TSTP Solution File: SEU703^2 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU703^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n018.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 03:39:10 EDT 2024

% Result   : Theorem 163.41s 30.68s
% Output   : Refutation 163.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   23
% Syntax   : Number of formulae    :  307 (  58 unt;  16 typ;   6 def)
%            Number of atoms       : 1099 ( 528 equ;   0 cnn)
%            Maximal formula atoms :   21 (   3 avg)
%            Number of connectives : 3692 ( 573   ~; 416   |;  90   &;2562   @)
%                                         (   0 <=>;  51  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   42 (  42   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  16 usr;  13 con; 0-2 aty)
%            Number of variables   :  815 ( 278   ^ 537   !;   0   ?; 815   :)

% Comments : 
%------------------------------------------------------------------------------
thf(in_type,type,
    in: $i > $i > $o ).

thf(emptyset_type,type,
    emptyset: $i ).

thf(setadjoin_type,type,
    setadjoin: $i > $i > $i ).

thf(dsetconstr_type,type,
    dsetconstr: $i > ( $i > $o ) > $i ).

thf(dsetconstrER_type,type,
    dsetconstrER: $o ).

thf(dsetconstrER_def,definition,
    ( dsetconstrER
    = ( ! [A: $i,B: $i > $o,C: $i] :
          ( ( in @ C @ ( dsetconstr @ A @ B ) )
         => ( B @ C ) ) ) ) ).

thf(setext_type,type,
    setext: $o ).

thf(setext_def,definition,
    ( setext
    = ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ A )
             => ( in @ C @ B ) )
         => ( ! [C: $i] :
                ( ( in @ C @ B )
               => ( in @ C @ A ) )
           => ( A = B ) ) ) ) ) ).

thf(uniqinunit_type,type,
    uniqinunit: $o ).

thf(uniqinunit_def,definition,
    ( uniqinunit
    = ( ! [A: $i,B: $i] :
          ( ( in @ A @ ( setadjoin @ B @ emptyset ) )
         => ( A = B ) ) ) ) ).

thf(eqinunit_type,type,
    eqinunit: $o ).

thf(eqinunit_def,definition,
    ( eqinunit
    = ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ( in @ A @ ( setadjoin @ B @ emptyset ) ) ) ) ) ).

thf(in__Cong_type,type,
    in__Cong: $o ).

thf(in__Cong_def,definition,
    ( in__Cong
    = ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ! [C: $i,D: $i] :
              ( ( C = D )
             => ( ( in @ C @ A )
                = ( in @ D @ B ) ) ) ) ) ) ).

thf(iftrueProp1_type,type,
    iftrueProp1: $o ).

thf(iftrueProp1_def,definition,
    ( iftrueProp1
    = ( ! [A: $i,B: $o,C: $i] :
          ( ( in @ C @ A )
         => ! [D: $i] :
              ( ( in @ D @ A )
             => ( B
               => ( in @ C
                  @ ( dsetconstr @ A
                    @ ^ [E: $i] :
                        ( ( B
                          & ( E = C ) )
                        | ( ~ B
                          & ( E = D ) ) ) ) ) ) ) ) ) ) ).

thf(sk1_type,type,
    sk1: $i > $i > $i ).

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

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

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

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

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

thf(1,conjecture,
    ( dsetconstrER
   => ( setext
     => ( uniqinunit
       => ( eqinunit
         => ( in__Cong
           => ( iftrueProp1
             => ! [A: $i,B: $o,C: $i] :
                  ( ( in @ C @ A )
                 => ! [D: $i] :
                      ( ( in @ D @ A )
                     => ( B
                       => ( ( dsetconstr @ A
                            @ ^ [E: $i] :
                                ( ( B
                                  & ( E = C ) )
                                | ( ~ B
                                  & ( E = D ) ) ) )
                          = ( setadjoin @ C @ emptyset ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp2) ).

thf(2,negated_conjecture,
    ~ ( dsetconstrER
     => ( setext
       => ( uniqinunit
         => ( eqinunit
           => ( in__Cong
             => ( iftrueProp1
               => ! [A: $i,B: $o,C: $i] :
                    ( ( in @ C @ A )
                   => ! [D: $i] :
                        ( ( in @ D @ A )
                       => ( B
                         => ( ( dsetconstr @ A
                              @ ^ [E: $i] :
                                  ( ( B
                                    & ( E = C ) )
                                  | ( ~ B
                                    & ( E = D ) ) ) )
                            = ( setadjoin @ C @ emptyset ) ) ) ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: $i,B: $i > $o,C: $i] :
          ( ( in @ C @ ( dsetconstr @ A @ B ) )
         => ( B @ C ) )
     => ( ! [A: $i,B: $i] :
            ( ! [C: $i] :
                ( ( in @ C @ A )
               => ( in @ C @ B ) )
           => ( ! [C: $i] :
                  ( ( in @ C @ B )
                 => ( in @ C @ A ) )
             => ( A = B ) ) )
       => ( ! [A: $i,B: $i] :
              ( ( in @ A @ ( setadjoin @ B @ emptyset ) )
             => ( A = B ) )
         => ( ! [A: $i,B: $i] :
                ( ( A = B )
               => ( in @ A @ ( setadjoin @ B @ emptyset ) ) )
           => ( ! [A: $i,B: $i] :
                  ( ( A = B )
                 => ! [C: $i,D: $i] :
                      ( ( C = D )
                     => ( ( in @ C @ A )
                        = ( in @ D @ B ) ) ) )
             => ( ! [A: $i,B: $o,C: $i] :
                    ( ( in @ C @ A )
                   => ! [D: $i] :
                        ( ( in @ D @ A )
                       => ( B
                         => ( in @ C
                            @ ( dsetconstr @ A
                              @ ^ [E: $i] :
                                  ( ( B
                                    & ( E = C ) )
                                  | ( ~ B
                                    & ( E = D ) ) ) ) ) ) ) )
               => ! [A: $i,B: $o,C: $i] :
                    ( ( in @ C @ A )
                   => ! [D: $i] :
                        ( ( in @ D @ A )
                       => ( B
                         => ( ( dsetconstr @ A
                              @ ^ [E: $i] :
                                  ( ( B
                                    & ( E = C ) )
                                  | ( ~ B
                                    & ( E = D ) ) ) )
                            = ( setadjoin @ C @ emptyset ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(8,plain,
    in @ sk6 @ sk3,
    inference(cnf,[status(esa)],[3]) ).

thf(4,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(29,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( in @ A @ ( setadjoin @ B @ emptyset ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(30,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( in @ A @ ( setadjoin @ B @ emptyset ) ) ),
    inference(simp,[status(thm)],[29]) ).

thf(174,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( in @ sk6 @ sk3 )
       != ( in @ A @ ( setadjoin @ B @ emptyset ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8,30]) ).

thf(224,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( sk6 != A )
      | ( ( setadjoin @ B @ emptyset )
       != sk3 ) ),
    inference(simp,[status(thm)],[174]) ).

thf(243,plain,
    ! [A: $i] :
      ( ( sk6 = A )
      | ( ( setadjoin @ A @ emptyset )
       != sk3 ) ),
    inference(simp,[status(thm)],[224]) ).

thf(6,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( sk1 @ B @ A ) @ A )
      | ( in @ ( sk2 @ B @ A ) @ B )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(22,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( in @ ( sk1 @ B @ A ) @ A )
      | ( in @ ( sk2 @ B @ A ) @ B ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(23,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( in @ ( sk1 @ B @ A ) @ A )
      | ( in @ ( sk2 @ B @ A ) @ B ) ),
    inference(simp,[status(thm)],[22]) ).

thf(12,plain,
    in @ sk5 @ sk3,
    inference(cnf,[status(esa)],[3]) ).

thf(163,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( in @ sk5 @ A )
      | ( B != sk3 ) ),
    inference(paramod_ordered,[status(thm)],[30,12]) ).

thf(164,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ sk3 @ emptyset ) )
      | ( in @ sk5 @ A ) ),
    inference(pattern_uni,[status(thm)],[163:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).

thf(10891,plain,
    ! [A: $i] :
      ( ( in @ sk5 @ A )
      | ( ( in @ sk6 @ sk3 )
       != ( in @ A @ ( setadjoin @ sk3 @ emptyset ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8,164]) ).

thf(10924,plain,
    ! [A: $i] :
      ( ( in @ sk5 @ A )
      | ( sk6 != A )
      | ( ( setadjoin @ sk3 @ emptyset )
       != sk3 ) ),
    inference(simp,[status(thm)],[10891]) ).

thf(11017,plain,
    ( ( in @ sk5 @ sk6 )
    | ( ( setadjoin @ sk3 @ emptyset )
     != sk3 ) ),
    inference(simp,[status(thm)],[10924]) ).

thf(13389,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( sk1 @ B @ A ) @ A )
      | ( in @ ( sk2 @ B @ A ) @ B )
      | ( in @ sk5 @ sk6 )
      | ( A != sk3 )
      | ( B
       != ( setadjoin @ sk3 @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[23,11017]) ).

thf(13390,plain,
    ! [A: $i] :
      ( ( in @ ( sk1 @ ( setadjoin @ sk3 @ emptyset ) @ A ) @ A )
      | ( in @ ( sk2 @ ( setadjoin @ sk3 @ emptyset ) @ A ) @ ( setadjoin @ sk3 @ emptyset ) )
      | ( in @ sk5 @ sk6 )
      | ( A != sk3 ) ),
    inference(pattern_uni,[status(thm)],[13389:[bind(A,$thf( A )),bind(B,$thf( setadjoin @ sk3 @ emptyset ))]]) ).

thf(13412,plain,
    ( ( in @ ( sk1 @ ( setadjoin @ sk3 @ emptyset ) @ sk3 ) @ sk3 )
    | ( in @ ( sk2 @ ( setadjoin @ sk3 @ emptyset ) @ sk3 ) @ ( setadjoin @ sk3 @ emptyset ) )
    | ( in @ sk5 @ sk6 ) ),
    inference(simp,[status(thm)],[13390]) ).

thf(19263,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( sk1 @ ( setadjoin @ sk3 @ emptyset ) @ sk3 ) @ sk3 )
      | ( in @ sk5 @ sk6 )
      | ( A = B )
      | ( ( in @ ( sk2 @ ( setadjoin @ sk3 @ emptyset ) @ sk3 ) @ ( setadjoin @ sk3 @ emptyset ) )
       != ( in @ A @ ( setadjoin @ B @ emptyset ) ) ) ),
    inference(paramod_ordered,[status(thm)],[13412,30]) ).

thf(19264,plain,
    ( ( in @ ( sk1 @ ( setadjoin @ sk3 @ emptyset ) @ sk3 ) @ sk3 )
    | ( in @ sk5 @ sk6 )
    | ( ( sk2 @ ( setadjoin @ sk3 @ emptyset ) @ sk3 )
      = sk3 ) ),
    inference(pattern_uni,[status(thm)],[19263:[bind(A,$thf( sk2 @ ( setadjoin @ sk3 @ emptyset ) @ sk3 )),bind(B,$thf( sk3 ))]]) ).

thf(5,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( sk1 @ B @ A ) @ A )
      | ~ ( in @ ( sk2 @ B @ A ) @ A )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(17,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( in @ ( sk1 @ B @ A ) @ A )
      | ~ ( in @ ( sk2 @ B @ A ) @ A ) ),
    inference(lifteq,[status(thm)],[5]) ).

thf(18,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( in @ ( sk1 @ B @ A ) @ A )
      | ~ ( in @ ( sk2 @ B @ A ) @ A ) ),
    inference(simp,[status(thm)],[17]) ).

thf(16,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
      | ( B @ C ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(303,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ B
          @ ( dsetconstr @ A
            @ ^ [C: $i] : $false ) )
      | $false ),
    inference(prim_subst,[status(thm)],[16:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : $false ))]]) ).

thf(334,plain,
    ! [B: $i,A: $i] :
      ~ ( in @ B
        @ ( dsetconstr @ A
          @ ^ [C: $i] : $false ) ),
    inference(simp,[status(thm)],[303]) ).

thf(353,plain,
    ! [B: $i,A: $i] :
      ( ( in @ sk5 @ sk3 )
     != ( in @ B
        @ ( dsetconstr @ A
          @ ^ [C: $i] : $false ) ) ),
    inference(paramod_ordered,[status(thm)],[12,334]) ).

thf(369,plain,
    ! [B: $i,A: $i] :
      ( ( sk5 != B )
      | ( ( dsetconstr @ A
          @ ^ [C: $i] : $false )
       != sk3 ) ),
    inference(simp,[status(thm)],[353]) ).

thf(382,plain,
    ! [A: $i] :
      ( ( dsetconstr @ A
        @ ^ [B: $i] : $false )
     != sk3 ),
    inference(simp,[status(thm)],[369]) ).

thf(391,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( B != sk3 )
      | ( A
       != ( dsetconstr @ C
          @ ^ [D: $i] : $false ) ) ),
    inference(paramod_ordered,[status(thm)],[30,382]) ).

thf(392,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in
          @ ( dsetconstr @ B
            @ ^ [C: $i] : $false )
          @ ( setadjoin @ A @ emptyset ) )
      | ( A != sk3 ) ),
    inference(pattern_uni,[status(thm)],[391:[bind(A,$thf( dsetconstr @ D @ ^ [E: $i] : $false )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).

thf(400,plain,
    ! [A: $i] :
      ~ ( in
        @ ( dsetconstr @ A
          @ ^ [B: $i] : $false )
        @ ( setadjoin @ sk3 @ emptyset ) ),
    inference(simp,[status(thm)],[392]) ).

thf(14,plain,
    ( ( dsetconstr @ sk3
      @ ^ [A: $i] :
          ( ( sk4
            & ( A = sk5 ) )
          | ( ~ sk4
            & ( A = sk6 ) ) ) )
   != ( setadjoin @ sk5 @ emptyset ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(21,plain,
    ( ( dsetconstr @ sk3
      @ ^ [A: $i] :
          ( ( sk4
            & ( A = sk5 ) )
          | ( ~ sk4
            & ( A = sk6 ) ) ) )
   != ( setadjoin @ sk5 @ emptyset ) ),
    inference(lifteq,[status(thm)],[14]) ).

thf(11,plain,
    sk4,
    inference(cnf,[status(esa)],[3]) ).

thf(33,plain,
    ( ( dsetconstr @ sk3
      @ ^ [A: $i] :
          ( ( $true
            & ( A = sk5 ) )
          | ( ~ $true
            & ( A = sk6 ) ) ) )
   != ( setadjoin @ sk5 @ emptyset ) ),
    inference(rewrite,[status(thm)],[21,11]) ).

thf(34,plain,
    ( ( dsetconstr @ sk3
      @ ^ [A: $i] : ( A = sk5 ) )
   != ( setadjoin @ sk5 @ emptyset ) ),
    inference(simp,[status(thm)],[33]) ).

thf(199,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( A
       != ( setadjoin @ sk5 @ emptyset ) )
      | ( B
       != ( dsetconstr @ sk3
          @ ^ [C: $i] : ( C = sk5 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[30,34]) ).

thf(200,plain,
    ! [A: $i] :
      ( ~ ( in @ A
          @ ( setadjoin
            @ ( dsetconstr @ sk3
              @ ^ [B: $i] : ( B = sk5 ) )
            @ emptyset ) )
      | ( A
       != ( setadjoin @ sk5 @ emptyset ) ) ),
    inference(pattern_uni,[status(thm)],[199:[bind(A,$thf( A )),bind(B,$thf( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) ))]]) ).

thf(231,plain,
    ~ ( in @ ( setadjoin @ sk5 @ emptyset )
      @ ( setadjoin
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ emptyset ) ),
    inference(simp,[status(thm)],[200]) ).

thf(579,plain,
    ( ( in @ ( setadjoin @ sk5 @ emptyset )
      @ ( setadjoin
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ emptyset ) )
   != ( in @ sk6 @ sk3 ) ),
    inference(paramod_ordered,[status(thm)],[8,231]) ).

thf(648,plain,
    ( ( ( setadjoin @ sk5 @ emptyset )
     != sk6 )
    | ( ( setadjoin
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ emptyset )
     != sk3 ) ),
    inference(simp,[status(thm)],[579]) ).

thf(3036,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( B != sk6 )
      | ( ( setadjoin
          @ ( dsetconstr @ sk3
            @ ^ [C: $i] : ( C = sk5 ) )
          @ emptyset )
       != sk3 )
      | ( A
       != ( setadjoin @ sk5 @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[30,648]) ).

thf(3037,plain,
    ! [A: $i] :
      ( ~ ( in @ ( setadjoin @ sk5 @ emptyset ) @ ( setadjoin @ A @ emptyset ) )
      | ( A != sk6 )
      | ( ( setadjoin
          @ ( dsetconstr @ sk3
            @ ^ [B: $i] : ( B = sk5 ) )
          @ emptyset )
       != sk3 ) ),
    inference(pattern_uni,[status(thm)],[3036:[bind(A,$thf( setadjoin @ sk5 @ emptyset )),bind(B,$thf( B ))]]) ).

thf(3096,plain,
    ( ~ ( in @ ( setadjoin @ sk5 @ emptyset ) @ ( setadjoin @ sk6 @ emptyset ) )
    | ( ( setadjoin
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ emptyset )
     != sk3 ) ),
    inference(simp,[status(thm)],[3037]) ).

thf(13,plain,
    ! [D: $i,C: $i,B: $o,A: $i] :
      ( ~ ( in @ C @ A )
      | ~ ( in @ D @ A )
      | ~ B
      | ( in @ C
        @ ( dsetconstr @ A
          @ ^ [E: $i] :
              ( ( B
                & ( E = C ) )
              | ( ~ B
                & ( E = D ) ) ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(26,plain,
    ! [D: $i,C: $i,B: $o,A: $i] :
      ( ~ ( in @ C @ A )
      | ~ ( in @ D @ A )
      | ~ B
      | ( in @ C
        @ ( dsetconstr @ A
          @ ^ [E: $i] :
              ( ( B
                & ( E = C ) )
              | ( ~ B
                & ( E = D ) ) ) ) ) ),
    inference(simp,[status(thm)],[13]) ).

thf(40,plain,
    ! [H: $i,G: $i,F: $o,E: $i,D: $i,C: $i,B: $o,A: $i] :
      ( ~ ( in @ C @ A )
      | ~ ( in @ D @ A )
      | ~ B
      | ~ ( in @ H @ E )
      | ~ F
      | ( in @ G
        @ ( dsetconstr @ E
          @ ^ [I: $i] :
              ( ( F
                & ( I = G ) )
              | ( ~ F
                & ( I = H ) ) ) ) )
      | ( ( in @ C
          @ ( dsetconstr @ A
            @ ^ [I: $i] :
                ( ( B
                  & ( I = C ) )
                | ( ~ B
                  & ( I = D ) ) ) ) )
       != ( in @ G @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[26,26]) ).

thf(41,plain,
    ! [F: $i,E: $i,D: $o,C: $i,B: $i,A: $o] :
      ( ~ ( in @ B @ F )
      | ~ ( in @ C @ F )
      | ~ A
      | ~ ( in @ E
          @ ( dsetconstr @ F
            @ ^ [G: $i] :
                ( ( A
                  & ( G = B ) )
                | ( ~ A
                  & ( G = C ) ) ) ) )
      | ~ D
      | ( in @ B
        @ ( dsetconstr
          @ ( dsetconstr @ F
            @ ^ [G: $i] :
                ( ( A
                  & ( G = B ) )
                | ( ~ A
                  & ( G = C ) ) ) )
          @ ^ [G: $i] :
              ( ( D
                & ( G = B ) )
              | ( ~ D
                & ( G = E ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( dsetconstr @ I @ ^ [J: $i] : ( ( B & ( J = C ) ) | ( ~ ( B ) & ( J = D ) ) ) )),bind(F,$thf( F )),bind(G,$thf( C )),bind(H,$thf( H ))]]) ).

thf(69,plain,
    ! [F: $i,E: $i,D: $o,C: $i,B: $i,A: $o] :
      ( ~ ( in @ B @ F )
      | ~ ( in @ C @ F )
      | ~ A
      | ~ ( in @ E
          @ ( dsetconstr @ F
            @ ^ [G: $i] :
                ( ( A
                  & ( G = B ) )
                | ( ~ A
                  & ( G = C ) ) ) ) )
      | ~ D
      | ( in @ B
        @ ( dsetconstr
          @ ( dsetconstr @ F
            @ ^ [G: $i] :
                ( ( A
                  & ( G = B ) )
                | ( ~ A
                  & ( G = C ) ) ) )
          @ ^ [G: $i] :
              ( ( D
                & ( G = B ) )
              | ( ~ D
                & ( G = E ) ) ) ) ) ),
    inference(simp,[status(thm)],[41]) ).

thf(15,plain,
    ! [B: $i,A: $i] :
      ( ( A != B )
      | ( in @ A @ ( setadjoin @ B @ emptyset ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(31,plain,
    ! [B: $i,A: $i] :
      ( ( A != B )
      | ( in @ A @ ( setadjoin @ B @ emptyset ) ) ),
    inference(lifteq,[status(thm)],[15]) ).

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

thf(424,plain,
    ! [B: $i,A: $i] :
      ( ( in @ A @ ( setadjoin @ A @ emptyset ) )
     != ( in
        @ ( dsetconstr @ B
          @ ^ [C: $i] : $false )
        @ ( setadjoin @ sk3 @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[32,400]) ).

thf(447,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( dsetconstr @ B
          @ ^ [C: $i] : $false ) )
      | ( ( setadjoin @ A @ emptyset )
       != ( setadjoin @ sk3 @ emptyset ) ) ),
    inference(simp,[status(thm)],[424]) ).

thf(479,plain,
    ! [A: $i] :
      ( ( setadjoin
        @ ( dsetconstr @ A
          @ ^ [B: $i] : $false )
        @ emptyset )
     != ( setadjoin @ sk3 @ emptyset ) ),
    inference(simp,[status(thm)],[447]) ).

thf(283,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ( B @ C )
      | ( ( in @ sk6 @ sk3 )
       != ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8,16]) ).

thf(319,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ( B @ C )
      | ( sk6 != C )
      | ( ( dsetconstr @ A @ B )
       != sk3 ) ),
    inference(simp,[status(thm)],[283]) ).

thf(352,plain,
    ! [B: $i > $o,A: $i] :
      ( ( B @ sk6 )
      | ( ( dsetconstr @ A @ B )
       != sk3 ) ),
    inference(simp,[status(thm)],[319]) ).

thf(301,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
      | ( ( B @ C )
       != ( ~ ( in @ C @ ( dsetconstr @ A @ B ) ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[16]) ).

thf(311,plain,
    ! [A: $i] :
      ~ ( in
        @ ( dsetconstr @ A
          @ ^ [B: $i] :
              ~ ( in @ B @ B ) )
        @ ( dsetconstr @ A
          @ ^ [B: $i] :
              ~ ( in @ B @ B ) ) ),
    inference(pre_uni,[status(thm)],[301:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ~ ( in @ D @ D ) )),bind(C,$thf( dsetconstr @ A @ ^ [D: $i] : ~ ( in @ D @ D ) ))]]) ).

thf(4248,plain,
    ! [D: $i,C: $i,B: $i > $o,A: $i] :
      ( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
      | ( ( B @ C )
       != ( in
          @ ( dsetconstr @ D
            @ ^ [E: $i] :
                ~ ( in @ E @ E ) )
          @ ( dsetconstr @ D
            @ ^ [E: $i] :
                ~ ( in @ E @ E ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[16,311]) ).

thf(4286,plain,
    ! [B: $i,A: $i] :
      ~ ( in
        @ ( dsetconstr @ B
          @ ^ [C: $i] :
              ~ ( in @ C @ C ) )
        @ ( dsetconstr @ A
          @ ^ [C: $i] : ( in @ C @ C ) ) ),
    inference(pre_uni,[status(thm)],[4248:[bind(A,$thf( A )),bind(B,$thf( ^ [E: $i] : ( in @ E @ E ) )),bind(C,$thf( dsetconstr @ D @ ^ [E: $i] : ~ ( in @ E @ E ) )),bind(D,$thf( D ))]]) ).

thf(4319,plain,
    ! [B: $i,A: $i] :
      ~ ( in
        @ ( dsetconstr @ B
          @ ^ [C: $i] :
              ~ ( in @ C @ C ) )
        @ ( dsetconstr @ A
          @ ^ [C: $i] : ( in @ C @ C ) ) ),
    inference(simp,[status(thm)],[4286]) ).

thf(4347,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ A @ ( setadjoin @ A @ emptyset ) )
     != ( in
        @ ( dsetconstr @ C
          @ ^ [D: $i] :
              ~ ( in @ D @ D ) )
        @ ( dsetconstr @ B
          @ ^ [D: $i] : ( in @ D @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[32,4319]) ).

thf(4375,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( dsetconstr @ C
          @ ^ [D: $i] :
              ~ ( in @ D @ D ) ) )
      | ( ( setadjoin @ A @ emptyset )
       != ( dsetconstr @ B
          @ ^ [D: $i] : ( in @ D @ D ) ) ) ),
    inference(simp,[status(thm)],[4347]) ).

thf(4391,plain,
    ! [B: $i,A: $i] :
      ( ( setadjoin
        @ ( dsetconstr @ B
          @ ^ [C: $i] :
              ~ ( in @ C @ C ) )
        @ emptyset )
     != ( dsetconstr @ A
        @ ^ [C: $i] : ( in @ C @ C ) ) ),
    inference(simp,[status(thm)],[4375]) ).

thf(425,plain,
    ! [A: $i] :
      ( ( in
        @ ( dsetconstr @ A
          @ ^ [B: $i] : $false )
        @ ( setadjoin @ sk3 @ emptyset ) )
     != ( in @ sk5 @ sk3 ) ),
    inference(paramod_ordered,[status(thm)],[12,400]) ).

thf(449,plain,
    ! [A: $i] :
      ( ( ( dsetconstr @ A
          @ ^ [B: $i] : $false )
       != sk5 )
      | ( ( setadjoin @ sk3 @ emptyset )
       != sk3 ) ),
    inference(simp,[status(thm)],[425]) ).

thf(193,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( B
       != ( setadjoin @ sk5 @ emptyset ) )
      | ( A
       != ( dsetconstr @ sk3
          @ ^ [C: $i] : ( C = sk5 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[30,34]) ).

thf(194,plain,
    ! [A: $i] :
      ( ~ ( in
          @ ( dsetconstr @ sk3
            @ ^ [B: $i] : ( B = sk5 ) )
          @ ( setadjoin @ A @ emptyset ) )
      | ( A
       != ( setadjoin @ sk5 @ emptyset ) ) ),
    inference(pattern_uni,[status(thm)],[193:[bind(A,$thf( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) )),bind(B,$thf( B ))]]) ).

thf(228,plain,
    ~ ( in
      @ ( dsetconstr @ sk3
        @ ^ [A: $i] : ( A = sk5 ) )
      @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) ),
    inference(simp,[status(thm)],[194]) ).

thf(481,plain,
    ( ( in
      @ ( dsetconstr @ sk3
        @ ^ [A: $i] : ( A = sk5 ) )
      @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) )
   != ( in @ sk6 @ sk3 ) ),
    inference(paramod_ordered,[status(thm)],[8,228]) ).

thf(550,plain,
    ( ( ( dsetconstr @ sk3
        @ ^ [A: $i] : ( A = sk5 ) )
     != sk6 )
    | ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
     != sk3 ) ),
    inference(simp,[status(thm)],[481]) ).

thf(117,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( sk1 @ B @ A ) @ A )
      | ( in @ ( sk2 @ B @ A ) @ B )
      | ( A
       != ( setadjoin @ sk5 @ emptyset ) )
      | ( B
       != ( dsetconstr @ sk3
          @ ^ [C: $i] : ( C = sk5 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[23,34]) ).

thf(118,plain,
    ! [A: $i] :
      ( ( in
        @ ( sk1
          @ ( dsetconstr @ sk3
            @ ^ [B: $i] : ( B = sk5 ) )
          @ A )
        @ A )
      | ( in
        @ ( sk2
          @ ( dsetconstr @ sk3
            @ ^ [B: $i] : ( B = sk5 ) )
          @ A )
        @ ( dsetconstr @ sk3
          @ ^ [B: $i] : ( B = sk5 ) ) )
      | ( A
       != ( setadjoin @ sk5 @ emptyset ) ) ),
    inference(pattern_uni,[status(thm)],[117:[bind(A,$thf( A )),bind(B,$thf( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) ))]]) ).

thf(154,plain,
    ( ( in
      @ ( sk1
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ ( setadjoin @ sk5 @ emptyset ) )
      @ ( setadjoin @ sk5 @ emptyset ) )
    | ( in
      @ ( sk2
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ ( setadjoin @ sk5 @ emptyset ) )
      @ ( dsetconstr @ sk3
        @ ^ [A: $i] : ( A = sk5 ) ) ) ),
    inference(simp,[status(thm)],[118]) ).

thf(5138,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ( in
        @ ( sk1
          @ ( dsetconstr @ sk3
            @ ^ [D: $i] : ( D = sk5 ) )
          @ ( setadjoin @ sk5 @ emptyset ) )
        @ ( setadjoin @ sk5 @ emptyset ) )
      | ( B @ C )
      | ( ( in
          @ ( sk2
            @ ( dsetconstr @ sk3
              @ ^ [D: $i] : ( D = sk5 ) )
            @ ( setadjoin @ sk5 @ emptyset ) )
          @ ( dsetconstr @ sk3
            @ ^ [D: $i] : ( D = sk5 ) ) )
       != ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[154,16]) ).

thf(5139,plain,
    ( ( in
      @ ( sk1
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ ( setadjoin @ sk5 @ emptyset ) )
      @ ( setadjoin @ sk5 @ emptyset ) )
    | ( ( sk2
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ ( setadjoin @ sk5 @ emptyset ) )
      = sk5 ) ),
    inference(pattern_uni,[status(thm)],[5138:[bind(A,$thf( sk3 )),bind(B,$thf( ^ [D: $i] : ( D = sk5 ) )),bind(C,$thf( sk2 @ ( dsetconstr @ sk3 @ ^ [D: $i] : ( D = sk5 ) ) @ ( setadjoin @ sk5 @ emptyset ) ))]]) ).

thf(5277,plain,
    ( ( ( sk2
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ ( setadjoin @ sk5 @ emptyset ) )
      = sk5 )
    | ( in
      @ ( sk1
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ ( setadjoin @ sk5 @ emptyset ) )
      @ ( setadjoin @ sk5 @ emptyset ) ) ),
    inference(lifteq,[status(thm)],[5139]) ).

thf(6850,plain,
    ( ( in
      @ ( sk1
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ ( setadjoin @ sk5 @ emptyset ) )
      @ ( setadjoin @ sk5 @ emptyset ) )
    | ( in @ sk5
      @ ( dsetconstr @ sk3
        @ ^ [A: $i] : ( A = sk5 ) ) )
    | ( ( sk2
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ ( setadjoin @ sk5 @ emptyset ) )
     != ( sk2
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ ( setadjoin @ sk5 @ emptyset ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5277,154]) ).

thf(6851,plain,
    ( ( in
      @ ( sk1
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ ( setadjoin @ sk5 @ emptyset ) )
      @ ( setadjoin @ sk5 @ emptyset ) )
    | ( in @ sk5
      @ ( dsetconstr @ sk3
        @ ^ [A: $i] : ( A = sk5 ) ) ) ),
    inference(pattern_uni,[status(thm)],[6850:[]]) ).

thf(4259,plain,
    ! [B: $i,A: $i] :
      ( ( in @ A @ ( setadjoin @ A @ emptyset ) )
     != ( in
        @ ( dsetconstr @ B
          @ ^ [C: $i] :
              ~ ( in @ C @ C ) )
        @ ( dsetconstr @ B
          @ ^ [C: $i] :
              ~ ( in @ C @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[32,311]) ).

thf(4289,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( dsetconstr @ B
          @ ^ [C: $i] :
              ~ ( in @ C @ C ) ) )
      | ( ( setadjoin @ A @ emptyset )
       != ( dsetconstr @ B
          @ ^ [C: $i] :
              ~ ( in @ C @ C ) ) ) ),
    inference(simp,[status(thm)],[4259]) ).

thf(4294,plain,
    ! [A: $i] :
      ( ( setadjoin
        @ ( dsetconstr @ A
          @ ^ [B: $i] :
              ~ ( in @ B @ B ) )
        @ emptyset )
     != ( dsetconstr @ A
        @ ^ [B: $i] :
            ~ ( in @ B @ B ) ) ),
    inference(simp,[status(thm)],[4289]) ).

thf(1433,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( A != sk6 )
      | ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
       != sk3 )
      | ( B
       != ( dsetconstr @ sk3
          @ ^ [C: $i] : ( C = sk5 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[30,550]) ).

thf(1434,plain,
    ! [A: $i] :
      ( ~ ( in @ A
          @ ( setadjoin
            @ ( dsetconstr @ sk3
              @ ^ [B: $i] : ( B = sk5 ) )
            @ emptyset ) )
      | ( A != sk6 )
      | ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
       != sk3 ) ),
    inference(pattern_uni,[status(thm)],[1433:[bind(A,$thf( A )),bind(B,$thf( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) ))]]) ).

thf(1458,plain,
    ( ~ ( in @ sk6
        @ ( setadjoin
          @ ( dsetconstr @ sk3
            @ ^ [A: $i] : ( A = sk5 ) )
          @ emptyset ) )
    | ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
     != sk3 ) ),
    inference(simp,[status(thm)],[1434]) ).

thf(393,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( A != sk3 )
      | ( B
       != ( dsetconstr @ C
          @ ^ [D: $i] : $false ) ) ),
    inference(paramod_ordered,[status(thm)],[30,382]) ).

thf(394,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A
          @ ( setadjoin
            @ ( dsetconstr @ B
              @ ^ [C: $i] : $false )
            @ emptyset ) )
      | ( A != sk3 ) ),
    inference(pattern_uni,[status(thm)],[393:[bind(A,$thf( A )),bind(B,$thf( dsetconstr @ D @ ^ [E: $i] : $false )),bind(C,$thf( D ))]]) ).

thf(401,plain,
    ! [A: $i] :
      ~ ( in @ sk3
        @ ( setadjoin
          @ ( dsetconstr @ A
            @ ^ [B: $i] : $false )
          @ emptyset ) ),
    inference(simp,[status(thm)],[394]) ).

thf(1156,plain,
    ! [A: $i] :
      ( ( in @ sk5 @ sk3 )
     != ( in @ sk3
        @ ( setadjoin
          @ ( dsetconstr @ A
            @ ^ [B: $i] : $false )
          @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[12,401]) ).

thf(1196,plain,
    ! [A: $i] :
      ( ( sk5 != sk3 )
      | ( ( setadjoin
          @ ( dsetconstr @ A
            @ ^ [B: $i] : $false )
          @ emptyset )
       != sk3 ) ),
    inference(simp,[status(thm)],[1156]) ).

thf(613,plain,
    ( ( in @ ( setadjoin @ sk5 @ emptyset )
      @ ( setadjoin
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ emptyset ) )
   != ( in @ sk5 @ sk3 ) ),
    inference(paramod_ordered,[status(thm)],[12,231]) ).

thf(654,plain,
    ( ( ( setadjoin @ sk5 @ emptyset )
     != sk5 )
    | ( ( setadjoin
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ emptyset )
     != sk3 ) ),
    inference(simp,[status(thm)],[613]) ).

thf(3204,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( B != sk5 )
      | ( ( setadjoin
          @ ( dsetconstr @ sk3
            @ ^ [C: $i] : ( C = sk5 ) )
          @ emptyset )
       != sk3 )
      | ( A
       != ( setadjoin @ sk5 @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[30,654]) ).

thf(3205,plain,
    ! [A: $i] :
      ( ~ ( in @ ( setadjoin @ sk5 @ emptyset ) @ ( setadjoin @ A @ emptyset ) )
      | ( A != sk5 )
      | ( ( setadjoin
          @ ( dsetconstr @ sk3
            @ ^ [B: $i] : ( B = sk5 ) )
          @ emptyset )
       != sk3 ) ),
    inference(pattern_uni,[status(thm)],[3204:[bind(A,$thf( setadjoin @ sk5 @ emptyset )),bind(B,$thf( B ))]]) ).

thf(3236,plain,
    ( ~ ( in @ ( setadjoin @ sk5 @ emptyset ) @ ( setadjoin @ sk5 @ emptyset ) )
    | ( ( setadjoin
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ emptyset )
     != sk3 ) ),
    inference(simp,[status(thm)],[3205]) ).

thf(9,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ ( sk1 @ B @ A ) @ B )
      | ~ ( in @ ( sk2 @ B @ A ) @ A )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(24,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( in @ ( sk1 @ B @ A ) @ B )
      | ~ ( in @ ( sk2 @ B @ A ) @ A ) ),
    inference(lifteq,[status(thm)],[9]) ).

thf(25,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( in @ ( sk1 @ B @ A ) @ B )
      | ~ ( in @ ( sk2 @ B @ A ) @ A ) ),
    inference(simp,[status(thm)],[24]) ).

thf(1269,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( A
       != ( setadjoin @ sk3 @ emptyset ) )
      | ( B
       != ( setadjoin
          @ ( dsetconstr @ C
            @ ^ [D: $i] : $false )
          @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[30,479]) ).

thf(1270,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A
          @ ( setadjoin
            @ ( setadjoin
              @ ( dsetconstr @ B
                @ ^ [C: $i] : $false )
              @ emptyset )
            @ emptyset ) )
      | ( A
       != ( setadjoin @ sk3 @ emptyset ) ) ),
    inference(pattern_uni,[status(thm)],[1269:[bind(A,$thf( A )),bind(B,$thf( setadjoin @ ( dsetconstr @ F @ ^ [E: $i] : $false ) @ emptyset )),bind(C,$thf( F ))]]) ).

thf(1287,plain,
    ! [A: $i] :
      ~ ( in @ ( setadjoin @ sk3 @ emptyset )
        @ ( setadjoin
          @ ( setadjoin
            @ ( dsetconstr @ A
              @ ^ [B: $i] : $false )
            @ emptyset )
          @ emptyset ) ),
    inference(simp,[status(thm)],[1270]) ).

thf(281,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ( B @ C )
      | ( ( in @ sk5 @ sk3 )
       != ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12,16]) ).

thf(318,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ( B @ C )
      | ( sk5 != C )
      | ( ( dsetconstr @ A @ B )
       != sk3 ) ),
    inference(simp,[status(thm)],[281]) ).

thf(351,plain,
    ! [B: $i > $o,A: $i] :
      ( ( B @ sk5 )
      | ( ( dsetconstr @ A @ B )
       != sk3 ) ),
    inference(simp,[status(thm)],[318]) ).

thf(1760,plain,
    ! [B: $i > $o,A: $i] :
      ( ~ ( B @ sk5 )
      | ( ( dsetconstr @ A
          @ ^ [C: $i] :
              ~ ( B @ C ) )
       != sk3 ) ),
    inference(prim_subst,[status(thm)],[351:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).

thf(1791,plain,
    ! [B: $i > $o,A: $i] :
      ( ( ( dsetconstr @ A
          @ ^ [C: $i] :
              ~ ( B @ C ) )
       != sk3 )
      | ~ ( B @ sk5 ) ),
    inference(cnf,[status(esa)],[1760]) ).

thf(1792,plain,
    ! [B: $i > $o,A: $i] :
      ( ( ( dsetconstr @ A
          @ ^ [C: $i] :
              ~ ( B @ C ) )
       != sk3 )
      | ~ ( B @ sk5 ) ),
    inference(simp,[status(thm)],[1791]) ).

thf(361,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ A @ ( setadjoin @ A @ emptyset ) )
     != ( in @ C
        @ ( dsetconstr @ B
          @ ^ [D: $i] : $false ) ) ),
    inference(paramod_ordered,[status(thm)],[32,334]) ).

thf(370,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != C )
      | ( ( setadjoin @ A @ emptyset )
       != ( dsetconstr @ B
          @ ^ [D: $i] : $false ) ) ),
    inference(simp,[status(thm)],[361]) ).

thf(383,plain,
    ! [B: $i,A: $i] :
      ( ( setadjoin @ B @ emptyset )
     != ( dsetconstr @ A
        @ ^ [C: $i] : $false ) ),
    inference(simp,[status(thm)],[370]) ).

thf(1321,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( B
       != ( dsetconstr @ C
          @ ^ [E: $i] : $false ) )
      | ( A
       != ( setadjoin @ D @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[30,383]) ).

thf(1322,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ ( setadjoin @ C @ emptyset ) @ ( setadjoin @ A @ emptyset ) )
      | ( A
       != ( dsetconstr @ B
          @ ^ [D: $i] : $false ) ) ),
    inference(pattern_uni,[status(thm)],[1321:[bind(A,$thf( setadjoin @ E @ emptyset )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( E ))]]) ).

thf(1339,plain,
    ! [B: $i,A: $i] :
      ~ ( in @ ( setadjoin @ B @ emptyset )
        @ ( setadjoin
          @ ( dsetconstr @ A
            @ ^ [C: $i] : $false )
          @ emptyset ) ),
    inference(simp,[status(thm)],[1322]) ).

thf(4448,plain,
    ! [E: $i,D: $i,C: $i,B: $i > $o,A: $i] :
      ( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
      | ( ( B @ C )
       != ( in @ ( setadjoin @ E @ emptyset )
          @ ( setadjoin
            @ ( dsetconstr @ D
              @ ^ [F: $i] : $false )
            @ emptyset ) ) ) ),
    inference(paramod_ordered,[status(thm)],[16,1339]) ).

thf(4528,plain,
    ! [B: $i,A: $i] :
      ~ ( in
        @ ( setadjoin
          @ ( dsetconstr @ B
            @ ^ [C: $i] : $false )
          @ emptyset )
        @ ( dsetconstr @ A
          @ ^ [C: $i] : ( in @ C @ C ) ) ),
    inference(pre_uni,[status(thm)],[4448:[bind(A,$thf( A )),bind(B,$thf( ^ [F: $i] : ( in @ F @ F ) )),bind(C,$thf( setadjoin @ ( dsetconstr @ D @ ^ [F: $i] : $false ) @ emptyset )),bind(D,$thf( D )),bind(E,$thf( dsetconstr @ D @ ^ [F: $i] : $false ))]]) ).

thf(4563,plain,
    ! [B: $i,A: $i] :
      ~ ( in
        @ ( setadjoin
          @ ( dsetconstr @ B
            @ ^ [C: $i] : $false )
          @ emptyset )
        @ ( dsetconstr @ A
          @ ^ [C: $i] : ( in @ C @ C ) ) ),
    inference(simp,[status(thm)],[4528]) ).

thf(6978,plain,
    ! [B: $i > $o,A: $i] :
      ( ( ( dsetconstr @ A
          @ ^ [C: $i] :
              ~ ( B @ C ) )
       != sk3 )
      | ( ( in @ sk5 @ sk3 )
       != ( B @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[12,1792]) ).

thf(7015,plain,
    ! [A: $i] :
      ( ( dsetconstr @ A
        @ ^ [B: $i] :
            ~ ( in @ B @ sk3 ) )
     != sk3 ),
    inference(pre_uni,[status(thm)],[6978:[bind(A,$thf( A )),bind(B,$thf( ^ [C: $i] : ( in @ C @ sk3 ) ))]]) ).

thf(7278,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( B != sk3 )
      | ( A
       != ( dsetconstr @ C
          @ ^ [D: $i] :
              ~ ( in @ D @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[30,7015]) ).

thf(7279,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in
          @ ( dsetconstr @ B
            @ ^ [C: $i] :
                ~ ( in @ C @ sk3 ) )
          @ ( setadjoin @ A @ emptyset ) )
      | ( A != sk3 ) ),
    inference(pattern_uni,[status(thm)],[7278:[bind(A,$thf( dsetconstr @ D @ ^ [E: $i] : ~ ( in @ E @ sk3 ) )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).

thf(7294,plain,
    ! [A: $i] :
      ~ ( in
        @ ( dsetconstr @ A
          @ ^ [B: $i] :
              ~ ( in @ B @ sk3 ) )
        @ ( setadjoin @ sk3 @ emptyset ) ),
    inference(simp,[status(thm)],[7279]) ).

thf(407,plain,
    ! [A: $i] :
      ( ( in
        @ ( dsetconstr @ A
          @ ^ [B: $i] : $false )
        @ ( setadjoin @ sk3 @ emptyset ) )
     != ( in @ sk6 @ sk3 ) ),
    inference(paramod_ordered,[status(thm)],[8,400]) ).

thf(448,plain,
    ! [A: $i] :
      ( ( ( dsetconstr @ A
          @ ^ [B: $i] : $false )
       != sk6 )
      | ( ( setadjoin @ sk3 @ emptyset )
       != sk3 ) ),
    inference(simp,[status(thm)],[407]) ).

thf(1417,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( B != sk6 )
      | ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
       != sk3 )
      | ( A
       != ( dsetconstr @ sk3
          @ ^ [C: $i] : ( C = sk5 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[30,550]) ).

thf(1418,plain,
    ! [A: $i] :
      ( ~ ( in
          @ ( dsetconstr @ sk3
            @ ^ [B: $i] : ( B = sk5 ) )
          @ ( setadjoin @ A @ emptyset ) )
      | ( A != sk6 )
      | ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
       != sk3 ) ),
    inference(pattern_uni,[status(thm)],[1417:[bind(A,$thf( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) )),bind(B,$thf( B ))]]) ).

thf(1450,plain,
    ( ~ ( in
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ ( setadjoin @ sk6 @ emptyset ) )
    | ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
     != sk3 ) ),
    inference(simp,[status(thm)],[1418]) ).

thf(4472,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ A @ ( setadjoin @ A @ emptyset ) )
     != ( in @ ( setadjoin @ C @ emptyset )
        @ ( setadjoin
          @ ( dsetconstr @ B
            @ ^ [D: $i] : $false )
          @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[32,1339]) ).

thf(4520,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( setadjoin @ C @ emptyset ) )
      | ( ( setadjoin @ A @ emptyset )
       != ( setadjoin
          @ ( dsetconstr @ B
            @ ^ [D: $i] : $false )
          @ emptyset ) ) ),
    inference(simp,[status(thm)],[4472]) ).

thf(4556,plain,
    ! [B: $i,A: $i] :
      ( ( setadjoin @ ( setadjoin @ B @ emptyset ) @ emptyset )
     != ( setadjoin
        @ ( dsetconstr @ A
          @ ^ [C: $i] : $false )
        @ emptyset ) ),
    inference(simp,[status(thm)],[4520]) ).

thf(1263,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( B
       != ( setadjoin @ sk3 @ emptyset ) )
      | ( A
       != ( setadjoin
          @ ( dsetconstr @ C
            @ ^ [D: $i] : $false )
          @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[30,479]) ).

thf(1264,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in
          @ ( setadjoin
            @ ( dsetconstr @ B
              @ ^ [C: $i] : $false )
            @ emptyset )
          @ ( setadjoin @ A @ emptyset ) )
      | ( A
       != ( setadjoin @ sk3 @ emptyset ) ) ),
    inference(pattern_uni,[status(thm)],[1263:[bind(A,$thf( setadjoin @ ( dsetconstr @ F @ ^ [E: $i] : $false ) @ emptyset )),bind(B,$thf( B )),bind(C,$thf( F ))]]) ).

thf(1283,plain,
    ! [A: $i] :
      ~ ( in
        @ ( setadjoin
          @ ( dsetconstr @ A
            @ ^ [B: $i] : $false )
          @ emptyset )
        @ ( setadjoin @ ( setadjoin @ sk3 @ emptyset ) @ emptyset ) ),
    inference(simp,[status(thm)],[1264]) ).

thf(1153,plain,
    ! [D: $i,C: $i,B: $i > $o,A: $i] :
      ( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
      | ( ( B @ C )
       != ( in @ sk3
          @ ( setadjoin
            @ ( dsetconstr @ D
              @ ^ [E: $i] : $false )
            @ emptyset ) ) ) ),
    inference(paramod_ordered,[status(thm)],[16,401]) ).

thf(1198,plain,
    ! [B: $i,A: $i] :
      ~ ( in
        @ ( setadjoin
          @ ( dsetconstr @ B
            @ ^ [C: $i] : $false )
          @ emptyset )
        @ ( dsetconstr @ A @ ( in @ sk3 ) ) ),
    inference(pre_uni,[status(thm)],[1153:[bind(A,$thf( A )),bind(B,$thf( in @ sk3 )),bind(C,$thf( setadjoin @ ( dsetconstr @ D @ ^ [E: $i] : $false ) @ emptyset )),bind(D,$thf( D ))]]) ).

thf(1223,plain,
    ! [B: $i,A: $i] :
      ~ ( in
        @ ( setadjoin
          @ ( dsetconstr @ B
            @ ^ [C: $i] : $false )
          @ emptyset )
        @ ( dsetconstr @ A @ ( in @ sk3 ) ) ),
    inference(simp,[status(thm)],[1198]) ).

thf(42,plain,
    ! [H: $i,G: $i,F: $o,E: $i,D: $i,C: $i,B: $o,A: $i] :
      ( ~ ( in @ C @ A )
      | ~ ( in @ D @ A )
      | ~ B
      | ~ ( in @ G @ E )
      | ~ F
      | ( in @ G
        @ ( dsetconstr @ E
          @ ^ [I: $i] :
              ( ( F
                & ( I = G ) )
              | ( ~ F
                & ( I = H ) ) ) ) )
      | ( ( in @ C
          @ ( dsetconstr @ A
            @ ^ [I: $i] :
                ( ( B
                  & ( I = C ) )
                | ( ~ B
                  & ( I = D ) ) ) ) )
       != ( in @ H @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[26,26]) ).

thf(43,plain,
    ! [F: $i,E: $i,D: $o,C: $i,B: $i,A: $o] :
      ( ~ ( in @ B @ F )
      | ~ ( in @ C @ F )
      | ~ A
      | ~ ( in @ E
          @ ( dsetconstr @ F
            @ ^ [G: $i] :
                ( ( A
                  & ( G = B ) )
                | ( ~ A
                  & ( G = C ) ) ) ) )
      | ~ D
      | ( in @ E
        @ ( dsetconstr
          @ ( dsetconstr @ F
            @ ^ [G: $i] :
                ( ( A
                  & ( G = B ) )
                | ( ~ A
                  & ( G = C ) ) ) )
          @ ^ [G: $i] :
              ( ( D
                & ( G = E ) )
              | ( ~ D
                & ( G = B ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( dsetconstr @ I @ ^ [J: $i] : ( ( B & ( J = C ) ) | ( ~ ( B ) & ( J = D ) ) ) )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( C ))]]) ).

thf(70,plain,
    ! [F: $i,E: $i,D: $o,C: $i,B: $i,A: $o] :
      ( ~ ( in @ B @ F )
      | ~ ( in @ C @ F )
      | ~ A
      | ~ ( in @ E
          @ ( dsetconstr @ F
            @ ^ [G: $i] :
                ( ( A
                  & ( G = B ) )
                | ( ~ A
                  & ( G = C ) ) ) ) )
      | ~ D
      | ( in @ E
        @ ( dsetconstr
          @ ( dsetconstr @ F
            @ ^ [G: $i] :
                ( ( A
                  & ( G = B ) )
                | ( ~ A
                  & ( G = C ) ) ) )
          @ ^ [G: $i] :
              ( ( D
                & ( G = E ) )
              | ( ~ D
                & ( G = B ) ) ) ) ) ),
    inference(simp,[status(thm)],[43]) ).

thf(7,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ ( sk1 @ B @ A ) @ B )
      | ( in @ ( sk2 @ B @ A ) @ B )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(27,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( in @ ( sk1 @ B @ A ) @ B )
      | ( in @ ( sk2 @ B @ A ) @ B ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(28,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( in @ ( sk1 @ B @ A ) @ B )
      | ( in @ ( sk2 @ B @ A ) @ B ) ),
    inference(simp,[status(thm)],[27]) ).

thf(7880,plain,
    ! [B: $i,A: $i] :
      ( ( in @ sk5
        @ ( dsetconstr @ sk3
          @ ^ [C: $i] : ( C = sk5 ) ) )
      | ( A = B )
      | ( ( in
          @ ( sk1
            @ ( dsetconstr @ sk3
              @ ^ [C: $i] : ( C = sk5 ) )
            @ ( setadjoin @ sk5 @ emptyset ) )
          @ ( setadjoin @ sk5 @ emptyset ) )
       != ( in @ A @ ( setadjoin @ B @ emptyset ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6851,30]) ).

thf(7881,plain,
    ( ( in @ sk5
      @ ( dsetconstr @ sk3
        @ ^ [A: $i] : ( A = sk5 ) ) )
    | ( ( sk1
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ ( setadjoin @ sk5 @ emptyset ) )
      = sk5 ) ),
    inference(pattern_uni,[status(thm)],[7880:[bind(A,$thf( sk1 @ ( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) ) @ ( setadjoin @ sk5 @ emptyset ) )),bind(B,$thf( sk5 ))]]) ).

thf(54,plain,
    ! [D: $i,C: $i,B: $o,A: $i] :
      ( ~ ( in @ C @ A )
      | ~ ( in @ D @ A )
      | ( in @ C
        @ ( dsetconstr @ A
          @ ^ [E: $i] :
              ( ( B
                & ( E = C ) )
              | ( ~ B
                & ( E = D ) ) ) ) )
      | ( B
       != ( in @ D @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[26]) ).

thf(64,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ A @ C )
      | ~ ( in @ B @ C )
      | ( in @ A
        @ ( dsetconstr @ C
          @ ^ [D: $i] :
              ( ( ( in @ B @ C )
                & ( D = A ) )
              | ( ~ ( in @ B @ C )
                & ( D = B ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[54:[bind(A,$thf( F )),bind(B,$thf( in @ E @ F )),bind(C,$thf( C )),bind(D,$thf( E ))]]) ).

thf(65,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ A @ C )
      | ~ ( in @ B @ C )
      | ( in @ A
        @ ( dsetconstr @ C
          @ ^ [D: $i] :
              ( ( ( in @ B @ C )
                & ( D = A ) )
              | ( ~ ( in @ B @ C )
                & ( D = B ) ) ) ) ) ),
    inference(simp,[status(thm)],[64]) ).

thf(405,plain,
    ! [D: $i,C: $i,B: $i > $o,A: $i] :
      ( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
      | ( ( B @ C )
       != ( in
          @ ( dsetconstr @ D
            @ ^ [E: $i] : $false )
          @ ( setadjoin @ sk3 @ emptyset ) ) ) ),
    inference(paramod_ordered,[status(thm)],[16,400]) ).

thf(451,plain,
    ! [B: $i > $i,A: $i] :
      ~ ( in @ ( setadjoin @ sk3 @ emptyset )
        @ ( dsetconstr @ A
          @ ^ [C: $i] :
              ( in
              @ ( dsetconstr @ ( B @ C )
                @ ^ [D: $i] : $false )
              @ C ) ) ),
    inference(pre_uni,[status(thm)],[405:[bind(A,$thf( A )),bind(B,$thf( ^ [F: $i] : ( in @ ( dsetconstr @ ( K @ F ) @ ^ [G: $i] : $false ) @ F ) )),bind(C,$thf( setadjoin @ sk3 @ emptyset )),bind(D,$thf( K @ ( setadjoin @ sk3 @ emptyset ) ))]]) ).

thf(456,plain,
    ! [B: $i > $i,A: $i] :
      ~ ( in @ ( setadjoin @ sk3 @ emptyset )
        @ ( dsetconstr @ A
          @ ^ [C: $i] :
              ( in
              @ ( dsetconstr @ ( B @ C )
                @ ^ [D: $i] : $false )
              @ C ) ) ),
    inference(simp,[status(thm)],[451]) ).

thf(3060,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( ( setadjoin @ sk5 @ emptyset )
       != sk6 )
      | ( A != sk3 )
      | ( B
       != ( setadjoin
          @ ( dsetconstr @ sk3
            @ ^ [C: $i] : ( C = sk5 ) )
          @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[30,648]) ).

thf(3061,plain,
    ! [A: $i] :
      ( ~ ( in @ A
          @ ( setadjoin
            @ ( setadjoin
              @ ( dsetconstr @ sk3
                @ ^ [B: $i] : ( B = sk5 ) )
              @ emptyset )
            @ emptyset ) )
      | ( ( setadjoin @ sk5 @ emptyset )
       != sk6 )
      | ( A != sk3 ) ),
    inference(pattern_uni,[status(thm)],[3060:[bind(A,$thf( A )),bind(B,$thf( setadjoin @ ( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) ) @ emptyset ))]]) ).

thf(3105,plain,
    ( ~ ( in @ sk3
        @ ( setadjoin
          @ ( setadjoin
            @ ( dsetconstr @ sk3
              @ ^ [A: $i] : ( A = sk5 ) )
            @ emptyset )
          @ emptyset ) )
    | ( ( setadjoin @ sk5 @ emptyset )
     != sk6 ) ),
    inference(simp,[status(thm)],[3061]) ).

thf(172,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( in @ sk6 @ A )
      | ( B != sk3 ) ),
    inference(paramod_ordered,[status(thm)],[30,8]) ).

thf(173,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ sk3 @ emptyset ) )
      | ( in @ sk6 @ A ) ),
    inference(pattern_uni,[status(thm)],[172:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).

thf(17299,plain,
    ! [A: $i] :
      ( ( in @ sk6 @ A )
      | ( ( in @ sk6 @ sk3 )
       != ( in @ A @ ( setadjoin @ sk3 @ emptyset ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8,173]) ).

thf(17348,plain,
    ! [A: $i] :
      ( ( in @ sk6 @ A )
      | ( sk6 != A )
      | ( ( setadjoin @ sk3 @ emptyset )
       != sk3 ) ),
    inference(simp,[status(thm)],[17299]) ).

thf(17462,plain,
    ( ( in @ sk6 @ sk6 )
    | ( ( setadjoin @ sk3 @ emptyset )
     != sk3 ) ),
    inference(simp,[status(thm)],[17348]) ).

thf(1201,plain,
    ! [B: $i > $i,A: $i] :
      ~ ( in @ emptyset
        @ ( dsetconstr @ A
          @ ^ [C: $i] :
              ( in @ sk3
              @ ( setadjoin
                @ ( dsetconstr @ ( B @ C )
                  @ ^ [D: $i] : $false )
                @ C ) ) ) ),
    inference(pre_uni,[status(thm)],[1153:[bind(A,$thf( A )),bind(B,$thf( ^ [F: $i] : ( in @ sk3 @ ( setadjoin @ ( dsetconstr @ ( I @ F ) @ ^ [G: $i] : $false ) @ F ) ) )),bind(C,$thf( emptyset )),bind(D,$thf( I @ emptyset ))]]) ).

thf(1227,plain,
    ! [B: $i > $i,A: $i] :
      ~ ( in @ emptyset
        @ ( dsetconstr @ A
          @ ^ [C: $i] :
              ( in @ sk3
              @ ( setadjoin
                @ ( dsetconstr @ ( B @ C )
                  @ ^ [D: $i] : $false )
                @ C ) ) ) ),
    inference(simp,[status(thm)],[1201]) ).

thf(354,plain,
    ! [E: $i,D: $i,C: $i,B: $i > $o,A: $i] :
      ( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
      | ( ( B @ C )
       != ( in @ E
          @ ( dsetconstr @ D
            @ ^ [F: $i] : $false ) ) ) ),
    inference(paramod_ordered,[status(thm)],[16,334]) ).

thf(375,plain,
    ! [C: $i > $i,B: $i,A: $i] :
      ~ ( in
        @ ( dsetconstr @ B
          @ ^ [D: $i] : $false )
        @ ( dsetconstr @ A
          @ ^ [D: $i] : ( in @ ( C @ D ) @ D ) ) ),
    inference(pre_uni,[status(thm)],[354:[bind(A,$thf( A )),bind(B,$thf( ^ [G: $i] : ( in @ ( F @ G ) @ G ) )),bind(C,$thf( dsetconstr @ D @ ^ [F: $i] : $false )),bind(D,$thf( D )),bind(E,$thf( F @ ( dsetconstr @ D @ ^ [G: $i] : $false ) ))]]) ).

thf(388,plain,
    ! [C: $i > $i,B: $i,A: $i] :
      ~ ( in
        @ ( dsetconstr @ B
          @ ^ [D: $i] : $false )
        @ ( dsetconstr @ A
          @ ^ [D: $i] : ( in @ ( C @ D ) @ D ) ) ),
    inference(simp,[status(thm)],[375]) ).

thf(6030,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ A @ ( setadjoin @ A @ emptyset ) )
     != ( in
        @ ( setadjoin
          @ ( dsetconstr @ C
            @ ^ [D: $i] : $false )
          @ emptyset )
        @ ( dsetconstr @ B
          @ ^ [D: $i] : ( in @ D @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[32,4563]) ).

thf(6073,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( setadjoin
          @ ( dsetconstr @ C
            @ ^ [D: $i] : $false )
          @ emptyset ) )
      | ( ( setadjoin @ A @ emptyset )
       != ( dsetconstr @ B
          @ ^ [D: $i] : ( in @ D @ D ) ) ) ),
    inference(simp,[status(thm)],[6030]) ).

thf(6111,plain,
    ! [B: $i,A: $i] :
      ( ( setadjoin
        @ ( setadjoin
          @ ( dsetconstr @ B
            @ ^ [C: $i] : $false )
          @ emptyset )
        @ emptyset )
     != ( dsetconstr @ A
        @ ^ [C: $i] : ( in @ C @ C ) ) ),
    inference(simp,[status(thm)],[6073]) ).

thf(515,plain,
    ( ( in
      @ ( dsetconstr @ sk3
        @ ^ [A: $i] : ( A = sk5 ) )
      @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) )
   != ( in @ sk5 @ sk3 ) ),
    inference(paramod_ordered,[status(thm)],[12,228]) ).

thf(554,plain,
    ( ( ( dsetconstr @ sk3
        @ ^ [A: $i] : ( A = sk5 ) )
     != sk5 )
    | ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
     != sk3 ) ),
    inference(simp,[status(thm)],[515]) ).

thf(1565,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( ( dsetconstr @ sk3
          @ ^ [C: $i] : ( C = sk5 ) )
       != sk5 )
      | ( A != sk3 )
      | ( B
       != ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[30,554]) ).

thf(1566,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) @ emptyset ) )
      | ( ( dsetconstr @ sk3
          @ ^ [B: $i] : ( B = sk5 ) )
       != sk5 )
      | ( A != sk3 ) ),
    inference(pattern_uni,[status(thm)],[1565:[bind(A,$thf( A )),bind(B,$thf( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ))]]) ).

thf(1584,plain,
    ( ~ ( in @ sk3 @ ( setadjoin @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) @ emptyset ) )
    | ( ( dsetconstr @ sk3
        @ ^ [A: $i] : ( A = sk5 ) )
     != sk5 ) ),
    inference(simp,[status(thm)],[1566]) ).

thf(452,plain,
    ! [B: $i,A: $i] :
      ~ ( in
        @ ( dsetconstr @ B
          @ ^ [C: $i] : $false )
        @ ( dsetconstr @ A
          @ ^ [C: $i] : ( in @ C @ ( setadjoin @ sk3 @ emptyset ) ) ) ),
    inference(pre_uni,[status(thm)],[405:[bind(A,$thf( A )),bind(B,$thf( ^ [E: $i] : ( in @ E @ ( setadjoin @ sk3 @ emptyset ) ) )),bind(C,$thf( dsetconstr @ D @ ^ [E: $i] : $false )),bind(D,$thf( D ))]]) ).

thf(457,plain,
    ! [B: $i,A: $i] :
      ~ ( in
        @ ( dsetconstr @ B
          @ ^ [C: $i] : $false )
        @ ( dsetconstr @ A
          @ ^ [C: $i] : ( in @ C @ ( setadjoin @ sk3 @ emptyset ) ) ) ),
    inference(simp,[status(thm)],[452]) ).

thf(514,plain,
    ! [A: $i] :
      ( ( in @ A @ ( setadjoin @ A @ emptyset ) )
     != ( in
        @ ( dsetconstr @ sk3
          @ ^ [B: $i] : ( B = sk5 ) )
        @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[32,228]) ).

thf(551,plain,
    ! [A: $i] :
      ( ( A
       != ( dsetconstr @ sk3
          @ ^ [B: $i] : ( B = sk5 ) ) )
      | ( ( setadjoin @ A @ emptyset )
       != ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) ) ),
    inference(simp,[status(thm)],[514]) ).

thf(569,plain,
    ( ( setadjoin
      @ ( dsetconstr @ sk3
        @ ^ [A: $i] : ( A = sk5 ) )
      @ emptyset )
   != ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) ),
    inference(simp,[status(thm)],[551]) ).

thf(48,plain,
    ! [E: $i,D: $i,C: $o,B: $i,A: $i] :
      ( ~ ( in @ E @ B )
      | ~ C
      | ( in @ D
        @ ( dsetconstr @ B
          @ ^ [F: $i] :
              ( ( C
                & ( F = D ) )
              | ( ~ C
                & ( F = E ) ) ) ) )
      | ( ( in @ A @ ( setadjoin @ A @ emptyset ) )
       != ( in @ D @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[32,26]) ).

thf(49,plain,
    ! [C: $i,B: $i,A: $o] :
      ( ~ ( in @ B @ ( setadjoin @ C @ emptyset ) )
      | ~ A
      | ( in @ C
        @ ( dsetconstr @ ( setadjoin @ C @ emptyset )
          @ ^ [D: $i] :
              ( ( A
                & ( D = C ) )
              | ( ~ A
                & ( D = B ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( F )),bind(B,$thf( setadjoin @ F @ emptyset )),bind(C,$thf( C )),bind(D,$thf( F )),bind(E,$thf( E ))]]) ).

thf(73,plain,
    ! [C: $i,B: $i,A: $o] :
      ( ~ ( in @ B @ ( setadjoin @ C @ emptyset ) )
      | ~ A
      | ( in @ C
        @ ( dsetconstr @ ( setadjoin @ C @ emptyset )
          @ ^ [D: $i] :
              ( ( A
                & ( D = C ) )
              | ( ~ A
                & ( D = B ) ) ) ) ) ),
    inference(simp,[status(thm)],[49]) ).

thf(165,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( in @ sk5 @ sk3 )
       != ( in @ A @ ( setadjoin @ B @ emptyset ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12,30]) ).

thf(225,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( sk5 != A )
      | ( ( setadjoin @ B @ emptyset )
       != sk3 ) ),
    inference(simp,[status(thm)],[165]) ).

thf(244,plain,
    ! [A: $i] :
      ( ( sk5 = A )
      | ( ( setadjoin @ A @ emptyset )
       != sk3 ) ),
    inference(simp,[status(thm)],[225]) ).

thf(44,plain,
    ! [D: $i,C: $i,B: $o,A: $i] :
      ( ~ ( in @ D @ A )
      | ~ B
      | ( in @ C
        @ ( dsetconstr @ A
          @ ^ [E: $i] :
              ( ( B
                & ( E = C ) )
              | ( ~ B
                & ( E = D ) ) ) ) )
      | ( ( in @ sk6 @ sk3 )
       != ( in @ C @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8,26]) ).

thf(45,plain,
    ! [B: $i,A: $o] :
      ( ~ ( in @ B @ sk3 )
      | ~ A
      | ( in @ sk6
        @ ( dsetconstr @ sk3
          @ ^ [C: $i] :
              ( ( A
                & ( C = sk6 ) )
              | ( ~ A
                & ( C = B ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[44:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk6 ))]]) ).

thf(71,plain,
    ! [B: $i,A: $o] :
      ( ~ ( in @ B @ sk3 )
      | ~ A
      | ( in @ sk6
        @ ( dsetconstr @ sk3
          @ ^ [C: $i] :
              ( ( A
                & ( C = sk6 ) )
              | ( ~ A
                & ( C = B ) ) ) ) ) ),
    inference(simp,[status(thm)],[45]) ).

thf(1199,plain,
    ! [B: $i,A: $i] :
      ~ ( in
        @ ( dsetconstr @ B
          @ ^ [C: $i] : $false )
        @ ( dsetconstr @ A
          @ ^ [C: $i] : ( in @ sk3 @ ( setadjoin @ C @ emptyset ) ) ) ),
    inference(pre_uni,[status(thm)],[1153:[bind(A,$thf( A )),bind(B,$thf( ^ [E: $i] : ( in @ sk3 @ ( setadjoin @ E @ emptyset ) ) )),bind(C,$thf( dsetconstr @ D @ ^ [E: $i] : $false )),bind(D,$thf( D ))]]) ).

thf(1224,plain,
    ! [B: $i,A: $i] :
      ~ ( in
        @ ( dsetconstr @ B
          @ ^ [C: $i] : $false )
        @ ( dsetconstr @ A
          @ ^ [C: $i] : ( in @ sk3 @ ( setadjoin @ C @ emptyset ) ) ) ),
    inference(simp,[status(thm)],[1199]) ).

thf(1154,plain,
    ! [A: $i] :
      ( ( in @ sk6 @ sk3 )
     != ( in @ sk3
        @ ( setadjoin
          @ ( dsetconstr @ A
            @ ^ [B: $i] : $false )
          @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[8,401]) ).

thf(1194,plain,
    ! [A: $i] :
      ( ( sk6 != sk3 )
      | ( ( setadjoin
          @ ( dsetconstr @ A
            @ ^ [B: $i] : $false )
          @ emptyset )
       != sk3 ) ),
    inference(simp,[status(thm)],[1154]) ).

thf(1325,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( B
       != ( setadjoin @ D @ emptyset ) )
      | ( A
       != ( dsetconstr @ C
          @ ^ [E: $i] : $false ) ) ),
    inference(paramod_ordered,[status(thm)],[30,383]) ).

thf(1326,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in
          @ ( dsetconstr @ C
            @ ^ [D: $i] : $false )
          @ ( setadjoin @ A @ emptyset ) )
      | ( A
       != ( setadjoin @ B @ emptyset ) ) ),
    inference(pattern_uni,[status(thm)],[1325:[bind(A,$thf( dsetconstr @ E @ ^ [F: $i] : $false )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( D ))]]) ).

thf(1341,plain,
    ! [B: $i,A: $i] :
      ~ ( in
        @ ( dsetconstr @ B
          @ ^ [C: $i] : $false )
        @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ emptyset ) ),
    inference(simp,[status(thm)],[1326]) ).

thf(4666,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ A @ ( setadjoin @ A @ emptyset ) )
     != ( in
        @ ( dsetconstr @ C
          @ ^ [D: $i] : $false )
        @ ( setadjoin @ ( setadjoin @ B @ emptyset ) @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[32,1341]) ).

thf(4729,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( dsetconstr @ C
          @ ^ [D: $i] : $false ) )
      | ( ( setadjoin @ A @ emptyset )
       != ( setadjoin @ ( setadjoin @ B @ emptyset ) @ emptyset ) ) ),
    inference(simp,[status(thm)],[4666]) ).

thf(4790,plain,
    ! [B: $i,A: $i] :
      ( ( setadjoin
        @ ( dsetconstr @ B
          @ ^ [C: $i] : $false )
        @ emptyset )
     != ( setadjoin @ ( setadjoin @ A @ emptyset ) @ emptyset ) ),
    inference(simp,[status(thm)],[4729]) ).

thf(161,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( in @ A @ sk3 )
      | ( B != sk5 ) ),
    inference(paramod_ordered,[status(thm)],[30,12]) ).

thf(162,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ sk5 @ emptyset ) )
      | ( in @ A @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[161:[bind(A,$thf( A )),bind(B,$thf( sk5 ))]]) ).

thf(9145,plain,
    ! [A: $i] :
      ( ( in @ sk5
        @ ( dsetconstr @ sk3
          @ ^ [B: $i] : ( B = sk5 ) ) )
      | ( in @ A @ sk3 )
      | ( ( in
          @ ( sk1
            @ ( dsetconstr @ sk3
              @ ^ [B: $i] : ( B = sk5 ) )
            @ ( setadjoin @ sk5 @ emptyset ) )
          @ ( setadjoin @ sk5 @ emptyset ) )
       != ( in @ A @ ( setadjoin @ sk5 @ emptyset ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6851,162]) ).

thf(9146,plain,
    ( ( in @ sk5
      @ ( dsetconstr @ sk3
        @ ^ [A: $i] : ( A = sk5 ) ) )
    | ( in
      @ ( sk1
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ ( setadjoin @ sk5 @ emptyset ) )
      @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[9145:[bind(A,$thf( sk1 @ ( dsetconstr @ sk3 @ ^ [B: $i] : ( B = sk5 ) ) @ ( setadjoin @ sk5 @ emptyset ) ))]]) ).

thf(8818,plain,
    ( ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
     != sk3 )
    | ( ( in @ sk6
        @ ( setadjoin
          @ ( dsetconstr @ sk3
            @ ^ [A: $i] : ( A = sk5 ) )
          @ emptyset ) )
     != ( in @ sk6 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[8,1458]) ).

thf(8879,plain,
    ( ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
     != sk3 )
    | ( sk6 != sk6 )
    | ( ( setadjoin
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ emptyset )
     != sk3 ) ),
    inference(simp,[status(thm)],[8818]) ).

thf(8926,plain,
    ( ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
     != sk3 )
    | ( ( setadjoin
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ emptyset )
     != sk3 ) ),
    inference(simp,[status(thm)],[8879]) ).

thf(111,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( sk1 @ B @ A ) @ A )
      | ( in @ ( sk2 @ B @ A ) @ B )
      | ( B
       != ( setadjoin @ sk5 @ emptyset ) )
      | ( A
       != ( dsetconstr @ sk3
          @ ^ [C: $i] : ( C = sk5 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[23,34]) ).

thf(112,plain,
    ! [A: $i] :
      ( ( in
        @ ( sk1 @ A
          @ ( dsetconstr @ sk3
            @ ^ [B: $i] : ( B = sk5 ) ) )
        @ ( dsetconstr @ sk3
          @ ^ [B: $i] : ( B = sk5 ) ) )
      | ( in
        @ ( sk2 @ A
          @ ( dsetconstr @ sk3
            @ ^ [B: $i] : ( B = sk5 ) ) )
        @ A )
      | ( A
       != ( setadjoin @ sk5 @ emptyset ) ) ),
    inference(pattern_uni,[status(thm)],[111:[bind(A,$thf( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) )),bind(B,$thf( B ))]]) ).

thf(151,plain,
    ( ( in
      @ ( sk1 @ ( setadjoin @ sk5 @ emptyset )
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) ) )
      @ ( dsetconstr @ sk3
        @ ^ [A: $i] : ( A = sk5 ) ) )
    | ( in
      @ ( sk2 @ ( setadjoin @ sk5 @ emptyset )
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) ) )
      @ ( setadjoin @ sk5 @ emptyset ) ) ),
    inference(simp,[status(thm)],[112]) ).

thf(725,plain,
    ! [B: $i,A: $i] :
      ( ( in
        @ ( sk1 @ ( setadjoin @ sk5 @ emptyset )
          @ ( dsetconstr @ sk3
            @ ^ [C: $i] : ( C = sk5 ) ) )
        @ ( dsetconstr @ sk3
          @ ^ [C: $i] : ( C = sk5 ) ) )
      | ( A = B )
      | ( ( in
          @ ( sk2 @ ( setadjoin @ sk5 @ emptyset )
            @ ( dsetconstr @ sk3
              @ ^ [C: $i] : ( C = sk5 ) ) )
          @ ( setadjoin @ sk5 @ emptyset ) )
       != ( in @ A @ ( setadjoin @ B @ emptyset ) ) ) ),
    inference(paramod_ordered,[status(thm)],[151,30]) ).

thf(726,plain,
    ( ( in
      @ ( sk1 @ ( setadjoin @ sk5 @ emptyset )
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) ) )
      @ ( dsetconstr @ sk3
        @ ^ [A: $i] : ( A = sk5 ) ) )
    | ( ( sk2 @ ( setadjoin @ sk5 @ emptyset )
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) ) )
      = sk5 ) ),
    inference(pattern_uni,[status(thm)],[725:[bind(A,$thf( sk2 @ ( setadjoin @ sk5 @ emptyset ) @ ( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) ) )),bind(B,$thf( sk5 ))]]) ).

thf(35,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ B
        @ ( dsetconstr @ A
          @ ^ [D: $i] :
              ( ( $true
                & ( D = B ) )
              | ( ~ $true
                & ( D = C ) ) ) ) )
      | ~ ( in @ B @ A )
      | ~ ( in @ C @ A ) ),
    inference(simp,[status(thm)],[26]) ).

thf(66,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ B
        @ ( dsetconstr @ A
          @ ^ [D: $i] : ( D = B ) ) )
      | ~ ( in @ B @ A )
      | ~ ( in @ C @ A ) ),
    inference(simp,[status(thm)],[35]) ).

thf(157,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( in @ B @ sk3 )
      | ( A != sk5 ) ),
    inference(paramod_ordered,[status(thm)],[30,12]) ).

thf(158,plain,
    ! [A: $i] :
      ( ~ ( in @ sk5 @ ( setadjoin @ A @ emptyset ) )
      | ( in @ A @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[157:[bind(A,$thf( sk5 ))]]) ).

thf(240,plain,
    ! [A: $i] :
      ( ~ ( in @ sk5 @ ( setadjoin @ A @ emptyset ) )
      | ( in @ A @ sk3 ) ),
    inference(simp,[status(thm)],[158]) ).

thf(2455,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( B
       != ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) )
      | ( A
       != ( setadjoin
          @ ( dsetconstr @ sk3
            @ ^ [C: $i] : ( C = sk5 ) )
          @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[30,569]) ).

thf(2456,plain,
    ! [A: $i] :
      ( ~ ( in
          @ ( setadjoin
            @ ( dsetconstr @ sk3
              @ ^ [B: $i] : ( B = sk5 ) )
            @ emptyset )
          @ ( setadjoin @ A @ emptyset ) )
      | ( A
       != ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) ) ),
    inference(pattern_uni,[status(thm)],[2455:[bind(A,$thf( setadjoin @ ( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) ) @ emptyset )),bind(B,$thf( B ))]]) ).

thf(2481,plain,
    ~ ( in
      @ ( setadjoin
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ emptyset )
      @ ( setadjoin @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) @ emptyset ) ),
    inference(simp,[status(thm)],[2456]) ).

thf(2564,plain,
    ! [B: $i,A: $i] :
      ( ( in @ A @ ( setadjoin @ A @ emptyset ) )
     != ( in
        @ ( setadjoin
          @ ( dsetconstr @ B
            @ ^ [C: $i] : $false )
          @ emptyset )
        @ ( setadjoin @ ( setadjoin @ sk3 @ emptyset ) @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[32,1283]) ).

thf(2643,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( setadjoin
          @ ( dsetconstr @ B
            @ ^ [C: $i] : $false )
          @ emptyset ) )
      | ( ( setadjoin @ A @ emptyset )
       != ( setadjoin @ ( setadjoin @ sk3 @ emptyset ) @ emptyset ) ) ),
    inference(simp,[status(thm)],[2564]) ).

thf(2693,plain,
    ! [A: $i] :
      ( ( setadjoin
        @ ( setadjoin
          @ ( dsetconstr @ A
            @ ^ [B: $i] : $false )
          @ emptyset )
        @ emptyset )
     != ( setadjoin @ ( setadjoin @ sk3 @ emptyset ) @ emptyset ) ),
    inference(simp,[status(thm)],[2643]) ).

thf(1559,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( A != sk5 )
      | ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
       != sk3 )
      | ( B
       != ( dsetconstr @ sk3
          @ ^ [C: $i] : ( C = sk5 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[30,554]) ).

thf(1560,plain,
    ! [A: $i] :
      ( ~ ( in @ A
          @ ( setadjoin
            @ ( dsetconstr @ sk3
              @ ^ [B: $i] : ( B = sk5 ) )
            @ emptyset ) )
      | ( A != sk5 )
      | ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
       != sk3 ) ),
    inference(pattern_uni,[status(thm)],[1559:[bind(A,$thf( A )),bind(B,$thf( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) ))]]) ).

thf(1583,plain,
    ( ~ ( in @ sk5
        @ ( setadjoin
          @ ( dsetconstr @ sk3
            @ ^ [A: $i] : ( A = sk5 ) )
          @ emptyset ) )
    | ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
     != sk3 ) ),
    inference(simp,[status(thm)],[1560]) ).

thf(7282,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( A != sk3 )
      | ( B
       != ( dsetconstr @ C
          @ ^ [D: $i] :
              ~ ( in @ D @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[30,7015]) ).

thf(7283,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A
          @ ( setadjoin
            @ ( dsetconstr @ B
              @ ^ [C: $i] :
                  ~ ( in @ C @ sk3 ) )
            @ emptyset ) )
      | ( A != sk3 ) ),
    inference(pattern_uni,[status(thm)],[7282:[bind(A,$thf( A )),bind(B,$thf( dsetconstr @ D @ ^ [E: $i] : ~ ( in @ E @ sk3 ) )),bind(C,$thf( D ))]]) ).

thf(7298,plain,
    ! [A: $i] :
      ~ ( in @ sk3
        @ ( setadjoin
          @ ( dsetconstr @ A
            @ ^ [B: $i] :
                ~ ( in @ B @ sk3 ) )
          @ emptyset ) ),
    inference(simp,[status(thm)],[7283]) ).

thf(36,plain,
    ! [D: $i,C: $i,B: $o,A: $i] :
      ( ~ ( in @ D @ A )
      | ~ B
      | ( in @ C
        @ ( dsetconstr @ A
          @ ^ [E: $i] :
              ( ( B
                & ( E = C ) )
              | ( ~ B
                & ( E = D ) ) ) ) )
      | ( ( in @ sk5 @ sk3 )
       != ( in @ C @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[12,26]) ).

thf(37,plain,
    ! [B: $i,A: $o] :
      ( ~ ( in @ B @ sk3 )
      | ~ A
      | ( in @ sk5
        @ ( dsetconstr @ sk3
          @ ^ [C: $i] :
              ( ( A
                & ( C = sk5 ) )
              | ( ~ A
                & ( C = B ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk5 ))]]) ).

thf(67,plain,
    ! [B: $i,A: $o] :
      ( ~ ( in @ B @ sk3 )
      | ~ A
      | ( in @ sk5
        @ ( dsetconstr @ sk3
          @ ^ [C: $i] :
              ( ( A
                & ( C = sk5 ) )
              | ( ~ A
                & ( C = B ) ) ) ) ) ),
    inference(simp,[status(thm)],[37]) ).

thf(10845,plain,
    ! [A: $i] :
      ( ( in @ sk5 @ A )
      | ( ( in @ sk5 @ sk3 )
       != ( in @ A @ ( setadjoin @ sk3 @ emptyset ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12,164]) ).

thf(10956,plain,
    ! [A: $i] :
      ( ( in @ sk5 @ A )
      | ( sk5 != A )
      | ( ( setadjoin @ sk3 @ emptyset )
       != sk3 ) ),
    inference(simp,[status(thm)],[10845]) ).

thf(11049,plain,
    ( ( in @ sk5 @ sk5 )
    | ( ( setadjoin @ sk3 @ emptyset )
     != sk3 ) ),
    inference(simp,[status(thm)],[10956]) ).

thf(46,plain,
    ! [D: $i,C: $i,B: $o,A: $i] :
      ( ~ ( in @ C @ A )
      | ~ B
      | ( in @ C
        @ ( dsetconstr @ A
          @ ^ [E: $i] :
              ( ( B
                & ( E = C ) )
              | ( ~ B
                & ( E = D ) ) ) ) )
      | ( ( in @ sk6 @ sk3 )
       != ( in @ D @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8,26]) ).

thf(47,plain,
    ! [B: $i,A: $o] :
      ( ~ ( in @ B @ sk3 )
      | ~ A
      | ( in @ B
        @ ( dsetconstr @ sk3
          @ ^ [C: $i] :
              ( ( A
                & ( C = B ) )
              | ( ~ A
                & ( C = sk6 ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[46:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( sk6 ))]]) ).

thf(72,plain,
    ! [B: $i,A: $o] :
      ( ~ ( in @ B @ sk3 )
      | ~ A
      | ( in @ B
        @ ( dsetconstr @ sk3
          @ ^ [C: $i] :
              ( ( A
                & ( C = B ) )
              | ( ~ A
                & ( C = sk6 ) ) ) ) ) ),
    inference(simp,[status(thm)],[47]) ).

thf(1439,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( ( dsetconstr @ sk3
          @ ^ [C: $i] : ( C = sk5 ) )
       != sk6 )
      | ( A != sk3 )
      | ( B
       != ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[30,550]) ).

thf(1440,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) @ emptyset ) )
      | ( ( dsetconstr @ sk3
          @ ^ [B: $i] : ( B = sk5 ) )
       != sk6 )
      | ( A != sk3 ) ),
    inference(pattern_uni,[status(thm)],[1439:[bind(A,$thf( A )),bind(B,$thf( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ))]]) ).

thf(1459,plain,
    ( ~ ( in @ sk3 @ ( setadjoin @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) @ emptyset ) )
    | ( ( dsetconstr @ sk3
        @ ^ [A: $i] : ( A = sk5 ) )
     != sk6 ) ),
    inference(simp,[status(thm)],[1440]) ).

thf(2465,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( A
       != ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) )
      | ( B
       != ( setadjoin
          @ ( dsetconstr @ sk3
            @ ^ [C: $i] : ( C = sk5 ) )
          @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[30,569]) ).

thf(2466,plain,
    ! [A: $i] :
      ( ~ ( in @ A
          @ ( setadjoin
            @ ( setadjoin
              @ ( dsetconstr @ sk3
                @ ^ [B: $i] : ( B = sk5 ) )
              @ emptyset )
            @ emptyset ) )
      | ( A
       != ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) ) ),
    inference(pattern_uni,[status(thm)],[2465:[bind(A,$thf( A )),bind(B,$thf( setadjoin @ ( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) ) @ emptyset ))]]) ).

thf(2490,plain,
    ~ ( in @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
      @ ( setadjoin
        @ ( setadjoin
          @ ( dsetconstr @ sk3
            @ ^ [A: $i] : ( A = sk5 ) )
          @ emptyset )
        @ emptyset ) ),
    inference(simp,[status(thm)],[2466]) ).

thf(1423,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( ( dsetconstr @ sk3
          @ ^ [C: $i] : ( C = sk5 ) )
       != sk6 )
      | ( B != sk3 )
      | ( A
       != ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[30,550]) ).

thf(1424,plain,
    ! [A: $i] :
      ( ~ ( in @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) @ ( setadjoin @ A @ emptyset ) )
      | ( ( dsetconstr @ sk3
          @ ^ [B: $i] : ( B = sk5 ) )
       != sk6 )
      | ( A != sk3 ) ),
    inference(pattern_uni,[status(thm)],[1423:[bind(A,$thf( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )),bind(B,$thf( B ))]]) ).

thf(1453,plain,
    ( ~ ( in @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) @ ( setadjoin @ sk3 @ emptyset ) )
    | ( ( dsetconstr @ sk3
        @ ^ [A: $i] : ( A = sk5 ) )
     != sk6 ) ),
    inference(simp,[status(thm)],[1424]) ).

thf(13383,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( sk1 @ B @ A ) @ A )
      | ( in @ ( sk2 @ B @ A ) @ B )
      | ( in @ sk5 @ sk6 )
      | ( B != sk3 )
      | ( A
       != ( setadjoin @ sk3 @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[23,11017]) ).

thf(13384,plain,
    ! [A: $i] :
      ( ( in @ ( sk1 @ A @ ( setadjoin @ sk3 @ emptyset ) ) @ ( setadjoin @ sk3 @ emptyset ) )
      | ( in @ ( sk2 @ A @ ( setadjoin @ sk3 @ emptyset ) ) @ A )
      | ( in @ sk5 @ sk6 )
      | ( A != sk3 ) ),
    inference(pattern_uni,[status(thm)],[13383:[bind(A,$thf( setadjoin @ sk3 @ emptyset )),bind(B,$thf( B ))]]) ).

thf(13409,plain,
    ( ( in @ ( sk1 @ sk3 @ ( setadjoin @ sk3 @ emptyset ) ) @ ( setadjoin @ sk3 @ emptyset ) )
    | ( in @ ( sk2 @ sk3 @ ( setadjoin @ sk3 @ emptyset ) ) @ sk3 )
    | ( in @ sk5 @ sk6 ) ),
    inference(simp,[status(thm)],[13384]) ).

thf(1543,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( B != sk5 )
      | ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
       != sk3 )
      | ( A
       != ( dsetconstr @ sk3
          @ ^ [C: $i] : ( C = sk5 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[30,554]) ).

thf(1544,plain,
    ! [A: $i] :
      ( ~ ( in
          @ ( dsetconstr @ sk3
            @ ^ [B: $i] : ( B = sk5 ) )
          @ ( setadjoin @ A @ emptyset ) )
      | ( A != sk5 )
      | ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
       != sk3 ) ),
    inference(pattern_uni,[status(thm)],[1543:[bind(A,$thf( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) )),bind(B,$thf( B ))]]) ).

thf(1575,plain,
    ( ~ ( in
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ ( setadjoin @ sk5 @ emptyset ) )
    | ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
     != sk3 ) ),
    inference(simp,[status(thm)],[1544]) ).

thf(3052,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( A != sk6 )
      | ( ( setadjoin
          @ ( dsetconstr @ sk3
            @ ^ [C: $i] : ( C = sk5 ) )
          @ emptyset )
       != sk3 )
      | ( B
       != ( setadjoin @ sk5 @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[30,648]) ).

thf(3053,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) )
      | ( A != sk6 )
      | ( ( setadjoin
          @ ( dsetconstr @ sk3
            @ ^ [B: $i] : ( B = sk5 ) )
          @ emptyset )
       != sk3 ) ),
    inference(pattern_uni,[status(thm)],[3052:[bind(A,$thf( A )),bind(B,$thf( setadjoin @ sk5 @ emptyset ))]]) ).

thf(3104,plain,
    ( ~ ( in @ sk6 @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) )
    | ( ( setadjoin
        @ ( dsetconstr @ sk3
          @ ^ [A: $i] : ( A = sk5 ) )
        @ emptyset )
     != sk3 ) ),
    inference(simp,[status(thm)],[3053]) ).

thf(170,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( in @ A @ sk3 )
      | ( B != sk6 ) ),
    inference(paramod_ordered,[status(thm)],[30,8]) ).

thf(171,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ sk6 @ emptyset ) )
      | ( in @ A @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[170:[bind(A,$thf( A )),bind(B,$thf( sk6 ))]]) ).

thf(21519,plain,
    ! [A: $i] :
      ( ( in @ A @ sk3 )
      | ( ( in @ sk5 @ ( setadjoin @ A @ emptyset ) )
       != ( in @ sk5 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[12,240]) ).

thf(21641,plain,
    ! [A: $i] :
      ( ( in @ A @ sk3 )
      | ( sk5 != sk5 )
      | ( ( setadjoin @ A @ emptyset )
       != sk3 ) ),
    inference(simp,[status(thm)],[21519]) ).

thf(21745,plain,
    ! [A: $i] :
      ( ( in @ A @ sk3 )
      | ( ( setadjoin @ A @ emptyset )
       != sk3 ) ),
    inference(simp,[status(thm)],[21641]) ).

thf(7373,plain,
    ! [B: $i,A: $i] :
      ( ( in @ A @ ( setadjoin @ A @ emptyset ) )
     != ( in
        @ ( dsetconstr @ B
          @ ^ [C: $i] :
              ~ ( in @ C @ sk3 ) )
        @ ( setadjoin @ sk3 @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[32,7294]) ).

thf(7426,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( dsetconstr @ B
          @ ^ [C: $i] :
              ~ ( in @ C @ sk3 ) ) )
      | ( ( setadjoin @ A @ emptyset )
       != ( setadjoin @ sk3 @ emptyset ) ) ),
    inference(simp,[status(thm)],[7373]) ).

thf(7437,plain,
    ! [A: $i] :
      ( ( setadjoin
        @ ( dsetconstr @ A
          @ ^ [B: $i] :
              ~ ( in @ B @ sk3 ) )
        @ emptyset )
     != ( setadjoin @ sk3 @ emptyset ) ),
    inference(simp,[status(thm)],[7426]) ).

thf(1549,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( ( dsetconstr @ sk3
          @ ^ [C: $i] : ( C = sk5 ) )
       != sk5 )
      | ( B != sk3 )
      | ( A
       != ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[30,554]) ).

thf(1550,plain,
    ! [A: $i] :
      ( ~ ( in @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) @ ( setadjoin @ A @ emptyset ) )
      | ( ( dsetconstr @ sk3
          @ ^ [B: $i] : ( B = sk5 ) )
       != sk5 )
      | ( A != sk3 ) ),
    inference(pattern_uni,[status(thm)],[1549:[bind(A,$thf( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )),bind(B,$thf( B ))]]) ).

thf(1578,plain,
    ( ~ ( in @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) @ ( setadjoin @ sk3 @ emptyset ) )
    | ( ( dsetconstr @ sk3
        @ ^ [A: $i] : ( A = sk5 ) )
     != sk5 ) ),
    inference(simp,[status(thm)],[1550]) ).

thf(18023,plain,
    ! [B: $i,A: $i] :
      ( ( ( dsetconstr @ B
          @ ^ [C: $i] : $false )
       != ( setadjoin @ A @ emptyset ) )
      | ( emptyset != emptyset ) ),
    inference(simp,[status(thm)],[4790]) ).

thf(18220,plain,
    ! [B: $i,A: $i] :
      ( ( dsetconstr @ B
        @ ^ [C: $i] : $false )
     != ( setadjoin @ A @ emptyset ) ),
    inference(simp,[status(thm)],[18023]) ).

thf(3044,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( ( setadjoin @ sk5 @ emptyset )
       != sk6 )
      | ( B != sk3 )
      | ( A
       != ( setadjoin
          @ ( dsetconstr @ sk3
            @ ^ [C: $i] : ( C = sk5 ) )
          @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[30,648]) ).

thf(3045,plain,
    ! [A: $i] :
      ( ~ ( in
          @ ( setadjoin
            @ ( dsetconstr @ sk3
              @ ^ [B: $i] : ( B = sk5 ) )
            @ emptyset )
          @ ( setadjoin @ A @ emptyset ) )
      | ( ( setadjoin @ sk5 @ emptyset )
       != sk6 )
      | ( A != sk3 ) ),
    inference(pattern_uni,[status(thm)],[3044:[bind(A,$thf( setadjoin @ ( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) ) @ emptyset )),bind(B,$thf( B ))]]) ).

thf(3100,plain,
    ( ~ ( in
        @ ( setadjoin
          @ ( dsetconstr @ sk3
            @ ^ [A: $i] : ( A = sk5 ) )
          @ emptyset )
        @ ( setadjoin @ sk3 @ emptyset ) )
    | ( ( setadjoin @ sk5 @ emptyset )
     != sk6 ) ),
    inference(simp,[status(thm)],[3045]) ).

thf(3336,plain,
    ! [B: $i > $o,A: $i] :
      ( ~ ( B @ sk6 )
      | ( ( dsetconstr @ A
          @ ^ [C: $i] :
              ~ ( B @ C ) )
       != sk3 ) ),
    inference(prim_subst,[status(thm)],[352:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).

thf(3361,plain,
    ! [B: $i > $o,A: $i] :
      ( ( ( dsetconstr @ A
          @ ^ [C: $i] :
              ~ ( B @ C ) )
       != sk3 )
      | ~ ( B @ sk6 ) ),
    inference(cnf,[status(esa)],[3336]) ).

thf(3362,plain,
    ! [B: $i > $o,A: $i] :
      ( ( ( dsetconstr @ A
          @ ^ [C: $i] :
              ~ ( B @ C ) )
       != sk3 )
      | ~ ( B @ sk6 ) ),
    inference(simp,[status(thm)],[3361]) ).

thf(17246,plain,
    ! [A: $i] :
      ( ( in @ sk6 @ A )
      | ( ( in @ sk5 @ sk3 )
       != ( in @ A @ ( setadjoin @ sk3 @ emptyset ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12,173]) ).

thf(17327,plain,
    ! [A: $i] :
      ( ( in @ sk6 @ A )
      | ( sk5 != A )
      | ( ( setadjoin @ sk3 @ emptyset )
       != sk3 ) ),
    inference(simp,[status(thm)],[17246]) ).

thf(17441,plain,
    ( ( in @ sk6 @ sk5 )
    | ( ( setadjoin @ sk3 @ emptyset )
     != sk3 ) ),
    inference(simp,[status(thm)],[17327]) ).

thf(454,plain,
    ! [B: $i > $i,A: $i] :
      ~ ( in @ emptyset
        @ ( dsetconstr @ A
          @ ^ [C: $i] :
              ( in
              @ ( dsetconstr @ ( B @ C )
                @ ^ [D: $i] : $false )
              @ ( setadjoin @ sk3 @ C ) ) ) ),
    inference(pre_uni,[status(thm)],[405:[bind(A,$thf( A )),bind(B,$thf( ^ [F: $i] : ( in @ ( dsetconstr @ ( I @ F ) @ ^ [G: $i] : $false ) @ ( setadjoin @ sk3 @ F ) ) )),bind(C,$thf( emptyset )),bind(D,$thf( I @ emptyset ))]]) ).

thf(459,plain,
    ! [B: $i > $i,A: $i] :
      ~ ( in @ emptyset
        @ ( dsetconstr @ A
          @ ^ [C: $i] :
              ( in
              @ ( dsetconstr @ ( B @ C )
                @ ^ [D: $i] : $false )
              @ ( setadjoin @ sk3 @ C ) ) ) ),
    inference(simp,[status(thm)],[454]) ).

thf(38,plain,
    ! [D: $i,C: $i,B: $o,A: $i] :
      ( ~ ( in @ C @ A )
      | ~ B
      | ( in @ C
        @ ( dsetconstr @ A
          @ ^ [E: $i] :
              ( ( B
                & ( E = C ) )
              | ( ~ B
                & ( E = D ) ) ) ) )
      | ( ( in @ sk5 @ sk3 )
       != ( in @ D @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[12,26]) ).

thf(39,plain,
    ! [B: $i,A: $o] :
      ( ~ ( in @ B @ sk3 )
      | ~ A
      | ( in @ B
        @ ( dsetconstr @ sk3
          @ ^ [C: $i] :
              ( ( A
                & ( C = B ) )
              | ( ~ A
                & ( C = sk5 ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[38:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( sk5 ))]]) ).

thf(68,plain,
    ! [B: $i,A: $o] :
      ( ~ ( in @ B @ sk3 )
      | ~ A
      | ( in @ B
        @ ( dsetconstr @ sk3
          @ ^ [C: $i] :
              ( ( A
                & ( C = B ) )
              | ( ~ A
                & ( C = sk5 ) ) ) ) ) ),
    inference(simp,[status(thm)],[39]) ).

thf(53836,plain,
    $false,
    inference(e,[status(thm)],[243,19264,18,400,3096,69,479,352,4391,449,550,6851,4294,1458,1196,3236,25,1287,1792,4563,7294,228,448,164,1450,7015,4556,1283,334,1223,70,28,7881,65,456,3105,17462,1227,388,6111,554,1584,654,457,173,569,73,244,311,32,34,71,12,382,1224,1194,4790,9146,8926,1339,13412,726,66,240,2481,3,2693,1583,162,7298,4319,648,67,16,11049,5277,154,11,72,11017,231,1459,2490,1453,13409,1575,1341,26,351,3104,401,171,23,21745,383,7437,8,151,1578,18220,30,3100,3362,17441,459,68]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU703^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n018.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sun May 19 17:36:24 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.99/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.32/0.99  % [INFO] 	 Parsing done (119ms). 
% 1.32/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.71/1.22  % [INFO] 	 eprover registered as external prover. 
% 1.71/1.22  % [INFO] 	 cvc4 registered as external prover. 
% 1.71/1.22  % [INFO] 	 Scanning for conjecture ... 
% 2.14/1.37  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.14/1.39  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.14/1.39  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.14/1.40  % [INFO] 	 Type checking passed. 
% 2.14/1.40  % [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 ... 
% 163.41/30.68  % External prover 'e' found a proof!
% 163.41/30.68  % [INFO] 	 Killing All external provers ... 
% 163.41/30.68  % Time passed: 30150ms (effective reasoning time: 29679ms)
% 163.41/30.68  % 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)>
% 163.41/30.68  % Axioms used in derivation (0): 
% 163.41/30.68  % No. of inferences in proof: 285
% 163.41/30.68  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 30150 ms resp. 29679 ms w/o parsing
% 163.96/30.83  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 163.96/30.83  % [INFO] 	 Killing All external provers ... 
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