

thf(67338,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( D @ ( sk4 @ set_union2 ) ) )
      | ( ( C @ ( A @ ( B @ set_union2 ) @ set_union2 ) )
       != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[139,66916]) ).

thf(67339,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( sk4 @ ( A @ set_union2 ) @ set_union2 ) )
     != empty_set ),
    inference(pattern_uni,[status(thm)],[67338:[bind(A,$thf( sk4 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).

thf(67391,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( sk4 @ ( A @ set_union2 ) @ set_union2 ) )
     != empty_set ),
    inference(simp,[status(thm)],[67339]) ).

thf(93343,plain,
    ! [B: $i,A: $i] :
      ( ( B != sk1 )
      | ( empty_set @ ( sk1 @ subset ) )
      | ( empty_set != empty_set )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7213,92946]) ).

thf(93344,plain,
    ! [B: $i,A: $i] :
      ( ( B != sk1 )
      | ( empty_set @ ( sk1 @ subset ) )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[93343]) ).

thf(93345,plain,
    ! [A: $i] :
      ( ( empty_set @ ( sk1 @ subset ) )
      | ( sk1 @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[93344:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).

thf(2656,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( E @ ( D @ set_union2 ) ) )
      | ~ ( D @ ( A @ ( B @ set_union2 ) @ ( C @ set_union2 ) @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[139,2298]) ).

thf(2657,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( A @ ( A @ ( B @ set_union2 ) @ ( C @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[2656:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).

thf(20024,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( B @ ( B @ ( C @ set_union2 ) @ ( D @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19907,2657]) ).

thf(20025,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
     != ( B @ ( B @ ( C @ set_union2 ) @ ( D @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[20024]) ).

thf(20147,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 != B )
      | ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
       != ( B @ ( C @ set_union2 ) @ ( D @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[20025]) ).

thf(20207,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
     != ( sk4 @ ( B @ set_union2 ) @ ( C @ set_union2 ) ) ),
    inference(simp,[status(thm)],[20147]) ).

thf(6,axiom,
    ? [A: $i] : ( A @ empty ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(43,plain,
    ? [A: $i] : ( A @ empty ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(44,plain,
    sk3 @ empty,
    inference(cnf,[status(esa)],[43]) ).

thf(1101,plain,
    ! [A: $i] :
      ( ( ( sk3 @ empty )
       != ( A @ empty ) )
      | ~ $true
      | ( A = empty_set ) ),
    inference(paramod_ordered,[status(thm)],[44,59]) ).

thf(1102,plain,
    ! [A: $i] :
      ( ( ( sk3 @ empty )
       != ( A @ empty ) )
      | ( A = empty_set ) ),
    inference(simp,[status(thm)],[1101]) ).

thf(1103,plain,
    sk3 = empty_set,
    inference(pattern_uni,[status(thm)],[1102:[bind(A,$thf( sk3 ))]]) ).

thf(70229,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk4 @ ( C @ set_union2 ) @ ( D @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) )
       != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[139,68526]) ).

thf(70230,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( sk4 @ ( B @ set_union2 ) @ set_union2 ) )
     != empty_set ),
    inference(pattern_uni,[status(thm)],[70229:[bind(A,$thf( A )),bind(B,$thf( sk4 @ ( E @ set_union2 ) )),bind(C,$thf( E )),bind(D,$thf( A ))]]) ).

thf(70321,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( sk4 @ ( B @ set_union2 ) @ set_union2 ) )
     != empty_set ),
    inference(simp,[status(thm)],[70230]) ).

thf(5817,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( sk2 @ ( sk1 @ sk6 ) ) )
       != ( C @ ( B @ ( A @ sk6 ) ) ) )
      | ~ $true
      | ( C @ ( A @ ( B @ ( C @ sk7 ) ) @ in ) )
      | ( C
        = ( B @ ( A @ set_union2 ) ) )
      | ( sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) )
      | ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[3088,88]) ).

thf(5818,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( sk2 @ ( sk1 @ sk6 ) ) )
       != ( C @ ( B @ ( A @ sk6 ) ) ) )
      | ( C @ ( A @ ( B @ ( C @ sk7 ) ) @ in ) )
      | ( C
        = ( B @ ( A @ set_union2 ) ) )
      | ( sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) )
      | ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) ) ),
    inference(simp,[status(thm)],[5817]) ).

thf(5819,plain,
    ( ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ sk7 ) ) @ in ) )
    | ( ( sk2 @ ( sk1 @ set_union2 ) )
      = sk1 )
    | ( sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) )
    | ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) ) ),
    inference(pattern_uni,[status(thm)],[5818:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk1 ))]]) ).

thf(88758,plain,
    ( ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ sk7 ) ) @ in ) )
    | ( sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) )
    | ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) ) ),
    inference(simplifyReflect,[status(thm)],[5819,147]) ).

thf(123459,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( D @ ( sk4 @ set_union2 ) @ ( C @ set_union2 ) ) )
      | ~ ( empty_set @ ( A @ ( B @ set_union2 ) @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[139,123101]) ).

thf(123460,plain,
    ! [B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( B @ ( sk4 @ set_union2 ) @ set_union2 ) @ subset ) ),
    inference(pattern_uni,[status(thm)],[123459:[bind(A,$thf( A )),bind(B,$thf( F @ ( sk4 @ set_union2 ) )),bind(C,$thf( A )),bind(D,$thf( F ))]]) ).

thf(123576,plain,
    ! [B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( B @ ( sk4 @ set_union2 ) @ set_union2 ) @ subset ) ),
    inference(simp,[status(thm)],[123460]) ).

thf(69435,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( D @ ( sk4 @ ( C @ set_union2 ) @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) )
       != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[139,67391]) ).

thf(69436,plain,
    ! [B: $i,A: $i] :
      ( ( sk4 @ ( B @ set_union2 ) @ ( A @ set_union2 ) )
     != empty_set ),
    inference(pattern_uni,[status(thm)],[69435:[bind(A,$thf( sk4 @ ( E @ set_union2 ) )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( B ))]]) ).

thf(69510,plain,
    ! [B: $i,A: $i] :
      ( ( sk4 @ ( B @ set_union2 ) @ ( A @ set_union2 ) )
     != empty_set ),
    inference(simp,[status(thm)],[69436]) ).

thf(832,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ ( D @ sk5 ) ) )
      | ( D @ ( C @ subset ) )
      | ( C @ ( B @ in ) )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,55]) ).

thf(833,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ subset ) )
      | ( C @ ( A @ in ) )
      | ~ ( C @ ( B @ sk5 ) @ ( A @ subset ) )
      | ~ ( A @ ( C @ ( B @ sk5 ) @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[832:[bind(A,$thf( F @ ( E @ sk5 ) )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( E ))]]) ).

thf(843,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ subset ) )
      | ( C @ ( A @ in ) )
      | ~ ( C @ ( B @ sk5 ) @ ( A @ subset ) )
      | ~ ( A @ ( C @ ( B @ sk5 ) @ subset ) ) ),
    inference(simp,[status(thm)],[833]) ).

thf(123860,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( D @ ( sk4 @ set_union2 ) ) )
      | ~ ( empty_set @ ( C @ ( A @ ( B @ set_union2 ) @ set_union2 ) @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[139,123576]) ).

thf(123861,plain,
    ! [B: $i,A: $i] :
      ~ ( empty_set @ ( B @ ( sk4 @ ( A @ set_union2 ) @ set_union2 ) @ subset ) ),
    inference(pattern_uni,[status(thm)],[123860:[bind(A,$thf( sk4 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).

thf(124043,plain,
    ! [B: $i,A: $i] :
      ~ ( empty_set @ ( B @ ( sk4 @ ( A @ set_union2 ) @ set_union2 ) @ subset ) ),
    inference(simp,[status(thm)],[123861]) ).

thf(1706,plain,
    ! [B: $i,A: $i] :
      ( ( empty_set != empty_set )
      | ( A @ empty )
      | ( A @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1599,48]) ).

thf(1707,plain,
    ! [B: $i,A: $i] :
      ( ( A @ empty )
      | ( A @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1706:[]]) ).

thf(15104,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( D @ ( C @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13960,2238]) ).

thf(15105,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
     != ( D @ ( D @ ( C @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[15104]) ).

thf(15117,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) )
       != D )
      | ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
       != ( D @ ( C @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[15105]) ).

thf(15160,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
     != ( sk2 @ ( A @ set_union2 ) @ ( C @ set_union2 ) ) ),
    inference(simp,[status(thm)],[15117]) ).

thf(57606,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
       != ( sk2 @ ( D @ set_union2 ) @ ( C @ set_union2 ) ) )
      | ( empty_set != empty_set )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7213,57425]) ).

thf(57607,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
       != ( sk2 @ ( D @ set_union2 ) @ ( C @ set_union2 ) ) )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[57606]) ).

thf(57608,plain,
    ! [C: $i,B: $i,A: $i] : ( sk2 @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ ( A @ ( empty_set @ sk9 ) ) ),
    inference(pattern_uni,[status(thm)],[57607:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( G @ set_union2 ) @ ( E @ set_union2 ) )),bind(C,$thf( E )),bind(D,$thf( G ))]]) ).

thf(57746,plain,
    ! [C: $i,B: $i,A: $i] : ( sk2 @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ ( A @ ( empty_set @ sk9 ) ) ),
    inference(simp,[status(thm)],[57608]) ).

thf(63761,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ ( C @ set_union2 ) @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( E @ ( D @ in ) ) )
      | ~ ( D @ ( E @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[15232,64]) ).

thf(63762,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ ( C @ set_union2 ) @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( E @ ( D @ in ) ) )
      | ~ ( D @ ( E @ in ) ) ),
    inference(simp,[status(thm)],[63761]) ).

thf(63763,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ ( B @ ( sk2 @ ( C @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[63762:[bind(A,$thf( J )),bind(B,$thf( G )),bind(C,$thf( K )),bind(D,$thf( empty_set @ ( G @ ( sk2 @ sk10 ) ) )),bind(E,$thf( J @ ( sk2 @ ( K @ set_union2 ) @ set_union2 ) ))]]) ).

thf(64029,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ ( B @ ( sk2 @ ( C @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[63763]) ).

thf(73,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( A @ set_union2 ) ) )
      | ~ ( C @ ( B @ ( A @ sk6 ) ) )
      | ~ ( A @ ( A @ ( B @ ( C @ sk7 ) ) @ in ) ) ),
    inference(cnfConj,[status(thm)],[70]) ).

thf(85,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ sk6 ) ) )
      | ~ ( A @ ( A @ ( B @ ( C @ sk7 ) ) @ in ) )
      | ( C
        = ( B @ ( A @ set_union2 ) ) ) ),
    inference(lifteq,[status(thm)],[73]) ).

thf(86,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ sk6 ) ) )
      | ~ ( A @ ( A @ ( B @ ( C @ sk7 ) ) @ in ) )
      | ( C
        = ( B @ ( A @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[85]) ).

thf(21088,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk4 @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( D @ ( C @ in ) ) )
      | ~ ( D @ empty )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[20241,62]) ).

thf(21089,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk4 @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( D @ ( C @ in ) ) )
      | ~ ( D @ empty ) ),
    inference(simp,[status(thm)],[21088]) ).

thf(21090,plain,
    ! [A: $i] :
      ~ ( A @ ( sk4 @ set_union2 ) @ empty ),
    inference(pattern_uni,[status(thm)],[21089:[bind(A,$thf( I )),bind(B,$thf( F )),bind(C,$thf( empty_set @ ( F @ ( sk4 @ sk10 ) ) )),bind(D,$thf( I @ ( sk4 @ set_union2 ) ))]]) ).

thf(21184,plain,
    ! [A: $i] :
      ~ ( A @ ( sk4 @ set_union2 ) @ empty ),
    inference(simp,[status(thm)],[21090]) ).

thf(21560,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ set_union2 ) )
       != ( C @ ( sk4 @ set_union2 ) ) )
      | ~ ( B @ ( A @ set_union2 ) @ empty ) ),
    inference(paramod_ordered,[status(thm)],[139,21184]) ).

thf(21561,plain,
    ! [A: $i] :
      ~ ( sk4 @ ( A @ set_union2 ) @ empty ),
    inference(pattern_uni,[status(thm)],[21560:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( A ))]]) ).

thf(21673,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ set_union2 ) )
       != ( C @ ( sk4 @ set_union2 ) ) )
      | ( ( B @ ( A @ set_union2 ) )
       != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[139,21236]) ).

thf(21674,plain,
    ! [A: $i] :
      ( ( sk4 @ ( A @ set_union2 ) )
     != empty_set ),
    inference(pattern_uni,[status(thm)],[21673:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( A ))]]) ).

thf(70231,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk4 @ ( C @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) @ ( D @ set_union2 ) )
       != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[139,68526]) ).

thf(70232,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( sk4 @ set_union2 ) @ ( B @ set_union2 ) )
     != empty_set ),
    inference(pattern_uni,[status(thm)],[70231:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( A ))]]) ).

thf(70322,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( sk4 @ set_union2 ) @ ( B @ set_union2 ) )
     != empty_set ),
    inference(simp,[status(thm)],[70232]) ).

thf(218,plain,
    ! [B: $i,A: $i] :
      ( ( B != sk2 )
      | ( ( A @ ( sk1 @ set_union2 ) )
       != sk1 )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,147]) ).

thf(219,plain,
    ! [A: $i] :
      ( ( ( A @ ( sk1 @ set_union2 ) )
       != sk1 )
      | ~ ( A @ ( sk2 @ subset ) )
      | ~ ( sk2 @ ( A @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[218:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).

thf(19923,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( D @ ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19907,3253]) ).

thf(19924,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
     != ( D @ ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[19923]) ).

thf(20145,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 != D )
      | ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
       != ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ ( B @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[19924]) ).

thf(20205,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
     != ( D @ ( sk4 @ set_union2 ) @ ( C @ set_union2 ) @ ( B @ set_union2 ) ) ),
    inference(simp,[status(thm)],[20145]) ).

thf(3182,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( F @ ( F @ ( E @ set_union2 ) @ ( D @ set_union2 ) @ in ) ) )
      | ~ $true
      | ~ ( B @ ( C @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[82,2492]) ).

thf(3183,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
       != ( F @ ( F @ ( E @ set_union2 ) @ ( D @ set_union2 ) @ in ) ) )
      | ~ ( B @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[3182]) ).

thf(3184,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( D @ ( D @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ ( A @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[3183:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( L @ ( K @ set_union2 ) @ ( I @ set_union2 ) @ ( G @ set_union2 ) )),bind(D,$thf( G )),bind(E,$thf( I )),bind(F,$thf( L @ ( K @ set_union2 ) ))]]) ).

thf(3270,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( D @ ( D @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ ( A @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[3184]) ).

thf(19972,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
       != ( empty_set @ ( C @ ( sk4 @ sk10 ) ) ) )
      | ( sk4 @ ( empty_set @ in ) )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7213,19907]) ).

thf(19973,plain,
    ! [B: $i,A: $i] :
      ( ( sk4 @ ( empty_set @ in ) )
      | ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[19972:[bind(A,$thf( A )),bind(B,$thf( empty_set @ ( E @ ( sk4 @ sk10 ) ) )),bind(C,$thf( E ))]]) ).

thf(20179,plain,
    ! [B: $i,A: $i] :
      ( ( sk4 @ ( empty_set @ in ) )
      | ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[19973]) ).

thf(5846,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) )
       != ( B @ ( C @ in ) ) )
      | ( B @ ( A @ set_union2 ) @ ( C @ in ) )
      | ~ $true
      | ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) )
      | ( sk1 @ ( sk2 @ ( sk1 @ sk6 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3088,82]) ).

thf(5847,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) )
       != ( B @ ( C @ in ) ) )
      | ( B @ ( A @ set_union2 ) @ ( C @ in ) )
      | ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) )
      | ( sk1 @ ( sk2 @ ( sk1 @ sk6 ) ) ) ),
    inference(simp,[status(thm)],[5846]) ).

thf(5848,plain,
    ! [A: $i] :
      ( ( sk2 @ ( A @ set_union2 ) @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) )
      | ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) )
      | ( sk1 @ ( sk2 @ ( sk1 @ sk6 ) ) ) ),
    inference(pattern_uni,[status(thm)],[5847:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) ))]]) ).

thf(16,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( A @ empty )
     => ~ ( B @ ( A @ set_union2 ) @ empty ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).

thf(98,plain,
    ! [A: $i,B: $i] :
      ( ~ ( A @ empty )
     => ~ ( B @ ( A @ set_union2 ) @ empty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(14922,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( C @ ( E @ ( C @ ( D @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13960,2565]) ).

thf(14923,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
     != ( C @ ( E @ ( C @ ( D @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[14922]) ).

thf(15113,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) )
       != C )
      | ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
       != ( E @ ( C @ ( D @ set_union2 ) @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[14923]) ).

thf(15155,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
     != ( D @ ( sk2 @ ( A @ set_union2 ) @ ( C @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[15113]) ).

thf(15099,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( E @ in ) ) )
      | ~ $true
      | ~ ( D @ ( C @ set_difference ) @ ( E @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[13960,122]) ).

thf(15100,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( E @ in ) ) )
      | ~ ( D @ ( C @ set_difference ) @ ( E @ in ) ) ),
    inference(simp,[status(thm)],[15099]) ).

thf(15101,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( sk2 @ ( C @ set_union2 ) @ ( A @ set_difference ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) ),
    inference(pattern_uni,[status(thm)],[15100:[bind(A,$thf( I )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( sk2 @ ( I @ set_union2 ) )),bind(E,$thf( empty_set @ ( G @ ( sk2 @ sk10 ) ) ))]]) ).

thf(15259,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( sk2 @ ( C @ set_union2 ) @ ( A @ set_difference ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) ),
    inference(simp,[status(thm)],[15101]) ).

thf(720,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != empty_set )
      | ( ( C @ ( B @ set_union2 ) )
        = C )
      | ~ ( B @ empty )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[42,399]) ).

thf(721,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
        = B )
      | ~ ( A @ empty )
      | ~ ( empty_set @ empty ) ),
    inference(pattern_uni,[status(thm)],[720:[bind(A,$thf( empty_set ))]]) ).

thf(743,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
        = B )
      | ~ ( A @ empty )
      | ~ ( empty_set @ empty ) ),
    inference(simp,[status(thm)],[721]) ).

thf(98763,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
        = B )
      | ~ ( A @ empty )
      | ~ $true ),
    inference(rewrite,[status(thm)],[743,48]) ).

thf(98764,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
        = B )
      | ~ ( A @ empty ) ),
    inference(simp,[status(thm)],[98763]) ).

thf(14928,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( E @ ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13960,2504]) ).

thf(14929,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
     != ( E @ ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[14928]) ).

thf(15126,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) )
       != E )
      | ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
       != ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[14929]) ).

thf(15173,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
     != ( C @ ( sk2 @ ( A @ set_union2 ) @ ( D @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[15126]) ).

thf(963,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
       != ( sk2 @ ( sk1 @ set_union2 ) ) )
      | ( ( B @ ( A @ set_difference ) )
       != empty_set )
      | ( ( sk2 @ ( sk1 @ set_difference ) )
       != empty_set )
      | ( A @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
      | ( C @ ( B @ ( A @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[132,150]) ).

thf(964,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ set_difference ) )
       != empty_set )
      | ( ( sk2 @ ( sk1 @ set_difference ) )
       != empty_set )
      | ( A @ ( A @ ( B @ ( sk2 @ ( sk1 @ set_union2 ) @ sk11 ) ) @ in ) )
      | ( sk2 @ ( sk1 @ set_union2 ) @ ( B @ ( A @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[963:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk2 @ ( sk1 @ set_union2 ) ))]]) ).

thf(114,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( A @ set_difference ) ) )
      | ~ ( C @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
      | ( C @ ( B @ ( A @ sk9 ) ) ) ),
    inference(cnfConj,[status(thm)],[112]) ).

thf(129,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
      | ( C @ ( B @ ( A @ sk9 ) ) )
      | ( C
        = ( B @ ( A @ set_difference ) ) ) ),
    inference(lifteq,[status(thm)],[114]) ).

thf(130,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
      | ( C @ ( B @ ( A @ sk9 ) ) )
      | ( C
        = ( B @ ( A @ set_difference ) ) ) ),
    inference(simp,[status(thm)],[129]) ).

thf(2705,plain,
    ! [B: $i,A: $i] :
      ( ( A != sk1 )
      | ( empty_set != empty_set )
      | ~ ( sk1 @ ( sk2 @ subset ) )
      | ( A @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1599,2116]) ).

thf(2706,plain,
    ! [B: $i,A: $i] :
      ( ( A != sk1 )
      | ~ ( sk1 @ ( sk2 @ subset ) )
      | ( A @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[2705]) ).

thf(2707,plain,
    ! [A: $i] :
      ( ~ ( sk1 @ ( sk2 @ subset ) )
      | ( sk1 @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[2706:[bind(A,$thf( sk1 ))]]) ).

thf(2752,plain,
    ! [A: $i] :
      ( ~ ( sk1 @ ( sk2 @ subset ) )
      | ( sk1 @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[2707]) ).

thf(58430,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( C @ ( sk2 @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) @ ( D @ set_union2 ) )
       != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[139,57786]) ).

thf(58431,plain,
    ! [B: $i,A: $i] :
      ( ( sk2 @ ( A @ set_union2 ) @ ( B @ set_union2 ) )
     != empty_set ),
    inference(pattern_uni,[status(thm)],[58430:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).

thf(58505,plain,
    ! [B: $i,A: $i] :
      ( ( sk2 @ ( A @ set_union2 ) @ ( B @ set_union2 ) )
     != empty_set ),
    inference(simp,[status(thm)],[58431]) ).

thf(59347,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
       != ( D @ ( C @ ( sk2 @ set_union2 ) @ set_union2 ) ) )
      | ( empty_set != empty_set )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7213,58265]) ).

thf(59348,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
       != ( D @ ( C @ ( sk2 @ set_union2 ) @ set_union2 ) ) )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[59347]) ).

thf(59349,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( sk2 @ set_union2 ) @ set_union2 ) @ ( A @ ( empty_set @ sk9 ) ) ),
    inference(pattern_uni,[status(thm)],[59348:[bind(A,$thf( A )),bind(B,$thf( F @ ( H @ ( sk2 @ set_union2 ) @ set_union2 ) )),bind(C,$thf( H )),bind(D,$thf( F ))]]) ).

thf(59535,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( sk2 @ set_union2 ) @ set_union2 ) @ ( A @ ( empty_set @ sk9 ) ) ),
    inference(simp,[status(thm)],[59349]) ).

thf(35453,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( E @ ( sk2 @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) @ ( C @ set_union2 ) )
       != ( empty_set @ ( D @ ( sk2 @ sk10 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,26182]) ).

thf(35454,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( A @ set_union2 ) @ ( B @ set_union2 ) )
     != ( empty_set @ ( C @ ( sk2 @ sk10 ) ) ) ),
    inference(pattern_uni,[status(thm)],[35453:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B ))]]) ).

thf(35577,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( A @ set_union2 ) @ ( B @ set_union2 ) )
     != ( empty_set @ ( C @ ( sk2 @ sk10 ) ) ) ),
    inference(simp,[status(thm)],[35454]) ).

thf(93415,plain,
    ! [A: $i] :
      ( ( ( empty_set @ ( sk2 @ ( A @ set_union2 ) @ subset ) )
       != ( empty_set @ ( sk1 @ subset ) ) )
      | ~ $true
      | ( sk1 != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[92946,26900]) ).

thf(93416,plain,
    ! [A: $i] :
      ( ( ( empty_set @ ( sk2 @ ( A @ set_union2 ) @ subset ) )
       != ( empty_set @ ( sk1 @ subset ) ) )
      | ( sk1 != empty_set ) ),
    inference(simp,[status(thm)],[93415]) ).

thf(93618,plain,
    ! [A: $i] :
      ( ( empty_set != empty_set )
      | ( ( sk2 @ ( A @ set_union2 ) )
       != sk1 )
      | ( sk1 != empty_set ) ),
    inference(simp,[status(thm)],[93416]) ).

thf(93703,plain,
    ! [A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) )
       != sk1 )
      | ( sk1 != empty_set ) ),
    inference(simp,[status(thm)],[93618]) ).

thf(19986,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( D @ ( B @ ( D @ ( C @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19907,2504]) ).

thf(19987,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
     != ( D @ ( B @ ( D @ ( C @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[19986]) ).

thf(20148,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 != D )
      | ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
       != ( B @ ( D @ ( C @ set_union2 ) @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[19987]) ).

thf(20208,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
     != ( B @ ( sk4 @ ( C @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[20148]) ).

thf(416,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( D @ ( C @ set_union2 ) ) )
      | ( B
        = ( C @ ( D @ set_union2 ) ) )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,139]) ).

thf(417,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( C @ set_union2 ) ) )
      | ~ ( C @ ( B @ set_union2 ) @ ( A @ subset ) )
      | ~ ( A @ ( C @ ( B @ set_union2 ) @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[416:[bind(A,$thf( F @ ( E @ set_union2 ) )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).

thf(426,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( C @ set_union2 ) ) )
      | ~ ( C @ ( B @ set_union2 ) @ ( A @ subset ) )
      | ~ ( A @ ( C @ ( B @ set_union2 ) @ subset ) ) ),
    inference(simp,[status(thm)],[417]) ).

thf(13800,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( C @ ( B @ in ) ) )
      | ~ ( B @ ( C @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13698,64]) ).

thf(13801,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( C @ ( B @ in ) ) )
      | ~ ( B @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[13800]) ).

thf(13802,plain,
    ! [A: $i] :
      ~ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ ( sk2 @ in ) ),
    inference(pattern_uni,[status(thm)],[13801:[bind(A,$thf( E )),bind(B,$thf( empty_set @ ( E @ ( sk2 @ sk10 ) ) )),bind(C,$thf( sk2 ))]]) ).

thf(14012,plain,
    ! [A: $i] :
      ~ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ ( sk2 @ in ) ),
    inference(simp,[status(thm)],[13802]) ).

thf(13851,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( B @ ( C @ ( B @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13698,2192]) ).

thf(13852,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
     != ( B @ ( C @ ( B @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[13851]) ).

thf(13942,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sk2 != B )
      | ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
       != ( C @ ( B @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[13852]) ).

thf(14026,plain,
    ! [B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
     != ( B @ ( sk2 @ set_union2 ) ) ),
    inference(simp,[status(thm)],[13942]) ).

thf(14713,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( D @ ( sk2 @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) )
       != ( empty_set @ ( C @ ( sk2 @ sk10 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,14026]) ).

thf(14714,plain,
    ! [B: $i,A: $i] :
      ( ( sk2 @ ( A @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk2 @ sk10 ) ) ) ),
    inference(pattern_uni,[status(thm)],[14713:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).

thf(14827,plain,
    ! [B: $i,A: $i] :
      ( ( sk2 @ ( A @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk2 @ sk10 ) ) ) ),
    inference(simp,[status(thm)],[14714]) ).

thf(13762,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
       != ( empty_set @ ( C @ ( sk2 @ sk10 ) ) ) )
      | ( sk2 @ ( empty_set @ in ) )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7213,13698]) ).

thf(13763,plain,
    ! [B: $i,A: $i] :
      ( ( sk2 @ ( empty_set @ in ) )
      | ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[13762:[bind(A,$thf( A )),bind(B,$thf( empty_set @ ( E @ ( sk2 @ sk10 ) ) )),bind(C,$thf( E ))]]) ).

thf(13985,plain,
    ! [B: $i,A: $i] :
      ( ( sk2 @ ( empty_set @ in ) )
      | ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[13763]) ).

thf(938,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
       != ( sk2 @ ( sk1 @ set_union2 ) ) )
      | ( ( sk2 @ ( B @ ( A @ set_difference ) @ set_difference ) )
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ( A @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
      | ( C @ ( B @ ( A @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[132,24]) ).

thf(939,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk2 @ ( B @ ( A @ set_difference ) @ set_difference ) )
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ( A @ ( A @ ( B @ ( sk2 @ ( sk1 @ set_union2 ) @ sk11 ) ) @ in ) )
      | ( sk2 @ ( sk1 @ set_union2 ) @ ( B @ ( A @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[938:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk2 @ ( sk1 @ set_union2 ) ))]]) ).

thf(41149,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( empty_set != empty_set )
      | ~ ( sk1 @ ( sk2 @ ( sk1 @ set_union2 ) @ subset ) )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[59,37719]) ).

thf(41150,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ~ ( sk1 @ ( sk2 @ ( sk1 @ set_union2 ) @ subset ) )
      | ~ ( A @ empty ) ),
    inference(simp,[status(thm)],[41149]) ).

thf(41151,plain,
    ( ~ ( sk1 @ ( sk2 @ ( sk1 @ set_union2 ) @ subset ) )
    | ~ ( sk1 @ empty ) ),
    inference(pattern_uni,[status(thm)],[41150:[bind(A,$thf( sk1 ))]]) ).

thf(93408,plain,
    ! [A: $i] :
      ( ( ( empty_set @ ( sk4 @ ( A @ set_union2 ) @ subset ) )
       != ( empty_set @ ( sk1 @ subset ) ) )
      | ~ $true
      | ( sk1 != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[92946,30864]) ).

thf(93409,plain,
    ! [A: $i] :
      ( ( ( empty_set @ ( sk4 @ ( A @ set_union2 ) @ subset ) )
       != ( empty_set @ ( sk1 @ subset ) ) )
      | ( sk1 != empty_set ) ),
    inference(simp,[status(thm)],[93408]) ).

thf(93604,plain,
    ! [A: $i] :
      ( ( empty_set != empty_set )
      | ( ( sk4 @ ( A @ set_union2 ) )
       != sk1 )
      | ( sk1 != empty_set ) ),
    inference(simp,[status(thm)],[93409]) ).

thf(93690,plain,
    ! [A: $i] :
      ( ( ( sk4 @ ( A @ set_union2 ) )
       != sk1 )
      | ( sk1 != empty_set ) ),
    inference(simp,[status(thm)],[93604]) ).

thf(13831,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( E @ ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13698,3270]) ).

thf(13832,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
     != ( E @ ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[13831]) ).

thf(13933,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 != E )
      | ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
       != ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ ( B @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[13832]) ).

thf(14017,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
     != ( sk2 @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ ( B @ set_union2 ) ) ),
    inference(simp,[status(thm)],[13933]) ).

thf(7493,plain,
    ! [B: $i,A: $i] :
      ( ( empty_set != empty_set )
      | ( B @ empty )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7213,48]) ).

thf(7494,plain,
    ! [B: $i,A: $i] :
      ( ( B @ empty )
      | ( B @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[7493:[]]) ).

thf(19908,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( E @ ( B @ ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19907,3784]) ).

thf(19909,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
     != ( E @ ( B @ ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[19908]) ).

thf(20158,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 != E )
      | ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
       != ( B @ ( E @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[19909]) ).

thf(20218,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
     != ( B @ ( sk4 @ ( D @ set_union2 ) @ ( C @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[20158]) ).

thf(506,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != empty_set )
      | ( ( B @ ( C @ set_difference ) )
        = C )
      | ~ ( B @ empty )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[42,109]) ).

thf(507,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ set_difference ) )
        = B )
      | ~ ( A @ empty )
      | ~ ( empty_set @ empty ) ),
    inference(pattern_uni,[status(thm)],[506:[bind(A,$thf( empty_set ))]]) ).

thf(687,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ set_difference ) )
        = B )
      | ~ ( A @ empty )
      | ~ ( empty_set @ empty ) ),
    inference(simp,[status(thm)],[507]) ).

thf(94266,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ set_difference ) )
        = B )
      | ~ ( A @ empty )
      | ~ $true ),
    inference(rewrite,[status(thm)],[687,48]) ).

thf(94267,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ set_difference ) )
        = B )
      | ~ ( A @ empty ) ),
    inference(simp,[status(thm)],[94266]) ).

thf(576,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( sk2 @ ( sk2 @ ( sk1 @ set_union2 ) @ set_difference ) ) )
      | ( B
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ~ ( B @ empty )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[42,24]) ).

thf(577,plain,
    ! [A: $i] :
      ( ( A
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ~ ( A @ empty )
      | ~ ( sk2 @ ( sk2 @ ( sk1 @ set_union2 ) @ set_difference ) @ empty ) ),
    inference(pattern_uni,[status(thm)],[576:[bind(A,$thf( sk2 @ ( sk2 @ ( sk1 @ set_union2 ) @ set_difference ) )),bind(B,$thf( B ))]]) ).

thf(656,plain,
    ( ~ ( sk2 @ ( sk1 @ set_difference ) @ empty )
    | ~ ( sk2 @ ( sk2 @ ( sk1 @ set_union2 ) @ set_difference ) @ empty ) ),
    inference(simp,[status(thm)],[577]) ).

thf(58373,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ ( sk2 @ set_union2 ) @ ( D @ set_union2 ) ) )
      | ( empty_set != empty_set )
      | ( A @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1599,57786]) ).

thf(58374,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ ( sk2 @ set_union2 ) @ ( D @ set_union2 ) ) )
      | ( A @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[58373]) ).

thf(58375,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( sk2 @ set_union2 ) @ ( B @ set_union2 ) @ ( A @ ( empty_set @ sk9 ) ) ),
    inference(pattern_uni,[status(thm)],[58374:[bind(A,$thf( H @ ( sk2 @ set_union2 ) @ ( E @ set_union2 ) )),bind(B,$thf( B )),bind(C,$thf( H )),bind(D,$thf( E ))]]) ).

thf(58481,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( sk2 @ set_union2 ) @ ( B @ set_union2 ) @ ( A @ ( empty_set @ sk9 ) ) ),
    inference(simp,[status(thm)],[58375]) ).

thf(18325,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( E @ in ) ) )
      | ( D @ ( C @ set_union2 ) @ ( E @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13962,82]) ).

thf(18326,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( E @ in ) ) )
      | ( D @ ( C @ set_union2 ) @ ( E @ in ) ) ),
    inference(simp,[status(thm)],[18325]) ).

thf(18327,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( sk2 @ set_union2 ) @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) ),
    inference(pattern_uni,[status(thm)],[18326:[bind(A,$thf( J )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( J @ ( sk2 @ set_union2 ) )),bind(E,$thf( empty_set @ ( G @ ( sk2 @ sk10 ) ) ))]]) ).

thf(18478,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( sk2 @ set_union2 ) @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) ),
    inference(simp,[status(thm)],[18327]) ).

thf(66547,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( sk4 @ set_union2 ) @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( E @ ( D @ in ) ) )
      | ~ ( D @ ( E @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[21163,64]) ).

thf(66548,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( sk4 @ set_union2 ) @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( E @ ( D @ in ) ) )
      | ~ ( D @ ( E @ in ) ) ),
    inference(simp,[status(thm)],[66547]) ).

thf(66549,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ ( B @ ( C @ ( sk4 @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[66548:[bind(A,$thf( J )),bind(B,$thf( G )),bind(C,$thf( L )),bind(D,$thf( empty_set @ ( G @ ( sk4 @ sk10 ) ) )),bind(E,$thf( J @ ( L @ ( sk4 @ set_union2 ) @ set_union2 ) ))]]) ).

thf(66967,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ ( B @ ( C @ ( sk4 @ set_union2 ) @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[66549]) ).

thf(52757,plain,
    ! [A: $i] :
      ( ( ( sk2 @ ( sk1 @ subset ) )
       != ( sk2 @ ( sk1 @ subset ) ) )
      | ~ $true
      | ~ ( sk1 @ ( sk2 @ subset ) )
      | ( ( A @ ( sk1 @ set_union2 ) )
       != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[43716,392]) ).

thf(52758,plain,
    ! [A: $i] :
      ( ( ( sk2 @ ( sk1 @ subset ) )
       != ( sk2 @ ( sk1 @ subset ) ) )
      | ~ ( sk1 @ ( sk2 @ subset ) )
      | ( ( A @ ( sk1 @ set_union2 ) )
       != empty_set ) ),
    inference(simp,[status(thm)],[52757]) ).

thf(52759,plain,
    ! [A: $i] :
      ( ~ ( sk1 @ ( sk2 @ subset ) )
      | ( ( A @ ( sk1 @ set_union2 ) )
       != empty_set ) ),
    inference(pattern_uni,[status(thm)],[52758:[]]) ).

thf(524,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != empty_set )
      | ( ( B @ ( C @ set_union2 ) )
        = C )
      | ~ ( B @ empty )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[42,103]) ).

thf(525,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ set_union2 ) )
        = B )
      | ~ ( A @ empty )
      | ~ ( empty_set @ empty ) ),
    inference(pattern_uni,[status(thm)],[524:[bind(A,$thf( empty_set ))]]) ).

thf(634,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ set_union2 ) )
        = B )
      | ~ ( A @ empty )
      | ~ ( empty_set @ empty ) ),
    inference(simp,[status(thm)],[525]) ).

thf(70358,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ set_union2 ) )
        = B )
      | ~ ( A @ empty )
      | ~ $true ),
    inference(rewrite,[status(thm)],[634,48]) ).

thf(70359,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ set_union2 ) )
        = B )
      | ~ ( A @ empty ) ),
    inference(simp,[status(thm)],[70358]) ).

thf(13704,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( E @ ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) @ ( B @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13698,2676]) ).

thf(13705,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
     != ( E @ ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) @ ( B @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[13704]) ).

thf(13938,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 != E )
      | ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
       != ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) @ ( B @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[13705]) ).

thf(14022,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
     != ( C @ ( sk2 @ ( D @ set_union2 ) @ set_union2 ) @ ( B @ set_union2 ) ) ),
    inference(simp,[status(thm)],[13938]) ).

thf(5955,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) )
       != ( A @ ( C @ in ) ) )
      | ( B @ ( A @ set_union2 ) @ ( C @ in ) )
      | ~ $true
      | ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) )
      | ( sk1 @ ( sk2 @ ( sk1 @ sk6 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3088,80]) ).

thf(5956,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) )
       != ( A @ ( C @ in ) ) )
      | ( B @ ( A @ set_union2 ) @ ( C @ in ) )
      | ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) )
      | ( sk1 @ ( sk2 @ ( sk1 @ sk6 ) ) ) ),
    inference(simp,[status(thm)],[5955]) ).

thf(5957,plain,
    ! [A: $i] :
      ( ( A @ ( sk2 @ set_union2 ) @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) )
      | ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) )
      | ( sk1 @ ( sk2 @ ( sk1 @ sk6 ) ) ) ),
    inference(pattern_uni,[status(thm)],[5956:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) ))]]) ).

thf(6073,plain,
    ! [A: $i] :
      ( ( A @ ( sk2 @ set_union2 ) @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) )
      | ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ sk8 ) ) @ in ) )
      | ( sk1 @ ( sk2 @ ( sk1 @ sk6 ) ) ) ),
    inference(simp,[status(thm)],[5957]) ).

thf(53792,plain,
    ! [A: $i] :
      ( ( ( sk2 @ ( sk1 @ subset ) )
       != ( sk2 @ ( sk1 @ subset ) ) )
      | ~ $true
      | ~ ( sk1 @ ( sk2 @ subset ) )
      | ~ ( sk1 @ ( A @ set_union2 ) @ empty ) ),
    inference(paramod_ordered,[status(thm)],[44123,392]) ).

thf(53793,plain,
    ! [A: $i] :
      ( ( ( sk2 @ ( sk1 @ subset ) )
       != ( sk2 @ ( sk1 @ subset ) ) )
      | ~ ( sk1 @ ( sk2 @ subset ) )
      | ~ ( sk1 @ ( A @ set_union2 ) @ empty ) ),
    inference(simp,[status(thm)],[53792]) ).

thf(53794,plain,
    ! [A: $i] :
      ( ~ ( sk1 @ ( sk2 @ subset ) )
      | ~ ( sk1 @ ( A @ set_union2 ) @ empty ) ),
    inference(pattern_uni,[status(thm)],[53793:[]]) ).

thf(123461,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( D @ ( sk4 @ set_union2 ) ) )
      | ~ ( empty_set @ ( A @ ( B @ set_union2 ) @ ( C @ set_union2 ) @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[139,123101]) ).

thf(123462,plain,
    ! [B: $i,A: $i] :
      ~ ( empty_set @ ( sk4 @ ( A @ set_union2 ) @ ( B @ set_union2 ) @ subset ) ),
    inference(pattern_uni,[status(thm)],[123461:[bind(A,$thf( sk4 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).

thf(123577,plain,
    ! [B: $i,A: $i] :
      ~ ( empty_set @ ( sk4 @ ( A @ set_union2 ) @ ( B @ set_union2 ) @ subset ) ),
    inference(simp,[status(thm)],[123462]) ).

thf(14887,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13960,2254]) ).

thf(14888,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
     != ( D @ ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[14887]) ).

thf(15144,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) )
       != D )
      | ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
       != ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[14888]) ).

thf(15196,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
     != ( C @ ( D @ ( sk2 @ ( A @ set_union2 ) @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[15144]) ).

thf(95089,plain,
    ! [B: $i,A: $i] :
      ( ( A != sk1 )
      | ~ ( sk1 @ ( B @ in ) )
      | ( empty_set != empty_set )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[59,93893]) ).

thf(95090,plain,
    ! [B: $i,A: $i] :
      ( ( A != sk1 )
      | ~ ( sk1 @ ( B @ in ) )
      | ~ ( A @ empty ) ),
    inference(simp,[status(thm)],[95089]) ).

thf(95091,plain,
    ! [A: $i] :
      ( ~ ( sk1 @ ( A @ in ) )
      | ~ ( sk1 @ empty ) ),
    inference(pattern_uni,[status(thm)],[95090:[bind(A,$thf( sk1 ))]]) ).

thf(95238,plain,
    ! [A: $i] :
      ( ~ ( sk1 @ ( A @ in ) )
      | ~ ( sk1 @ empty ) ),
    inference(simp,[status(thm)],[95091]) ).

thf(864,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
       != ( C @ ( D @ sk5 ) ) )
      | ( D @ ( C @ subset ) )
      | ~ ( D @ ( A @ in ) )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,56]) ).

thf(865,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ subset ) )
      | ~ ( B @ ( A @ in ) )
      | ~ ( A @ ( C @ ( B @ sk5 ) @ subset ) )
      | ~ ( C @ ( B @ sk5 ) @ ( A @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[864:[bind(A,$thf( A )),bind(B,$thf( F @ ( E @ sk5 ) )),bind(C,$thf( F )),bind(D,$thf( E ))]]) ).

thf(876,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ subset ) )
      | ~ ( B @ ( A @ in ) )
      | ~ ( A @ ( C @ ( B @ sk5 ) @ subset ) )
      | ~ ( C @ ( B @ sk5 ) @ ( A @ subset ) ) ),
    inference(simp,[status(thm)],[865]) ).

thf(836,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ ( D @ sk5 ) ) )
      | ( D @ ( C @ subset ) )
      | ( C @ ( B @ in ) )
      | ~ ( B @ empty )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[42,55]) ).

thf(837,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ subset ) )
      | ( C @ ( A @ in ) )
      | ~ ( A @ empty )
      | ~ ( C @ ( B @ sk5 ) @ empty ) ),
    inference(pattern_uni,[status(thm)],[836:[bind(A,$thf( F @ ( E @ sk5 ) )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( E ))]]) ).

thf(845,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ subset ) )
      | ( C @ ( A @ in ) )
      | ~ ( A @ empty )
      | ~ ( C @ ( B @ sk5 ) @ empty ) ),
    inference(simp,[status(thm)],[837]) ).

thf(54232,plain,
    ! [A: $i] :
      ( ( ( sk2 @ ( sk1 @ subset ) )
       != ( sk2 @ ( sk1 @ subset ) ) )
      | ~ $true
      | ~ ( sk1 @ ( sk2 @ subset ) )
      | ( ( sk1 @ ( A @ set_union2 ) )
       != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[44179,392]) ).

thf(54233,plain,
    ! [A: $i] :
      ( ( ( sk2 @ ( sk1 @ subset ) )
       != ( sk2 @ ( sk1 @ subset ) ) )
      | ~ ( sk1 @ ( sk2 @ subset ) )
      | ( ( sk1 @ ( A @ set_union2 ) )
       != empty_set ) ),
    inference(simp,[status(thm)],[54232]) ).

thf(54234,plain,
    ! [A: $i] :
      ( ~ ( sk1 @ ( sk2 @ subset ) )
      | ( ( sk1 @ ( A @ set_union2 ) )
       != empty_set ) ),
    inference(pattern_uni,[status(thm)],[54233:[]]) ).

thf(202,plain,
    ! [B: $i,A: $i] :
      ( ( B != sk1 )
      | ( ( sk2 @ ( sk2 @ ( A @ set_union2 ) @ set_difference ) )
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,24]) ).

thf(203,plain,
    ! [A: $i] :
      ( ( ( sk2 @ ( sk2 @ ( A @ set_union2 ) @ set_difference ) )
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ~ ( A @ ( sk1 @ subset ) )
      | ~ ( sk1 @ ( A @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[202:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).

thf(13715,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) @ ( B @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13698,2686]) ).

thf(13716,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
     != ( D @ ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) @ ( B @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[13715]) ).

thf(13949,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 != D )
      | ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
       != ( C @ ( E @ ( D @ set_union2 ) @ set_union2 ) @ ( B @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[13716]) ).

thf(14037,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
     != ( C @ ( D @ ( sk2 @ set_union2 ) @ set_union2 ) @ ( B @ set_union2 ) ) ),
    inference(simp,[status(thm)],[13949]) ).

thf(22717,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( C @ ( C @ ( D @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[20250,2236]) ).

thf(22718,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
     != ( C @ ( C @ ( D @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[22717]) ).

thf(22951,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( A @ set_union2 ) )
       != C )
      | ( ( empty_set @ ( B @ ( sk4 @ sk10 ) ) )
       != ( C @ ( D @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[22718]) ).

thf(23044,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk4 @ sk10 ) ) )
     != ( sk4 @ ( A @ set_union2 ) @ ( C @ set_union2 ) ) ),
    inference(simp,[status(thm)],[22951]) ).

thf(65457,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( sk2 @ set_union2 ) @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( E @ ( D @ in ) ) )
      | ~ ( D @ ( E @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[18478,64]) ).

thf(65458,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( sk2 @ set_union2 ) @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( E @ ( D @ in ) ) )
      | ~ ( D @ ( E @ in ) ) ),
    inference(simp,[status(thm)],[65457]) ).

thf(65459,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ ( C @ ( sk2 @ set_union2 ) @ ( B @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[65458:[bind(A,$thf( I )),bind(B,$thf( G )),bind(C,$thf( L )),bind(D,$thf( empty_set @ ( G @ ( sk2 @ sk10 ) ) )),bind(E,$thf( L @ ( sk2 @ set_union2 ) @ ( I @ set_union2 ) ))]]) ).

thf(65850,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ ( C @ ( sk2 @ set_union2 ) @ ( B @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[65459]) ).

thf(943,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_difference ) )
       != ( sk2 @ ( sk2 @ ( sk1 @ set_union2 ) @ set_difference ) ) )
      | ( C
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ( A @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
      | ( C @ ( B @ ( A @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[132,24]) ).

thf(944,plain,
    ! [A: $i] :
      ( ( A
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ( sk2 @ ( sk1 @ set_union2 ) @ ( sk2 @ ( sk1 @ set_union2 ) @ ( sk2 @ ( A @ sk11 ) ) @ in ) )
      | ( A @ ( sk2 @ ( sk2 @ ( sk1 @ set_union2 ) @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[943:[bind(A,$thf( sk2 @ ( sk1 @ set_union2 ) )),bind(B,$thf( sk2 )),bind(C,$thf( C ))]]) ).

thf(995,plain,
    ( ( sk2 @ ( sk1 @ set_union2 ) @ ( sk2 @ ( sk1 @ set_union2 ) @ ( sk2 @ ( sk2 @ ( sk1 @ set_difference ) @ sk11 ) ) @ in ) )
    | ( sk2 @ ( sk1 @ set_difference ) @ ( sk2 @ ( sk2 @ ( sk1 @ set_union2 ) @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[944]) ).

thf(492,plain,
    ! [B: $i,A: $i] :
      ( ( A != sk2 )
      | ( B != empty_set )
      | ~ ( B @ empty )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[42,165]) ).

thf(493,plain,
    ! [A: $i] :
      ( ( A != empty_set )
      | ~ ( A @ empty )
      | ~ ( sk2 @ empty ) ),
    inference(pattern_uni,[status(thm)],[492:[bind(A,$thf( sk2 ))]]) ).

thf(678,plain,
    ( ~ ( empty_set @ empty )
    | ~ ( sk2 @ empty ) ),
    inference(simp,[status(thm)],[493]) ).

thf(812,plain,
    ( ~ $true
    | ~ ( sk2 @ empty ) ),
    inference(rewrite,[status(thm)],[678,48]) ).

thf(813,plain,
    ~ ( sk2 @ empty ),
    inference(simp,[status(thm)],[812]) ).

thf(84113,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( C @ set_union2 ) @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( E @ ( D @ in ) ) )
      | ~ ( D @ ( E @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[23006,64]) ).

thf(84114,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( C @ set_union2 ) @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( E @ ( D @ in ) ) )
      | ~ ( D @ ( E @ in ) ) ),
    inference(simp,[status(thm)],[84113]) ).

thf(84115,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ ( sk4 @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[84114:[bind(A,$thf( I )),bind(B,$thf( G )),bind(C,$thf( K )),bind(D,$thf( empty_set @ ( G @ ( sk4 @ sk10 ) ) )),bind(E,$thf( sk4 @ ( K @ set_union2 ) @ ( I @ set_union2 ) ))]]) ).

thf(84450,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ ( sk4 @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[84115]) ).

thf(20964,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk4 @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( D @ ( C @ in ) ) )
      | ~ ( C @ ( D @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[20241,64]) ).

thf(20965,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk4 @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( D @ ( C @ in ) ) )
      | ~ ( C @ ( D @ in ) ) ),
    inference(simp,[status(thm)],[20964]) ).

thf(20966,plain,
    ! [B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ ( B @ ( sk4 @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[20965:[bind(A,$thf( I )),bind(B,$thf( F )),bind(C,$thf( empty_set @ ( F @ ( sk4 @ sk10 ) ) )),bind(D,$thf( I @ ( sk4 @ set_union2 ) ))]]) ).

thf(21264,plain,
    ! [B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ ( B @ ( sk4 @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[20966]) ).

thf(20063,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
       != ( C @ ( D @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19907,2298]) ).

thf(20064,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 @ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ in ) )
     != ( C @ ( D @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[20063]) ).

thf(20151,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk4 != C )
      | ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
       != ( D @ ( C @ set_union2 ) @ ( B @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[20064]) ).

thf(20210,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk4 @ sk10 ) ) )
     != ( C @ ( sk4 @ set_union2 ) @ ( B @ set_union2 ) ) ),
    inference(simp,[status(thm)],[20151]) ).

thf(206,plain,
    ! [B: $i,A: $i] :
      ( ( B != sk2 )
      | ( ( A @ ( sk2 @ ( sk1 @ set_union2 ) @ set_difference ) )
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,24]) ).

thf(207,plain,
    ! [A: $i] :
      ( ( ( A @ ( sk2 @ ( sk1 @ set_union2 ) @ set_difference ) )
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ~ ( A @ ( sk2 @ subset ) )
      | ~ ( sk2 @ ( A @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[206:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).

thf(18389,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( E @ in ) ) )
      | ~ $true
      | ~ ( D @ ( C @ set_difference ) @ ( E @ in ) ) ),
    inference(paramod_ordered,[status(thm)],[13962,122]) ).

thf(18390,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( E @ in ) ) )
      | ~ ( D @ ( C @ set_difference ) @ ( E @ in ) ) ),
    inference(simp,[status(thm)],[18389]) ).

thf(18391,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( C @ ( sk2 @ set_union2 ) @ ( A @ set_difference ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) ),
    inference(pattern_uni,[status(thm)],[18390:[bind(A,$thf( J )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( J @ ( sk2 @ set_union2 ) )),bind(E,$thf( empty_set @ ( G @ ( sk2 @ sk10 ) ) ))]]) ).

thf(18500,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( C @ ( sk2 @ set_union2 ) @ ( A @ set_difference ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) ),
    inference(simp,[status(thm)],[18391]) ).

thf(69437,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk4 @ ( C @ set_union2 ) ) )
      | ( ( D @ ( A @ ( B @ set_union2 ) @ set_union2 ) )
       != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[139,67391]) ).

thf(69438,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( sk4 @ set_union2 ) @ set_union2 ) )
     != empty_set ),
    inference(pattern_uni,[status(thm)],[69437:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( A ))]]) ).

thf(69511,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( sk4 @ set_union2 ) @ set_union2 ) )
     != empty_set ),
    inference(simp,[status(thm)],[69438]) ).

thf(104760,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( empty_set @ ( A @ ( sk1 @ sk10 ) ) @ in ) )
       != ( B @ ( D @ in ) ) )
      | ( C @ ( B @ set_union2 ) @ ( D @ in ) )
      | ~ $true
      | ( sk1 @ empty ) ),
    inference(paramod_ordered,[status(thm)],[102952,80]) ).

thf(104761,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( empty_set @ ( A @ ( sk1 @ sk10 ) ) @ in ) )
       != ( B @ ( D @ in ) ) )
      | ( C @ ( B @ set_union2 ) @ ( D @ in ) )
      | ( sk1 @ empty ) ),
    inference(simp,[status(thm)],[104760]) ).

thf(104762,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( sk1 @ set_union2 ) @ ( empty_set @ ( B @ ( sk1 @ sk10 ) ) @ in ) )
      | ( sk1 @ empty ) ),
    inference(pattern_uni,[status(thm)],[104761:[bind(A,$thf( F )),bind(B,$thf( sk1 )),bind(C,$thf( C )),bind(D,$thf( empty_set @ ( F @ ( sk1 @ sk10 ) ) ))]]) ).

thf(104946,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( sk1 @ set_union2 ) @ ( empty_set @ ( B @ ( sk1 @ sk10 ) ) @ in ) )
      | ( sk1 @ empty ) ),
    inference(simp,[status(thm)],[104762]) ).

thf(57936,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk2 @ ( D @ set_union2 ) ) )
      | ~ ( A @ ( B @ set_union2 ) @ ( C @ set_union2 ) @ empty ) ),
    inference(paramod_ordered,[status(thm)],[139,57561]) ).

thf(57937,plain,
    ! [B: $i,A: $i] :
      ~ ( A @ ( sk2 @ set_union2 ) @ ( B @ set_union2 ) @ empty ),
    inference(pattern_uni,[status(thm)],[57936:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).

thf(58020,plain,
    ! [B: $i,A: $i] :
      ~ ( A @ ( sk2 @ set_union2 ) @ ( B @ set_union2 ) @ empty ),
    inference(simp,[status(thm)],[57937]) ).

thf(21040,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk4 @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( D @ ( E @ in ) ) )
      | ( D @ ( C @ set_union2 ) @ ( E @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[20241,82]) ).

thf(21041,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk4 @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( D @ ( E @ in ) ) )
      | ( D @ ( C @ set_union2 ) @ ( E @ in ) ) ),
    inference(simp,[status(thm)],[21040]) ).

thf(21042,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( sk4 @ set_union2 ) @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) ),
    inference(pattern_uni,[status(thm)],[21041:[bind(A,$thf( J )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( J @ ( sk4 @ set_union2 ) )),bind(E,$thf( empty_set @ ( G @ ( sk4 @ sk10 ) ) ))]]) ).

thf(21167,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( sk4 @ set_union2 ) @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) ),
    inference(simp,[status(thm)],[21042]) ).

thf(98190,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk2 @ ( D @ set_union2 ) ) )
      | ~ ( empty_set @ ( A @ ( B @ set_union2 ) @ ( C @ set_union2 ) @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[139,97900]) ).

thf(98191,plain,
    ! [B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk2 @ set_union2 ) @ ( B @ set_union2 ) @ subset ) ),
    inference(pattern_uni,[status(thm)],[98190:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).

thf(98333,plain,
    ! [B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk2 @ set_union2 ) @ ( B @ set_union2 ) @ subset ) ),
    inference(simp,[status(thm)],[98191]) ).

thf(22541,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( D @ ( sk4 @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) )
       != ( empty_set @ ( C @ ( sk4 @ sk10 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,20197]) ).

thf(22542,plain,
    ! [B: $i,A: $i] :
      ( ( sk4 @ ( A @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk4 @ sk10 ) ) ) ),
    inference(pattern_uni,[status(thm)],[22541:[bind(A,$thf( sk4 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).

thf(22596,plain,
    ! [B: $i,A: $i] :
      ( ( sk4 @ ( A @ set_union2 ) )
     != ( empty_set @ ( B @ ( sk4 @ sk10 ) ) ) ),
    inference(simp,[status(thm)],[22542]) ).

thf(75,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( A @ set_union2 ) ) )
      | ~ ( C @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) )
      | ( C @ ( B @ ( A @ sk6 ) ) ) ),
    inference(cnfConj,[status(thm)],[70]) ).

thf(93,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) )
      | ( C @ ( B @ ( A @ sk6 ) ) )
      | ( C
        = ( B @ ( A @ set_union2 ) ) ) ),
    inference(lifteq,[status(thm)],[75]) ).

thf(94,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) )
      | ( C @ ( B @ ( A @ sk6 ) ) )
      | ( C
        = ( B @ ( A @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[93]) ).

thf(116486,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( sk1 @ set_difference ) )
       != ( empty_set @ ( C @ set_difference ) ) )
      | ( empty_set = C )
      | ( sk1 @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[114585,109]) ).

thf(116487,plain,
    ! [A: $i] :
      ( ( sk1 = empty_set )
      | ( sk1 @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[116486:[bind(A,$thf( A )),bind(B,$thf( empty_set )),bind(C,$thf( sk1 ))]]) ).

thf(118,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( A @ set_difference ) ) )
      | ~ ( C @ ( B @ ( A @ sk9 ) ) )
      | ( B @ ( A @ ( B @ ( C @ sk10 ) ) @ in ) )
      | ~ ( A @ ( A @ ( B @ ( C @ sk10 ) ) @ in ) ) ),
    inference(cnfConj,[status(thm)],[112]) ).

thf(125,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ sk9 ) ) )
      | ( B @ ( A @ ( B @ ( C @ sk10 ) ) @ in ) )
      | ~ ( A @ ( A @ ( B @ ( C @ sk10 ) ) @ in ) )
      | ( C
        = ( B @ ( A @ set_difference ) ) ) ),
    inference(lifteq,[status(thm)],[118]) ).

thf(126,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ sk9 ) ) )
      | ( B @ ( A @ ( B @ ( C @ sk10 ) ) @ in ) )
      | ~ ( A @ ( A @ ( B @ ( C @ sk10 ) ) @ in ) )
      | ( C
        = ( B @ ( A @ set_difference ) ) ) ),
    inference(simp,[status(thm)],[125]) ).

thf(120,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ in ) )
      | ( B @ ( D @ in ) )
      | ~ ( A @ ( D @ in ) )
      | ( C
       != ( B @ ( A @ set_difference ) ) ) ),
    inference(cnfConj,[status(thm)],[112]) ).

thf(135,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ in ) )
      | ( B @ ( D @ in ) )
      | ~ ( A @ ( D @ in ) )
      | ( C
       != ( B @ ( A @ set_difference ) ) ) ),
    inference(lifteq,[status(thm)],[120]) ).

thf(136,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ set_difference ) @ ( C @ in ) )
      | ( B @ ( C @ in ) )
      | ~ ( A @ ( C @ in ) ) ),
    inference(simp,[status(thm)],[135]) ).

thf(2729,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( empty_set != empty_set )
      | ~ ( sk1 @ ( sk2 @ subset ) )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[59,2116]) ).

thf(2730,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ~ ( sk1 @ ( sk2 @ subset ) )
      | ~ ( A @ empty ) ),
    inference(simp,[status(thm)],[2729]) ).

thf(2731,plain,
    ( ~ ( sk1 @ ( sk2 @ subset ) )
    | ~ ( sk1 @ empty ) ),
    inference(pattern_uni,[status(thm)],[2730:[bind(A,$thf( sk1 ))]]) ).

thf(59428,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( D @ ( C @ ( sk2 @ set_union2 ) @ set_union2 ) ) )
      | ( ( A @ ( B @ set_union2 ) )
       != empty_set ) ),
    inference(paramod_ordered,[status(thm)],[139,58265]) ).

thf(59429,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( sk2 @ set_union2 ) @ ( A @ set_union2 ) )
     != empty_set ),
    inference(pattern_uni,[status(thm)],[59428:[bind(A,$thf( F @ ( sk2 @ set_union2 ) )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( B ))]]) ).

thf(59494,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( sk2 @ set_union2 ) @ ( A @ set_union2 ) )
     != empty_set ),
    inference(simp,[status(thm)],[59429]) ).

thf(907,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
       != ( sk2 @ ( sk1 @ set_union2 ) ) )
      | ( sk1 != empty_set )
      | ( ( B @ ( A @ set_difference ) )
       != empty_set )
      | ( A @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
      | ( C @ ( B @ ( A @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[132,154]) ).

thf(908,plain,
    ! [B: $i,A: $i] :
      ( ( sk1 != empty_set )
      | ( ( B @ ( A @ set_difference ) )
       != empty_set )
      | ( A @ ( A @ ( B @ ( sk2 @ ( sk1 @ set_union2 ) @ sk11 ) ) @ in ) )
      | ( sk2 @ ( sk1 @ set_union2 ) @ ( B @ ( A @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[907:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk2 @ ( sk1 @ set_union2 ) ))]]) ).

thf(96531,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != sk1 )
      | ( empty_set != empty_set )
      | ( C @ ( sk1 @ subset ) )
      | ( A @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1599,95184]) ).

thf(96532,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != sk1 )
      | ( C @ ( sk1 @ subset ) )
      | ( A @ ( B @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[96531]) ).

thf(96533,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( sk1 @ subset ) )
      | ( sk1 @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(pattern_uni,[status(thm)],[96532:[bind(A,$thf( sk1 ))]]) ).

thf(96706,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( sk1 @ subset ) )
      | ( sk1 @ ( A @ ( empty_set @ sk9 ) ) ) ),
    inference(simp,[status(thm)],[96533]) ).

thf(76,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( A @ set_union2 ) ) )
      | ~ ( C @ ( B @ ( A @ sk6 ) ) )
      | ~ ( B @ ( A @ ( B @ ( C @ sk7 ) ) @ in ) ) ),
    inference(cnfConj,[status(thm)],[70]) ).

thf(89,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ sk6 ) ) )
      | ~ ( B @ ( A @ ( B @ ( C @ sk7 ) ) @ in ) )
      | ( C
        = ( B @ ( A @ set_union2 ) ) ) ),
    inference(lifteq,[status(thm)],[76]) ).

thf(90,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ sk6 ) ) )
      | ~ ( B @ ( A @ ( B @ ( C @ sk7 ) ) @ in ) )
      | ( C
        = ( B @ ( A @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[89]) ).

thf(15102,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( C @ ( D @ set_union2 ) @ ( E @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13960,3227]) ).

thf(15103,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
     != ( D @ ( C @ ( D @ set_union2 ) @ ( E @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[15102]) ).

thf(15121,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) )
       != D )
      | ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
       != ( C @ ( D @ set_union2 ) @ ( E @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[15103]) ).

thf(15166,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
     != ( C @ ( sk2 @ ( A @ set_union2 ) @ set_union2 ) @ ( D @ set_union2 ) ) ),
    inference(simp,[status(thm)],[15121]) ).

thf(14958,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( C @ in ) ) )
      | ~ ( C @ ( D @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13960,64]) ).

thf(14959,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( C @ in ) ) )
      | ~ ( C @ ( D @ in ) ) ),
    inference(simp,[status(thm)],[14958]) ).

thf(14960,plain,
    ! [B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ ( sk2 @ ( B @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[14959:[bind(A,$thf( H )),bind(B,$thf( F )),bind(C,$thf( empty_set @ ( F @ ( sk2 @ sk10 ) ) )),bind(D,$thf( sk2 @ ( H @ set_union2 ) ))]]) ).

thf(15219,plain,
    ! [B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ ( sk2 @ ( B @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[14960]) ).

thf(308,plain,
    ! [B: $i,A: $i] :
      ( ( B != sk2 )
      | ( ( A @ ( sk1 @ set_union2 ) )
       != empty_set )
      | ( ( sk2 @ ( sk1 @ set_difference ) )
       != empty_set )
      | ~ ( A @ ( B @ subset ) )
      | ~ ( B @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[36,150]) ).

thf(309,plain,
    ! [A: $i] :
      ( ( ( A @ ( sk1 @ set_union2 ) )
       != empty_set )
      | ( ( sk2 @ ( sk1 @ set_difference ) )
       != empty_set )
      | ~ ( A @ ( sk2 @ subset ) )
      | ~ ( sk2 @ ( A @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[308:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).

thf(18213,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( C @ ( E @ ( C @ ( D @ set_union2 ) @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13962,2565]) ).

thf(18214,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
     != ( C @ ( E @ ( C @ ( D @ set_union2 ) @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[18213]) ).

thf(18435,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) )
       != C )
      | ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
       != ( E @ ( C @ ( D @ set_union2 ) @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[18214]) ).

thf(18440,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
     != ( D @ ( A @ ( sk2 @ set_union2 ) @ ( C @ set_union2 ) @ set_union2 ) ) ),
    inference(simp,[status(thm)],[18435]) ).

thf(534,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ ( C @ set_union2 ) ) )
      | ( B = C )
      | ~ ( B @ empty )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[42,67]) ).

thf(535,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( A @ empty )
      | ~ ( B @ ( B @ set_union2 ) @ empty ) ),
    inference(pattern_uni,[status(thm)],[534:[bind(A,$thf( E @ ( E @ set_union2 ) )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).

thf(639,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( A @ empty )
      | ~ ( B @ ( B @ set_union2 ) @ empty ) ),
    inference(simp,[status(thm)],[535]) ).

thf(54371,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ set_union2 ) )
       != ( sk1 @ ( C @ set_union2 ) ) )
      | ( B != empty_set )
      | ( sk2 @ ( sk1 @ subset ) )
      | ~ ( empty_set @ ( A @ subset ) ) ),
    inference(paramod_ordered,[status(thm)],[24051,44179]) ).

thf(54372,plain,
    ! [A: $i] :
      ( ( A != empty_set )
      | ( sk2 @ ( sk1 @ subset ) )
      | ~ ( empty_set @ ( sk1 @ subset ) ) ),
    inference(pattern_uni,[status(thm)],[54371:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).

thf(54472,plain,
    ( ( sk2 @ ( sk1 @ subset ) )
    | ~ ( empty_set @ ( sk1 @ subset ) ) ),
    inference(simp,[status(thm)],[54372]) ).

thf(36331,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ set_union2 ) )
       != ( sk2 @ ( E @ set_union2 ) ) )
      | ( ( C @ ( A @ ( B @ set_union2 ) @ set_union2 ) )
       != ( empty_set @ ( D @ ( sk2 @ sk10 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,26884]) ).

thf(36332,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( sk2 @ set_union2 ) @ set_union2 ) )
     != ( empty_set @ ( C @ ( sk2 @ sk10 ) ) ) ),
    inference(pattern_uni,[status(thm)],[36331:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A ))]]) ).

thf(36488,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( sk2 @ set_union2 ) @ set_union2 ) )
     != ( empty_set @ ( C @ ( sk2 @ sk10 ) ) ) ),
    inference(simp,[status(thm)],[36332]) ).

thf(99,plain,
    ! [A: $i] :
      ( ~ ( A @ empty )
     => ~ ? [B: $i] : ( B @ ( A @ set_union2 ) @ empty ) ),
    inference(miniscope,[status(thm)],[98]) ).

thf(100,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ set_union2 ) @ empty )
      | ( A @ empty ) ),
    inference(cnf,[status(esa)],[99]) ).

thf(13849,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
       != ( C @ ( D @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13698,2298]) ).

thf(13850,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ ( empty_set @ ( A @ ( sk2 @ sk10 ) ) @ in ) )
     != ( C @ ( D @ ( C @ set_union2 ) @ ( B @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[13849]) ).

thf(13925,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 != C )
      | ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
       != ( D @ ( C @ set_union2 ) @ ( B @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[13850]) ).

thf(14006,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( A @ ( sk2 @ sk10 ) ) )
     != ( C @ ( sk2 @ set_union2 ) @ ( B @ set_union2 ) ) ),
    inference(simp,[status(thm)],[13925]) ).

thf(16808,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( empty_set != empty_set )
      | ( ( sk2 @ ( sk2 @ set_difference ) )
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ~ ( A @ empty ) ),
    inference(paramod_ordered,[status(thm)],[59,747]) ).

thf(16809,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( ( sk2 @ ( sk2 @ set_difference ) )
       != ( sk2 @ ( sk1 @ set_difference ) ) )
      | ~ ( A @ empty ) ),
    inference(simp,[status(thm)],[16808]) ).

thf(16810,plain,
    ( ( ( sk2 @ ( sk2 @ set_difference ) )
     != ( sk2 @ ( sk1 @ set_difference ) ) )
    | ~ ( sk1 @ empty ) ),
    inference(pattern_uni,[status(thm)],[16809:[bind(A,$thf( sk1 ))]]) ).

thf(18307,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
       != ( D @ ( D @ ( C @ set_union2 ) @ ( E @ set_union2 ) @ in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[13962,2661]) ).

thf(18308,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( sk2 @ set_union2 ) @ ( empty_set @ ( B @ ( sk2 @ sk10 ) ) @ in ) )
     != ( D @ ( D @ ( C @ set_union2 ) @ ( E @ set_union2 ) @ in ) ) ),
    inference(simp,[status(thm)],[18307]) ).

thf(18420,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk2 @ set_union2 ) )
       != D )
      | ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
       != ( D @ ( C @ set_union2 ) @ ( E @ set_union2 ) ) ) ),
    inference(simp,[status(thm)],[18308]) ).

thf(18534,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( empty_set @ ( B @ ( sk2 @ sk10 ) ) )
     != ( A @ ( sk2 @ set_union2 ) @ ( C @ set_union2 ) @ ( D @ set_union2 ) ) ),
    inference(simp,[status(thm)],[18420]) ).

thf(82213,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( sk4 @ set_union2 ) @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( E @ ( D @ in ) ) )
      | ~ ( D @ ( E @ in ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[21167,64]) ).

thf(82214,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( sk4 @ set_union2 ) @ ( A @ set_union2 ) @ ( empty_set @ ( B @ ( sk4 @ sk10 ) ) @ in ) )
       != ( E @ ( D @ in ) ) )
      | ~ ( D @ ( E @ in ) ) ),
    inference(simp,[status(thm)],[82213]) ).

thf(82215,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ ( C @ ( sk4 @ set_union2 ) @ ( B @ set_union2 ) @ in ) ),
    inference(pattern_uni,[status(thm)],[82214:[bind(A,$thf( I )),bind(B,$thf( G )),bind(C,$thf( L )),bind(D,$thf( empty_set @ ( G @ ( sk4 @ sk10 ) ) )),bind(E,$thf( L @ ( sk4 @ set_union2 ) @ ( I @ set_union2 ) ))]]) ).

thf(82616,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( empty_set @ ( A @ ( sk4 @ sk10 ) ) @ ( C @ ( sk4 @ set_union2 ) @ ( B @ set_union2 ) @ in ) ),
    inference(simp,[status(thm)],[82215]) ).

thf(177442,plain,
    $false,
    inference(e,[status(thm)],[13955,95184,22210,101,37220,16124,94083,88,20194,20200,41015,18514,217,20813,58750,66895,57471,42387,37719,67150,37040,23056,94115,2676,98332,92580,3745,2686,14014,21192,18438,22989,93777,15175,23002,3253,340,14025,384,56,13960,747,44123,93446,32032,42,13997,24,3088,21203,67631,1529,23030,37,25,20209,44179,56595,102952,18437,52,58504,53651,21985,23006,802,8069,20191,26884,43218,110,69049,14002,31340,59495,20203,15161,57,3231,14019,18511,13992,18528,54521,36743,26534,591,2236,106,58019,43203,2254,84,58265,937,147,36013,15186,877,37277,132,7213,40632,12966,18507,92946,100212,93701,2103,92170,14537,18520,60,48722,133765,14004,38090,201,381,43716,93692,36131,334,131021,83890,123101,392,70061,165,26182,14000,30864,15169,20188,275,137,92,847,65,18535,97,20220,20197,41598,15368,57561,2492,2565,879,14011,93634,3784,52321,13996,100722,109,124,56306,125835,26900,92308,114585,31685,489,2504,647,65170,96708,15232,1599,68526,15431,58240,134,205,14008,20241,1563,21226,128,1991,18462,953,104948,14003,20226,41569,15147,32,64,42125,67391,93345,20207,1103,45,70321,88758,123576,3741,69510,3768,1884,22,843,2657,93716,59,124043,21703,281,1707,15160,49,93298,68562,57746,64029,86,21561,21674,70322,15192,219,20205,15316,1524,3270,2116,39,20179,20250,5848,48873,98,15155,15259,103,98764,15173,964,30764,11173,130,399,20201,2752,58505,59535,35577,67390,93703,20208,80,27004,95261,1809,426,14012,14827,13985,939,41151,15252,20196,145,93690,1845,63,9926,2661,95,14017,35744,66916,21163,57786,2298,48,27470,13698,2192,19907,67,7494,97900,20218,94267,2599,15148,2569,13957,656,58481,18478,66967,52759,70359,14022,6073,67430,53794,67149,123577,1485,15196,43,95238,876,845,54234,203,14037,20199,98760,104,52988,23044,30748,55,2608,139,13998,65850,995,813,84450,21264,14026,20210,40161,207,18500,43665,69511,104946,82,43217,58020,36,2287,21167,98333,24051,22596,94,116487,107,126,136,2731,93893,18474,57785,47,59494,62,21236,908,96706,68,90,57425,122,3227,15166,15219,309,21184,18440,2238,639,13962,54472,36488,100,14006,16810,18534,82616]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SEU136+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.41  % Computer : n012.cluster.edu
% 0.13/0.41  % Model    : x86_64 x86_64
% 0.13/0.41  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41  % Memory   : 8046.5625MB
% 0.13/0.41  % OS       : Linux 6.8.0-71-generic
% 0.13/0.41  % CPULimit : 300
% 0.13/0.41  % WCLimit  : 300
% 0.13/0.41  % DateTime : Sat Sep 26 08:38:37 UTC 2026
% 0.13/0.41  % CPUTime  : 
% 0.13/0.41  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.87/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.09/1.06  % [INFO] 	 Parsing done (164ms). 
% 1.09/1.08  % [INFO] 	 Running in sequential loop mode. 
% 1.76/1.42  % [INFO] 	 eprover registered as external prover. 
% 1.76/1.43  % [INFO] 	 Scanning for conjecture ... 
% 1.97/1.51  % [INFO] 	 Found a conjecture (or negated_conjecture) and 22 axioms. Running axiom selection ... 
% 1.97/1.57  % [INFO] 	 Axiom selection finished. Selected 19 axioms (removed 3 axioms). 
% 2.15/1.60  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.15/1.61  % [INFO] 	 Type checking passed. 
% 2.15/1.61  % [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 ... 
% 179.05/50.75  % External prover 'e' found a proof!
% 179.05/50.75  % [INFO] 	 Killing All external provers ... 
% 179.05/50.75  % Time passed: 50212ms (effective reasoning time: 49665ms)
% 179.05/50.75  % 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)>
% 179.05/50.75  % Axioms used in derivation (19): t1_boole, fc1_xboole_0, fc2_xboole_0, t6_boole, commutativity_k2_xboole_0, t7_boole, d4_xboole_0, t3_boole, rc2_xboole_0, antisymmetry_r2_hidden, t4_boole, fc3_xboole_0, d2_xboole_0, d3_tarski, reflexivity_r1_tarski, t8_boole, rc1_xboole_0, idempotence_k2_xboole_0, d10_xboole_0
% 179.05/50.75  % No. of inferences in proof: 1275
% 179.05/50.75  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 50212 ms resp. 49665 ms w/o parsing
% 180.00/50.93  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 180.00/50.94  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------