TSTP Solution File: SEU711^2 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEU711^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:39:15 EDT 2024
% Result : Theorem 111.64s 20.16s
% Output : Refutation 112.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 14
% Syntax : Number of formulae : 878 ( 62 unt; 10 typ; 3 def)
% Number of atoms : 2810 (1195 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 10261 (1483 ~;1376 |; 0 &;7355 @)
% ( 0 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 1111 ( 0 ^1111 !; 0 ?;1111 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(powersetI_type,type,
powersetI: $o ).
thf(powersetI_def,definition,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ) ).
thf(powersetE_type,type,
powersetE: $o ).
thf(powersetE_def,definition,
( powersetE
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ C @ B )
=> ( in @ C @ A ) ) ) ) ) ).
thf(binunion_type,type,
binunion: $i > $i > $i ).
thf(binunionEcases_type,type,
binunionEcases: $o ).
thf(binunionEcases_def,definition,
( binunionEcases
= ( ! [A: $i,B: $i,C: $i,D: $o] :
( ( in @ C @ ( binunion @ A @ B ) )
=> ( ( ( in @ C @ A )
=> D )
=> ( ( ( in @ C @ B )
=> D )
=> D ) ) ) ) ) ).
thf(sk1_type,type,
sk1: $i > $i > $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(1,conjecture,
( powersetI
=> ( powersetE
=> ( binunionEcases
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( in @ ( binunion @ B @ C ) @ ( powerset @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionT_lem) ).
thf(2,negated_conjecture,
~ ( powersetI
=> ( powersetE
=> ( binunionEcases
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( in @ ( binunion @ B @ C ) @ ( powerset @ A ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ C @ B )
=> ( in @ C @ A ) ) )
=> ( ! [A: $i,B: $i,C: $i,D: $o] :
( ( in @ C @ ( binunion @ A @ B ) )
=> ( ( ( in @ C @ A )
=> D )
=> ( ( ( in @ C @ B )
=> D )
=> D ) ) )
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( in @ ( binunion @ B @ C ) @ ( powerset @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( binunion @ A @ B ) )
=> ! [D: $o] :
( ( ( in @ C @ A )
=> D )
=> ( ( ( in @ C @ B )
=> D )
=> D ) ) )
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( in @ ( binunion @ B @ C ) @ ( powerset @ A ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(14,plain,
in @ sk3 @ ( powerset @ sk2 ),
inference(cnf,[status(esa)],[4]) ).
thf(11,plain,
in @ sk4 @ ( powerset @ sk2 ),
inference(cnf,[status(esa)],[4]) ).
thf(7,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ~ ( in @ C @ B )
| ( in @ C @ A ) ),
inference(cnf,[status(esa)],[4]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ~ ( in @ C @ B )
| ( in @ C @ A ) ),
inference(simp,[status(thm)],[7]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A )
| ( ( in @ sk4 @ ( powerset @ sk2 ) )
!= ( in @ B @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,19]) ).
thf(33,plain,
! [A: $i] :
( ~ ( in @ A @ sk4 )
| ( in @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(42,plain,
! [A: $i] :
( ~ ( in @ A @ sk4 )
| ( in @ A @ sk2 ) ),
inference(simp,[status(thm)],[33]) ).
thf(60,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ sk3 @ ( powerset @ sk2 ) )
!= ( in @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[14,42]) ).
thf(66,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( sk3 != A )
| ( ( powerset @ sk2 )
!= sk4 ) ),
inference(simp,[status(thm)],[60]) ).
thf(69,plain,
( ( in @ sk3 @ sk2 )
| ( ( powerset @ sk2 )
!= sk4 ) ),
inference(simp,[status(thm)],[66]) ).
thf(8,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ B )
| ( in @ B @ ( powerset @ A ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk1 @ B @ A ) @ A )
| ( in @ B @ ( powerset @ A ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(85,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( in @ D @ ( powerset @ C ) )
| ( ( in @ ( sk1 @ B @ A ) @ B )
!= ( in @ ( sk1 @ D @ C ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[8,12]) ).
thf(86,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
| ( in @ A @ ( powerset @ A ) ) ),
inference(pattern_uni,[status(thm)],[85:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( B ))]]) ).
thf(92,plain,
! [A: $i] : ( in @ A @ ( powerset @ A ) ),
inference(simp,[status(thm)],[86]) ).
thf(98,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ C @ ( powerset @ B ) )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( sk1 @ C @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[92,12]) ).
thf(105,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ C @ ( powerset @ B ) )
| ( A
!= ( sk1 @ C @ B ) )
| ( ( powerset @ A )
!= B ) ),
inference(simp,[status(thm)],[98]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( ( powerset @ ( sk1 @ B @ A ) )
!= A ) ),
inference(simp,[status(thm)],[105]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A )
| ( ( in @ sk3 @ ( powerset @ sk2 ) )
!= ( in @ B @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,19]) ).
thf(27,plain,
! [A: $i] :
( ~ ( in @ A @ sk3 )
| ( in @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[26:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(45,plain,
! [A: $i] :
( ~ ( in @ A @ sk3 )
| ( in @ A @ sk2 ) ),
inference(simp,[status(thm)],[27]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ( in @ B @ sk2 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ B @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[92,45]) ).
thf(154,plain,
! [B: $i,A: $i] :
( ( in @ B @ sk2 )
| ( A != B )
| ( ( powerset @ A )
!= sk3 ) ),
inference(simp,[status(thm)],[145]) ).
thf(162,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( powerset @ A )
!= sk3 ) ),
inference(simp,[status(thm)],[154]) ).
thf(13,plain,
~ ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ~ ( in @ C @ B )
| ( ( in @ C @ A )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,13]) ).
thf(31,plain,
! [A: $i] :
( ~ ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A ) ),
inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( B )),bind(C,$thf( binunion @ sk3 @ sk4 ))]]) ).
thf(46,plain,
! [A: $i] :
( ~ ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A ) ),
inference(simp,[status(thm)],[31]) ).
thf(1288,plain,
! [B: $i,A: $i] :
( ( ( powerset @ A )
!= sk3 )
| ~ ( in @ B @ ( powerset @ ( powerset @ sk2 ) ) )
| ( ( in @ A @ sk2 )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[162,46]) ).
thf(1289,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 )
| ~ ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[1288:[bind(A,$thf( binunion @ sk3 @ sk4 )),bind(B,$thf( sk2 ))]]) ).
thf(8929,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ B @ A ) )
!= A )
| ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 )
| ( ( in @ B @ ( powerset @ A ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,1289]) ).
thf(8930,plain,
( ( ( powerset @ ( sk1 @ sk2 @ ( powerset @ sk2 ) ) )
!= ( powerset @ sk2 ) )
| ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[8929:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(50,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ~ ( in @ D @ ( powerset @ C ) )
| ( in @ E @ C )
| ( ( in @ ( sk1 @ B @ A ) @ B )
!= ( in @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[8,19]) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ B @ ( powerset @ C ) )
| ~ ( in @ B @ ( powerset @ A ) )
| ( in @ ( sk1 @ B @ C ) @ A ) ),
inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F )),bind(E,$thf( sk1 @ F @ G ))]]) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ B @ ( powerset @ C ) )
| ~ ( in @ B @ ( powerset @ A ) )
| ( in @ ( sk1 @ B @ C ) @ A ) ),
inference(simp,[status(thm)],[51]) ).
thf(87,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ~ ( in @ C @ B )
| ( in @ E @ ( powerset @ D ) )
| ( ( in @ C @ A )
!= ( in @ ( sk1 @ E @ D ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[19,12]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ~ ( in @ ( sk1 @ C @ A ) @ B )
| ( in @ C @ ( powerset @ A ) ) ),
inference(pattern_uni,[status(thm)],[87:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk1 @ F @ A )),bind(D,$thf( A )),bind(E,$thf( F ))]]) ).
thf(93,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ~ ( in @ ( sk1 @ C @ A ) @ B )
| ( in @ C @ ( powerset @ A ) ) ),
inference(simp,[status(thm)],[88]) ).
thf(6013,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ ( sk1 @ C @ A ) @ B )
| ( in @ C @ ( powerset @ A ) )
| ( ( in @ sk4 @ ( powerset @ sk2 ) )
!= ( in @ B @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,93]) ).
thf(6014,plain,
! [A: $i] :
( ~ ( in @ ( sk1 @ A @ sk2 ) @ sk4 )
| ( in @ A @ ( powerset @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[6013:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(6160,plain,
! [A: $i] :
( ~ ( in @ ( sk1 @ A @ sk2 ) @ sk4 )
| ( in @ A @ ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[6014]) ).
thf(29448,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( in @ B @ ( powerset @ C ) )
| ~ ( in @ B @ ( powerset @ A ) )
| ( in @ D @ ( powerset @ sk2 ) )
| ( ( in @ ( sk1 @ B @ C ) @ A )
!= ( in @ ( sk1 @ D @ sk2 ) @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[57,6160]) ).
thf(29449,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ sk2 ) )
| ~ ( in @ A @ ( powerset @ sk4 ) )
| ( in @ A @ ( powerset @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[29448:[bind(A,$thf( sk4 )),bind(B,$thf( B )),bind(C,$thf( sk2 )),bind(D,$thf( B ))]]) ).
thf(29675,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ sk2 ) )
| ~ ( in @ A @ ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[29449]) ).
thf(40288,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( in @ C @ ( powerset @ sk2 ) )
| ( ( in @ ( sk1 @ B @ A ) @ B )
!= ( in @ C @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,29675]) ).
thf(40289,plain,
! [A: $i] :
( ( in @ ( powerset @ sk4 ) @ ( powerset @ A ) )
| ( in @ ( sk1 @ ( powerset @ sk4 ) @ A ) @ ( powerset @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[40288:[bind(A,$thf( E )),bind(B,$thf( powerset @ sk4 )),bind(C,$thf( sk1 @ ( powerset @ sk4 ) @ E ))]]) ).
thf(40459,plain,
! [A: $i] :
( ( in @ ( powerset @ sk4 ) @ ( powerset @ A ) )
| ( in @ ( sk1 @ ( powerset @ sk4 ) @ A ) @ ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[40289]) ).
thf(46819,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ ( powerset @ sk4 ) @ ( powerset @ A ) )
| ( in @ C @ ( powerset @ B ) )
| ( ( in @ ( sk1 @ ( powerset @ sk4 ) @ A ) @ ( powerset @ sk2 ) )
!= ( in @ ( sk1 @ C @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[40459,12]) ).
thf(46820,plain,
( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
| ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[46819:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( powerset @ sk2 )),bind(C,$thf( powerset @ sk4 ))]]) ).
thf(47023,plain,
in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ),
inference(simp,[status(thm)],[46820]) ).
thf(47042,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[47023,42]) ).
thf(47205,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( powerset @ sk4 )
!= A )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk4 ) ),
inference(simp,[status(thm)],[47042]) ).
thf(47281,plain,
( ( in @ ( powerset @ sk4 ) @ sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk4 ) ),
inference(simp,[status(thm)],[47205]) ).
thf(1297,plain,
! [A: $i] :
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
| ( ( in @ sk3 @ ( powerset @ sk2 ) )
!= ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,46]) ).
thf(1365,plain,
! [A: $i] :
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
| ( sk3 != A )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[1297]) ).
thf(1411,plain,
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[1365]) ).
thf(9,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( binunion @ A @ B ) )
| ( in @ C @ A )
| ( in @ C @ B )
| D ),
inference(cnf,[status(esa)],[4]) ).
thf(18,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( binunion @ A @ B ) )
| ( in @ C @ A )
| ( in @ C @ B )
| D ),
inference(simp,[status(thm)],[9]) ).
thf(193,plain,
! [F: $o,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( in @ E @ C )
| ( in @ E @ D )
| F
| ( ( in @ ( sk1 @ B @ A ) @ B )
!= ( in @ E @ ( binunion @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,18]) ).
thf(194,plain,
! [D: $i,C: $i,B: $i,A: $o] :
( ( in @ ( binunion @ C @ D ) @ ( powerset @ B ) )
| ( in @ ( sk1 @ ( binunion @ C @ D ) @ B ) @ C )
| ( in @ ( sk1 @ ( binunion @ C @ D ) @ B ) @ D )
| A ),
inference(pattern_uni,[status(thm)],[193:[bind(A,$thf( H )),bind(B,$thf( binunion @ I @ J )),bind(C,$thf( I )),bind(D,$thf( J )),bind(E,$thf( sk1 @ ( binunion @ I @ J ) @ H )),bind(F,$thf( F ))]]) ).
thf(226,plain,
! [D: $i,C: $i,B: $i,A: $o] :
( ( in @ ( binunion @ C @ D ) @ ( powerset @ B ) )
| ( in @ ( sk1 @ ( binunion @ C @ D ) @ B ) @ C )
| ( in @ ( sk1 @ ( binunion @ C @ D ) @ B ) @ D )
| A ),
inference(simp,[status(thm)],[194]) ).
thf(496,plain,
! [D: $i,C: $i,B: $i,A: $o] :
( ( in @ ( binunion @ C @ D ) @ ( powerset @ B ) )
| ( in @ ( sk1 @ ( binunion @ C @ D ) @ B ) @ C )
| A
| ( ( in @ ( sk1 @ ( binunion @ C @ D ) @ B ) @ D )
!= ( in @ ( sk1 @ ( binunion @ C @ D ) @ B ) @ C ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[226]) ).
thf(518,plain,
! [C: $i,B: $i,A: $o] :
( ( in @ ( binunion @ C @ C ) @ ( powerset @ B ) )
| ( in @ ( sk1 @ ( binunion @ C @ C ) @ B ) @ C )
| A ),
inference(pattern_uni,[status(thm)],[496:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(526,plain,
! [C: $i,B: $i,A: $o] :
( ( in @ ( binunion @ C @ C ) @ ( powerset @ B ) )
| ( in @ ( sk1 @ ( binunion @ C @ C ) @ B ) @ C )
| A ),
inference(simp,[status(thm)],[518]) ).
thf(874,plain,
! [D: $i,C: $i,B: $i,A: $o] :
( ( in @ ( binunion @ C @ C ) @ ( powerset @ B ) )
| A
| ( in @ D @ sk2 )
| ( ( in @ ( sk1 @ ( binunion @ C @ C ) @ B ) @ C )
!= ( in @ D @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[526,45]) ).
thf(875,plain,
! [B: $i,A: $o] :
( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ B ) )
| A
| ( in @ ( sk1 @ ( binunion @ sk3 @ sk3 ) @ B ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[874:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( sk3 )),bind(D,$thf( sk1 @ ( binunion @ sk3 @ sk3 ) @ F ))]]) ).
thf(946,plain,
! [B: $i,A: $o] :
( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ B ) )
| A
| ( in @ ( sk1 @ ( binunion @ sk3 @ sk3 ) @ B ) @ sk2 ) ),
inference(simp,[status(thm)],[875]) ).
thf(13247,plain,
! [D: $i,C: $i,B: $i,A: $o] :
( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ B ) )
| A
| ( in @ D @ ( powerset @ C ) )
| ( ( in @ ( sk1 @ ( binunion @ sk3 @ sk3 ) @ B ) @ sk2 )
!= ( in @ ( sk1 @ D @ C ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[946,12]) ).
thf(13248,plain,
! [A: $o] :
( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
| A
| ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[13247:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk2 )),bind(D,$thf( binunion @ sk3 @ sk3 ))]]) ).
thf(13470,plain,
! [A: $o] :
( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
| A ),
inference(simp,[status(thm)],[13248]) ).
thf(878,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $o] :
( ( in @ ( binunion @ C @ C ) @ ( powerset @ B ) )
| A
| ( in @ E @ ( powerset @ D ) )
| ( ( in @ ( sk1 @ ( binunion @ C @ C ) @ B ) @ C )
!= ( in @ ( sk1 @ E @ D ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[526,12]) ).
thf(879,plain,
! [B: $i,A: $o] :
( ( in @ ( binunion @ B @ B ) @ ( powerset @ B ) )
| A
| ( in @ ( binunion @ B @ B ) @ ( powerset @ B ) ) ),
inference(pattern_uni,[status(thm)],[878:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( G )),bind(E,$thf( binunion @ G @ G ))]]) ).
thf(948,plain,
! [B: $i,A: $o] :
( ( in @ ( binunion @ B @ B ) @ ( powerset @ B ) )
| A ),
inference(simp,[status(thm)],[879]) ).
thf(1617,plain,
! [B: $i,A: $o] :
( ( in @ ( binunion @ B @ B ) @ ( powerset @ B ) )
| ( A
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[948,13]) ).
thf(1618,plain,
! [A: $i] : ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) ),
inference(pattern_uni,[status(thm)],[1617:[bind(A,$thf( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) )),bind(B,$thf( B ))]]) ).
thf(1710,plain,
! [A: $i] : ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) ),
inference(simp,[status(thm)],[1618]) ).
thf(1814,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ B )
| ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
!= ( in @ B @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1710,46]) ).
thf(1815,plain,
~ ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[1814:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ))]]) ).
thf(13530,plain,
! [A: $o] :
( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
| ( A
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[13470,1815]) ).
thf(13531,plain,
in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ),
inference(pattern_uni,[status(thm)],[13530:[bind(A,$thf( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ))]]) ).
thf(13873,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A )
| ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
!= ( in @ B @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[13531,19]) ).
thf(13874,plain,
! [A: $i] :
( ~ ( in @ A @ ( binunion @ sk3 @ sk3 ) )
| ( in @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[13873:[bind(A,$thf( sk2 )),bind(B,$thf( binunion @ sk3 @ sk3 )),bind(C,$thf( C ))]]) ).
thf(13955,plain,
! [A: $i] :
( ~ ( in @ A @ ( binunion @ sk3 @ sk3 ) )
| ( in @ A @ sk2 ) ),
inference(simp,[status(thm)],[13874]) ).
thf(143,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ sk3 @ ( powerset @ sk2 ) )
!= ( in @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[14,45]) ).
thf(155,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( sk3 != A )
| ( ( powerset @ sk2 )
!= sk3 ) ),
inference(simp,[status(thm)],[143]) ).
thf(163,plain,
( ( in @ sk3 @ sk2 )
| ( ( powerset @ sk2 )
!= sk3 ) ),
inference(simp,[status(thm)],[155]) ).
thf(1276,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ ( powerset @ sk2 ) ) )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[92,46]) ).
thf(1277,plain,
~ ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[1276:[bind(A,$thf( binunion @ sk3 @ sk4 )),bind(B,$thf( powerset @ ( binunion @ sk3 @ sk4 ) ))]]) ).
thf(1436,plain,
( ( ( powerset @ sk2 )
!= sk3 )
| ( ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[163,1277]) ).
thf(1469,plain,
( ( ( powerset @ sk2 )
!= sk3 )
| ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1436]) ).
thf(62,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( in @ C @ sk2 )
| ( ( in @ ( sk1 @ B @ A ) @ B )
!= ( in @ C @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[8,42]) ).
thf(63,plain,
! [A: $i] :
( ( in @ sk4 @ ( powerset @ A ) )
| ( in @ ( sk1 @ sk4 @ A ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[62:[bind(A,$thf( E )),bind(B,$thf( sk4 )),bind(C,$thf( sk1 @ sk4 @ E ))]]) ).
thf(71,plain,
! [A: $i] :
( ( in @ sk4 @ ( powerset @ A ) )
| ( in @ ( sk1 @ sk4 @ A ) @ sk2 ) ),
inference(simp,[status(thm)],[63]) ).
thf(127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( in @ sk4 @ ( powerset @ A ) )
| ~ ( in @ C @ ( powerset @ B ) )
| ( in @ D @ B )
| ( ( in @ ( sk1 @ sk4 @ A ) @ sk2 )
!= ( in @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[71,19]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( in @ sk4 @ ( powerset @ B ) )
| ~ ( in @ sk2 @ ( powerset @ A ) )
| ( in @ ( sk1 @ sk4 @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[127:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( sk2 )),bind(D,$thf( sk1 @ sk4 @ F ))]]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ( in @ sk4 @ ( powerset @ B ) )
| ~ ( in @ sk2 @ ( powerset @ A ) )
| ( in @ ( sk1 @ sk4 @ B ) @ A ) ),
inference(simp,[status(thm)],[128]) ).
thf(867,plain,
! [D: $i,C: $i,B: $i,A: $o] :
( ( in @ ( binunion @ C @ C ) @ ( powerset @ B ) )
| A
| ( in @ D @ sk2 )
| ( ( in @ ( sk1 @ ( binunion @ C @ C ) @ B ) @ C )
!= ( in @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[526,42]) ).
thf(868,plain,
! [B: $i,A: $o] :
( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ B ) )
| A
| ( in @ ( sk1 @ ( binunion @ sk4 @ sk4 ) @ B ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[867:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( sk4 )),bind(D,$thf( sk1 @ ( binunion @ sk4 @ sk4 ) @ F ))]]) ).
thf(943,plain,
! [B: $i,A: $o] :
( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ B ) )
| A
| ( in @ ( sk1 @ ( binunion @ sk4 @ sk4 ) @ B ) @ sk2 ) ),
inference(simp,[status(thm)],[868]) ).
thf(3436,plain,
! [D: $i,C: $i,B: $i,A: $o] :
( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ B ) )
| A
| ( in @ D @ ( powerset @ C ) )
| ( ( in @ ( sk1 @ ( binunion @ sk4 @ sk4 ) @ B ) @ sk2 )
!= ( in @ ( sk1 @ D @ C ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[943,12]) ).
thf(3437,plain,
! [A: $o] :
( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
| A
| ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[3436:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk2 )),bind(D,$thf( binunion @ sk4 @ sk4 ))]]) ).
thf(3558,plain,
! [A: $o] :
( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
| A ),
inference(simp,[status(thm)],[3437]) ).
thf(3586,plain,
! [A: $o] :
( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
| ( A
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3558,1815]) ).
thf(3587,plain,
in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ),
inference(pattern_uni,[status(thm)],[3586:[bind(A,$thf( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ))]]) ).
thf(64,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ~ ( in @ C @ B )
| ( in @ D @ sk2 )
| ( ( in @ C @ A )
!= ( in @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[19,42]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk4 ) )
| ~ ( in @ B @ A )
| ( in @ B @ sk2 ) ),
inference(pattern_uni,[status(thm)],[64:[bind(A,$thf( sk4 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk4 ) )
| ~ ( in @ B @ A )
| ( in @ B @ sk2 ) ),
inference(simp,[status(thm)],[65]) ).
thf(3883,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk4 ) )
| ( in @ B @ sk2 )
| ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
!= ( in @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3587,68]) ).
thf(3884,plain,
( ~ ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) )
| ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3883:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( binunion @ sk4 @ sk4 ))]]) ).
thf(5696,plain,
! [A: $i] :
( ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,3884]) ).
thf(5779,plain,
! [A: $i] :
( ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
| ( A
!= ( powerset @ sk2 ) )
| ( ( powerset @ A )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[5696]) ).
thf(5857,plain,
( ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[5779]) ).
thf(13859,plain,
( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
!= ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[13531,1277]) ).
thf(13896,plain,
( ( ( binunion @ sk3 @ sk3 )
!= ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[13859]) ).
thf(22012,plain,
( ( ( binunion @ sk3 @ sk3 )
!= ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
| ( ( powerset @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[13896]) ).
thf(5907,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ ( sk1 @ C @ A ) @ B )
| ( in @ C @ ( powerset @ A ) )
| ( ( in @ sk3 @ ( powerset @ sk2 ) )
!= ( in @ B @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,93]) ).
thf(5908,plain,
! [A: $i] :
( ~ ( in @ ( sk1 @ A @ sk2 ) @ sk3 )
| ( in @ A @ ( powerset @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[5907:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(6124,plain,
! [A: $i] :
( ~ ( in @ ( sk1 @ A @ sk2 ) @ sk3 )
| ( in @ A @ ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[5908]) ).
thf(28178,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( in @ B @ ( powerset @ C ) )
| ~ ( in @ B @ ( powerset @ A ) )
| ( in @ D @ ( powerset @ sk2 ) )
| ( ( in @ ( sk1 @ B @ C ) @ A )
!= ( in @ ( sk1 @ D @ sk2 ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[57,6124]) ).
thf(28179,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ sk2 ) )
| ~ ( in @ A @ ( powerset @ sk3 ) )
| ( in @ A @ ( powerset @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[28178:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk2 )),bind(D,$thf( B ))]]) ).
thf(28398,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ sk2 ) )
| ~ ( in @ A @ ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[28179]) ).
thf(28769,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( in @ C @ ( powerset @ sk2 ) )
| ( ( in @ ( sk1 @ B @ A ) @ B )
!= ( in @ C @ ( powerset @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,28398]) ).
thf(28770,plain,
! [A: $i] :
( ( in @ ( powerset @ sk3 ) @ ( powerset @ A ) )
| ( in @ ( sk1 @ ( powerset @ sk3 ) @ A ) @ ( powerset @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[28769:[bind(A,$thf( E )),bind(B,$thf( powerset @ sk3 )),bind(C,$thf( sk1 @ ( powerset @ sk3 ) @ E ))]]) ).
thf(28903,plain,
! [A: $i] :
( ( in @ ( powerset @ sk3 ) @ ( powerset @ A ) )
| ( in @ ( sk1 @ ( powerset @ sk3 ) @ A ) @ ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[28770]) ).
thf(29773,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ ( powerset @ sk3 ) @ ( powerset @ A ) )
| ( in @ C @ ( powerset @ B ) )
| ( ( in @ ( sk1 @ ( powerset @ sk3 ) @ A ) @ ( powerset @ sk2 ) )
!= ( in @ ( sk1 @ C @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[28903,12]) ).
thf(29774,plain,
( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
| ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[29773:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( powerset @ sk2 )),bind(C,$thf( powerset @ sk3 ))]]) ).
thf(29915,plain,
in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ),
inference(simp,[status(thm)],[29774]) ).
thf(149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ~ ( in @ C @ B )
| ( in @ D @ sk2 )
| ( ( in @ C @ A )
!= ( in @ D @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[19,45]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk3 ) )
| ~ ( in @ B @ A )
| ( in @ B @ sk2 ) ),
inference(pattern_uni,[status(thm)],[149:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(159,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk3 ) )
| ~ ( in @ B @ A )
| ( in @ B @ sk2 ) ),
inference(simp,[status(thm)],[150]) ).
thf(30002,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk3 ) )
| ( in @ B @ sk2 )
| ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29915,159]) ).
thf(30003,plain,
( ~ ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk3 ) )
| ( in @ ( powerset @ sk3 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[30002:[bind(A,$thf( powerset @ ( powerset @ sk2 ) )),bind(B,$thf( powerset @ sk3 ))]]) ).
thf(147,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( in @ C @ sk2 )
| ( ( in @ ( sk1 @ B @ A ) @ B )
!= ( in @ C @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[8,45]) ).
thf(148,plain,
! [A: $i] :
( ( in @ sk3 @ ( powerset @ A ) )
| ( in @ ( sk1 @ sk3 @ A ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[147:[bind(A,$thf( E )),bind(B,$thf( sk3 )),bind(C,$thf( sk1 @ sk3 @ E ))]]) ).
thf(158,plain,
! [A: $i] :
( ( in @ sk3 @ ( powerset @ A ) )
| ( in @ ( sk1 @ sk3 @ A ) @ sk2 ) ),
inference(simp,[status(thm)],[148]) ).
thf(5900,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( in @ sk3 @ ( powerset @ A ) )
| ~ ( in @ C @ ( powerset @ B ) )
| ( in @ D @ ( powerset @ B ) )
| ( ( in @ ( sk1 @ sk3 @ A ) @ sk2 )
!= ( in @ ( sk1 @ D @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[158,93]) ).
thf(5901,plain,
! [A: $i] :
( ( in @ sk3 @ ( powerset @ A ) )
| ~ ( in @ sk2 @ ( powerset @ A ) )
| ( in @ sk3 @ ( powerset @ A ) ) ),
inference(pattern_uni,[status(thm)],[5900:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 )),bind(D,$thf( sk3 ))]]) ).
thf(6122,plain,
! [A: $i] :
( ( in @ sk3 @ ( powerset @ A ) )
| ~ ( in @ sk2 @ ( powerset @ A ) ) ),
inference(simp,[status(thm)],[5901]) ).
thf(7525,plain,
! [B: $i,A: $i] :
( ~ ( in @ sk2 @ ( powerset @ A ) )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ B )
| ( ( in @ sk3 @ ( powerset @ A ) )
!= ( in @ B @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6122,46]) ).
thf(7526,plain,
( ~ ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[7525:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(8911,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ B @ A ) )
!= A )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 )
| ( ( in @ B @ ( powerset @ A ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,7526]) ).
thf(8912,plain,
( ( ( powerset @ ( sk1 @ sk2 @ ( powerset @ sk2 ) ) )
!= ( powerset @ sk2 ) )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[8911:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(10901,plain,
( ( ( sk1 @ sk2 @ ( powerset @ sk2 ) )
!= sk2 )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 ) ),
inference(simp,[status(thm)],[8912]) ).
thf(47092,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk3 ) )
| ( in @ B @ sk2 )
| ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47023,159]) ).
thf(47093,plain,
( ~ ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk3 ) )
| ( in @ ( powerset @ sk4 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[47092:[bind(A,$thf( powerset @ ( powerset @ sk2 ) )),bind(B,$thf( powerset @ sk4 ))]]) ).
thf(52139,plain,
( ( in @ ( powerset @ sk4 ) @ sk2 )
| ( ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk3 ) )
!= ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29915,47093]) ).
thf(52247,plain,
( ( in @ ( powerset @ sk4 ) @ sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk3 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[52139]) ).
thf(52350,plain,
( ( in @ ( powerset @ sk4 ) @ sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[52247]) ).
thf(52387,plain,
( ( in @ ( powerset @ sk4 ) @ sk2 )
| ( ( powerset @ sk2 )
!= sk3 ) ),
inference(simp,[status(thm)],[52350]) ).
thf(3756,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A )
| ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
!= ( in @ B @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[3587,19]) ).
thf(3757,plain,
! [A: $i] :
( ~ ( in @ A @ ( binunion @ sk4 @ sk4 ) )
| ( in @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3756:[bind(A,$thf( sk2 )),bind(B,$thf( binunion @ sk4 @ sk4 )),bind(C,$thf( C ))]]) ).
thf(3794,plain,
! [A: $i] :
( ~ ( in @ A @ ( binunion @ sk4 @ sk4 ) )
| ( in @ A @ sk2 ) ),
inference(simp,[status(thm)],[3757]) ).
thf(6958,plain,
! [B: $i,A: $i] :
( ( in @ B @ sk2 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ B @ ( binunion @ sk4 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,3794]) ).
thf(7037,plain,
! [B: $i,A: $i] :
( ( in @ B @ sk2 )
| ( A != B )
| ( ( powerset @ A )
!= ( binunion @ sk4 @ sk4 ) ) ),
inference(simp,[status(thm)],[6958]) ).
thf(7109,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( powerset @ A )
!= ( binunion @ sk4 @ sk4 ) ) ),
inference(simp,[status(thm)],[7037]) ).
thf(11380,plain,
! [A: $i] :
( ( ( powerset @ A )
!= ( binunion @ sk4 @ sk4 ) )
| ( ( in @ A @ sk2 )
!= ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[7109,1277]) ).
thf(11447,plain,
! [A: $i] :
( ( ( powerset @ A )
!= ( binunion @ sk4 @ sk4 ) )
| ( A
!= ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[11380]) ).
thf(11504,plain,
( ( ( binunion @ sk4 @ sk4 )
!= ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[11447]) ).
thf(14962,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk3 ) )
| ( in @ B @ sk2 )
| ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
!= ( in @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3587,159]) ).
thf(14963,plain,
( ~ ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) )
| ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[14962:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( binunion @ sk4 @ sk4 ))]]) ).
thf(18392,plain,
! [A: $i] :
( ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,14963]) ).
thf(18552,plain,
! [A: $i] :
( ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
| ( A
!= ( powerset @ sk2 ) )
| ( ( powerset @ A )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[18392]) ).
thf(18691,plain,
( ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[18552]) ).
thf(169,plain,
! [C: $i,B: $i,A: $i] :
( ( ( powerset @ sk2 )
!= sk3 )
| ~ ( in @ B @ ( powerset @ A ) )
| ( in @ C @ A )
| ( ( in @ sk3 @ sk2 )
!= ( in @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[163,19]) ).
thf(170,plain,
! [A: $i] :
( ( ( powerset @ sk2 )
!= sk3 )
| ~ ( in @ sk2 @ ( powerset @ A ) )
| ( in @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[169:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(13880,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk4 ) )
| ( in @ B @ sk2 )
| ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
!= ( in @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13531,68]) ).
thf(13881,plain,
( ~ ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) )
| ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[13880:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( binunion @ sk3 @ sk3 ))]]) ).
thf(18017,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ B @ A ) )
!= A )
| ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
| ( ( in @ B @ ( powerset @ A ) )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,13881]) ).
thf(18018,plain,
( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk4 ) )
!= sk4 )
| ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[18017:[bind(A,$thf( sk4 )),bind(B,$thf( powerset @ sk2 ))]]) ).
thf(61,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ sk4 @ ( powerset @ sk2 ) )
!= ( in @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[11,42]) ).
thf(67,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( sk4 != A )
| ( ( powerset @ sk2 )
!= sk4 ) ),
inference(simp,[status(thm)],[61]) ).
thf(70,plain,
( ( in @ sk4 @ sk2 )
| ( ( powerset @ sk2 )
!= sk4 ) ),
inference(simp,[status(thm)],[67]) ).
thf(1305,plain,
! [A: $i] :
( ( ( powerset @ sk2 )
!= sk4 )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
| ( ( in @ sk4 @ sk2 )
!= ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[70,46]) ).
thf(1355,plain,
! [A: $i] :
( ( ( powerset @ sk2 )
!= sk4 )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
| ( sk4 != A )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1305]) ).
thf(1401,plain,
( ( ( powerset @ sk2 )
!= sk4 )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1355]) ).
thf(1430,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,1277]) ).
thf(1462,plain,
! [A: $i] :
( ( A
!= ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
| ( ( powerset @ A )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[1430]) ).
thf(1486,plain,
( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[1462]) ).
thf(1348,plain,
! [A: $i] :
( ~ ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) )
| ( ( in @ ( binunion @ sk3 @ sk4 ) @ A )
!= ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[46]) ).
thf(1381,plain,
! [A: $i] :
( ~ ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) )
| ( ( binunion @ sk3 @ sk4 )
!= A )
| ( A
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[1348]) ).
thf(1426,plain,
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
| ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[1381]) ).
thf(48,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ~ ( in @ E @ D )
| ( in @ E @ C )
| ( ( in @ ( sk1 @ B @ A ) @ B )
!= ( in @ D @ ( powerset @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,19]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ ( powerset @ C ) @ ( powerset @ B ) )
| ~ ( in @ A @ ( sk1 @ ( powerset @ C ) @ B ) )
| ( in @ A @ C ) ),
inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( G )),bind(B,$thf( powerset @ H )),bind(C,$thf( H )),bind(D,$thf( sk1 @ ( powerset @ H ) @ G )),bind(E,$thf( E ))]]) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ ( powerset @ C ) @ ( powerset @ B ) )
| ~ ( in @ A @ ( sk1 @ ( powerset @ C ) @ B ) )
| ( in @ A @ C ) ),
inference(simp,[status(thm)],[49]) ).
thf(22743,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
!= ( in @ A @ ( binunion @ sk3 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3587,13955]) ).
thf(22884,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( binunion @ sk4 @ sk4 )
!= A )
| ( ( binunion @ sk3 @ sk3 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[22743]) ).
thf(22970,plain,
( ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
| ( ( binunion @ sk3 @ sk3 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[22884]) ).
thf(1336,plain,
! [A: $i] :
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
| ( ( in @ sk4 @ ( powerset @ sk2 ) )
!= ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,46]) ).
thf(1374,plain,
! [A: $i] :
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
| ( sk4 != A )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[1336]) ).
thf(1420,plain,
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[1374]) ).
thf(2184,plain,
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 )
| ( ( powerset @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[1420]) ).
thf(22725,plain,
! [B: $i,A: $i] :
( ( in @ B @ sk2 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ B @ ( binunion @ sk3 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,13955]) ).
thf(22873,plain,
! [B: $i,A: $i] :
( ( in @ B @ sk2 )
| ( A != B )
| ( ( powerset @ A )
!= ( binunion @ sk3 @ sk3 ) ) ),
inference(simp,[status(thm)],[22725]) ).
thf(22961,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( powerset @ A )
!= ( binunion @ sk3 @ sk3 ) ) ),
inference(simp,[status(thm)],[22873]) ).
thf(25020,plain,
! [B: $i,A: $i] :
( ( ( powerset @ A )
!= ( binunion @ sk3 @ sk3 ) )
| ~ ( in @ B @ ( powerset @ ( powerset @ sk2 ) ) )
| ( ( in @ A @ sk2 )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[22961,46]) ).
thf(25021,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= ( binunion @ sk3 @ sk3 ) )
| ~ ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[25020:[bind(A,$thf( binunion @ sk3 @ sk4 )),bind(B,$thf( sk2 ))]]) ).
thf(47071,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= ( binunion @ sk3 @ sk3 ) )
| ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[47023,25021]) ).
thf(47164,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= ( binunion @ sk3 @ sk3 ) )
| ( ( powerset @ sk4 )
!= sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[47071]) ).
thf(47261,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= ( binunion @ sk3 @ sk3 ) )
| ( ( powerset @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[47164]) ).
thf(292,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( powerset @ A )
!= sk3 )
| ~ ( in @ C @ ( powerset @ B ) )
| ( in @ D @ B )
| ( ( in @ A @ sk2 )
!= ( in @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[162,19]) ).
thf(293,plain,
! [B: $i,A: $i] :
( ( ( powerset @ A )
!= sk3 )
| ~ ( in @ sk2 @ ( powerset @ B ) )
| ( in @ A @ B ) ),
inference(pattern_uni,[status(thm)],[292:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk2 )),bind(D,$thf( A ))]]) ).
thf(47048,plain,
! [A: $i] :
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
| ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[47023,46]) ).
thf(47049,plain,
~ ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk4 ) ),
inference(pattern_uni,[status(thm)],[47048:[bind(A,$thf( powerset @ sk4 ))]]) ).
thf(47325,plain,
! [B: $i,A: $i] :
( ( ( powerset @ A )
!= sk3 )
| ~ ( in @ sk2 @ ( powerset @ B ) )
| ( ( in @ A @ B )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[293,47049]) ).
thf(47326,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 )
| ~ ( in @ sk2 @ ( powerset @ ( powerset @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[47325:[bind(A,$thf( binunion @ sk3 @ sk4 )),bind(B,$thf( powerset @ sk4 ))]]) ).
thf(56832,plain,
! [A: $i] :
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ sk4 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,47326]) ).
thf(57075,plain,
! [A: $i] :
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 )
| ( A != sk2 )
| ( ( powerset @ A )
!= ( powerset @ ( powerset @ sk4 ) ) ) ),
inference(simp,[status(thm)],[56832]) ).
thf(57185,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 )
| ( ( powerset @ ( powerset @ sk4 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[57075]) ).
thf(13820,plain,
! [A: $i] :
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
| ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
!= ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[13531,46]) ).
thf(13908,plain,
! [A: $i] :
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
| ( ( binunion @ sk3 @ sk3 )
!= A )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[13820]) ).
thf(13960,plain,
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ sk3 @ sk3 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[13908]) ).
thf(22016,plain,
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ sk3 @ sk3 ) )
| ( ( powerset @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[13960]) ).
thf(33890,plain,
! [A: $i] :
( ( in @ ( powerset @ sk3 ) @ sk2 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,30003]) ).
thf(34011,plain,
! [A: $i] :
( ( in @ ( powerset @ sk3 ) @ sk2 )
| ( A
!= ( powerset @ ( powerset @ sk2 ) ) )
| ( ( powerset @ A )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[33890]) ).
thf(34139,plain,
( ( in @ ( powerset @ sk3 ) @ sk2 )
| ( ( powerset @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[34011]) ).
thf(22777,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ sk4 @ ( powerset @ sk2 ) )
!= ( in @ A @ ( binunion @ sk3 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,13955]) ).
thf(22834,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( sk4 != A )
| ( ( binunion @ sk3 @ sk3 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[22777]) ).
thf(22925,plain,
( ( in @ sk4 @ sk2 )
| ( ( binunion @ sk3 @ sk3 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[22834]) ).
thf(1429,plain,
( ( ( powerset @ sk2 )
!= sk4 )
| ( ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[69,1277]) ).
thf(1475,plain,
( ( ( powerset @ sk2 )
!= sk4 )
| ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1429]) ).
thf(317,plain,
! [A: $i] :
( ( in @ sk3 @ ( powerset @ A ) )
| ( ( in @ ( sk1 @ sk3 @ A ) @ sk2 )
!= ( in @ sk3 @ ( powerset @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[158]) ).
thf(320,plain,
! [A: $i] :
( ( in @ sk3 @ ( powerset @ A ) )
| ( ( sk1 @ sk3 @ A )
!= sk3 )
| ( ( powerset @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[317]) ).
thf(21,plain,
( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) )
!= ( in @ sk3 @ ( powerset @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[14,13]) ).
thf(23,plain,
( ( ( binunion @ sk3 @ sk4 )
!= sk3 )
| ( ( powerset @ sk2 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(25,plain,
( ( binunion @ sk3 @ sk4 )
!= sk3 ),
inference(simp,[status(thm)],[23]) ).
thf(20,plain,
( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) )
!= ( in @ sk4 @ ( powerset @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[11,13]) ).
thf(22,plain,
( ( ( binunion @ sk3 @ sk4 )
!= sk4 )
| ( ( powerset @ sk2 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(24,plain,
( ( binunion @ sk3 @ sk4 )
!= sk4 ),
inference(simp,[status(thm)],[22]) ).
thf(29956,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ sk2 ) )
| ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ A @ ( powerset @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29915,28398]) ).
thf(30103,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ sk2 ) )
| ( ( powerset @ sk3 )
!= A )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[29956]) ).
thf(30162,plain,
( ( in @ ( powerset @ sk3 ) @ ( powerset @ sk2 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[30103]) ).
thf(3809,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ sk4 ) )
| ( in @ C @ sk2 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[92,68]) ).
thf(3810,plain,
! [A: $i] :
( ~ ( in @ ( powerset @ A ) @ ( powerset @ sk4 ) )
| ( in @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3809:[bind(A,$thf( D )),bind(B,$thf( powerset @ D )),bind(C,$thf( D ))]]) ).
thf(4118,plain,
! [A: $i] :
( ~ ( in @ ( powerset @ A ) @ ( powerset @ sk4 ) )
| ( in @ A @ sk2 ) ),
inference(simp,[status(thm)],[3810]) ).
thf(7384,plain,
! [B: $i,A: $i] :
( ( in @ B @ sk2 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ B ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,4118]) ).
thf(7441,plain,
! [B: $i,A: $i] :
( ( in @ B @ sk2 )
| ( A
!= ( powerset @ B ) )
| ( ( powerset @ A )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[7384]) ).
thf(7492,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( powerset @ ( powerset @ A ) )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[7441]) ).
thf(11774,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( powerset @ A ) )
!= ( powerset @ sk4 ) )
| ~ ( in @ B @ ( powerset @ ( powerset @ sk2 ) ) )
| ( ( in @ A @ sk2 )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7492,46]) ).
thf(11775,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk4 ) )
| ~ ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[11774:[bind(A,$thf( binunion @ sk3 @ sk4 )),bind(B,$thf( sk2 ))]]) ).
thf(30013,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk4 ) )
| ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29915,11775]) ).
thf(30069,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk4 ) )
| ( ( powerset @ sk3 )
!= sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[30013]) ).
thf(30149,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk4 ) )
| ( ( powerset @ sk3 )
!= sk2 ) ),
inference(simp,[status(thm)],[30069]) ).
thf(3950,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk4 ) )
| ( in @ B @ sk2 )
| ( ( in @ sk4 @ ( powerset @ sk2 ) )
!= ( in @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11,68]) ).
thf(3951,plain,
( ~ ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) )
| ( in @ sk4 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3950:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(8874,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ B @ A ) )
!= A )
| ( in @ sk4 @ sk2 )
| ( ( in @ B @ ( powerset @ A ) )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,3951]) ).
thf(8875,plain,
( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk4 ) )
!= sk4 )
| ( in @ sk4 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8874:[bind(A,$thf( sk4 )),bind(B,$thf( powerset @ sk2 ))]]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ( in @ B @ sk2 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ B @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[92,42]) ).
thf(106,plain,
! [B: $i,A: $i] :
( ( in @ B @ sk2 )
| ( A != B )
| ( ( powerset @ A )
!= sk4 ) ),
inference(simp,[status(thm)],[103]) ).
thf(110,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( powerset @ A )
!= sk4 ) ),
inference(simp,[status(thm)],[106]) ).
thf(295,plain,
! [C: $i,B: $i,A: $i] :
( ( ( powerset @ A )
!= sk3 )
| ( in @ C @ ( powerset @ B ) )
| ( ( in @ A @ sk2 )
!= ( in @ ( sk1 @ C @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[162,12]) ).
thf(296,plain,
! [A: $i] :
( ( ( powerset @ ( sk1 @ A @ sk2 ) )
!= sk3 )
| ( in @ A @ ( powerset @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[295:[bind(A,$thf( sk1 @ D @ sk2 )),bind(B,$thf( sk2 )),bind(C,$thf( D ))]]) ).
thf(302,plain,
! [A: $i] :
( ( ( powerset @ ( sk1 @ A @ sk2 ) )
!= sk3 )
| ( in @ A @ ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[296]) ).
thf(801,plain,
! [A: $i] :
( ( ( powerset @ ( sk1 @ A @ sk2 ) )
!= sk3 )
| ( ( in @ A @ ( powerset @ sk2 ) )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[302,13]) ).
thf(802,plain,
( ( powerset @ ( sk1 @ ( binunion @ sk3 @ sk4 ) @ sk2 ) )
!= sk3 ),
inference(pattern_uni,[status(thm)],[801:[bind(A,$thf( binunion @ sk3 @ sk4 ))]]) ).
thf(47109,plain,
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 )
| ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[47023,7526]) ).
thf(47158,plain,
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 )
| ( ( powerset @ sk4 )
!= sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[47109]) ).
thf(47259,plain,
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 )
| ( ( powerset @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[47158]) ).
thf(14846,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk3 ) )
| ( in @ B @ sk2 )
| ( ( in @ sk3 @ ( powerset @ sk2 ) )
!= ( in @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14,159]) ).
thf(14847,plain,
( ~ ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) )
| ( in @ sk3 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[14846:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(15476,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ B @ A ) )
!= A )
| ( in @ sk3 @ sk2 )
| ( ( in @ B @ ( powerset @ A ) )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,14847]) ).
thf(15477,plain,
( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk3 ) )
!= sk3 )
| ( in @ sk3 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[15476:[bind(A,$thf( sk3 )),bind(B,$thf( powerset @ sk2 ))]]) ).
thf(11351,plain,
! [A: $i] :
( ( ( powerset @ A )
!= ( binunion @ sk4 @ sk4 ) )
| ( ( in @ A @ sk2 )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[7109,1815]) ).
thf(11453,plain,
! [A: $i] :
( ( ( powerset @ A )
!= ( binunion @ sk4 @ sk4 ) )
| ( A
!= ( binunion @ sk3 @ sk4 ) )
| ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[11351]) ).
thf(11510,plain,
( ( ( binunion @ sk4 @ sk4 )
!= ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
| ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[11453]) ).
thf(268,plain,
! [A: $i] :
( ( ( powerset @ A )
!= sk4 )
| ( ( in @ A @ sk2 )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[110,13]) ).
thf(278,plain,
! [A: $i] :
( ( ( powerset @ A )
!= sk4 )
| ( A
!= ( binunion @ sk3 @ sk4 ) )
| ( ( powerset @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[268]) ).
thf(284,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk4 )
| ( ( powerset @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[278]) ).
thf(311,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( in @ sk3 @ ( powerset @ A ) )
| ~ ( in @ D @ C )
| ( in @ D @ B )
| ( ( in @ ( sk1 @ sk3 @ A ) @ sk2 )
!= ( in @ C @ ( powerset @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[158,19]) ).
thf(321,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( in @ sk3 @ ( powerset @ A ) )
| ( in @ D @ B )
| ~ ( in @ D @ C )
| ( ( sk1 @ sk3 @ A )
!= C )
| ( ( powerset @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[311]) ).
thf(325,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ sk3 @ ( powerset @ A ) )
| ( in @ C @ B )
| ~ ( in @ C @ ( sk1 @ sk3 @ A ) )
| ( ( powerset @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[321]) ).
thf(15072,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk3 ) )
| ( in @ B @ sk2 )
| ( ( in @ sk4 @ ( powerset @ sk2 ) )
!= ( in @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11,159]) ).
thf(15073,plain,
( ~ ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) )
| ( in @ sk4 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[15072:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(1440,plain,
( ( ( powerset @ sk2 )
!= sk4 )
| ( ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ sk4 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[70,1277]) ).
thf(1479,plain,
( ( ( powerset @ sk2 )
!= sk4 )
| ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk4 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1440]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ( in @ C @ A )
| ( ( in @ sk3 @ ( powerset @ sk2 ) )
!= ( in @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14,19]) ).
thf(29,plain,
! [A: $i] :
( ~ ( in @ ( powerset @ sk2 ) @ ( powerset @ A ) )
| ( in @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[28:[bind(A,$thf( A )),bind(B,$thf( powerset @ sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(3846,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk4 ) )
| ( in @ B @ sk2 )
| ( ( in @ sk3 @ ( powerset @ sk2 ) )
!= ( in @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14,68]) ).
thf(3847,plain,
( ~ ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) )
| ( in @ sk3 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3846:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(4535,plain,
! [A: $i] :
( ( ( powerset @ A )
!= sk3 )
| ( in @ sk3 @ sk2 )
| ( ( in @ A @ sk2 )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[162,3847]) ).
thf(4558,plain,
! [A: $i] :
( ( in @ sk3 @ sk2 )
| ( ( powerset @ A )
!= sk3 )
| ( A
!= ( powerset @ sk2 ) )
| ( ( powerset @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[4535]) ).
thf(4595,plain,
( ( in @ sk3 @ sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk3 )
| ( ( powerset @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[4558]) ).
thf(1439,plain,
! [A: $i] :
( ( ( powerset @ ( sk1 @ A @ sk2 ) )
!= sk3 )
| ( ( in @ A @ ( powerset @ sk2 ) )
!= ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[302,1277]) ).
thf(1468,plain,
! [A: $i] :
( ( ( powerset @ ( sk1 @ A @ sk2 ) )
!= sk3 )
| ( A
!= ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[1439]) ).
thf(1489,plain,
( ( ( powerset @ ( sk1 @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ sk2 ) )
!= sk3 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[1468]) ).
thf(168,plain,
! [C: $i,B: $i,A: $i] :
( ( ( powerset @ sk2 )
!= sk3 )
| ~ ( in @ C @ B )
| ( in @ C @ A )
| ( ( in @ sk3 @ sk2 )
!= ( in @ B @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[163,19]) ).
thf(177,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ C @ A )
| ( ( powerset @ sk2 )
!= sk3 )
| ~ ( in @ C @ B )
| ( sk3 != B )
| ( ( powerset @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[168]) ).
thf(179,plain,
! [B: $i,A: $i] :
( ( in @ B @ A )
| ( ( powerset @ sk2 )
!= sk3 )
| ~ ( in @ B @ sk3 )
| ( ( powerset @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[177]) ).
thf(29984,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= ( binunion @ sk3 @ sk3 ) )
| ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29915,25021]) ).
thf(30052,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= ( binunion @ sk3 @ sk3 ) )
| ( ( powerset @ sk3 )
!= sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[29984]) ).
thf(30144,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= ( binunion @ sk3 @ sk3 ) )
| ( ( powerset @ sk3 )
!= sk2 ) ),
inference(simp,[status(thm)],[30052]) ).
thf(6996,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ sk4 @ ( powerset @ sk2 ) )
!= ( in @ A @ ( binunion @ sk4 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,3794]) ).
thf(7032,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( sk4 != A )
| ( ( binunion @ sk4 @ sk4 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[6996]) ).
thf(7104,plain,
( ( in @ sk4 @ sk2 )
| ( ( binunion @ sk4 @ sk4 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[7032]) ).
thf(185,plain,
! [E: $o,D: $i,C: $i,B: $i,A: $i] :
( ( in @ D @ B )
| ( in @ D @ C )
| E
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ D @ ( binunion @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,18]) ).
thf(215,plain,
! [E: $o,D: $i,C: $i,B: $i,A: $i] :
( ( in @ D @ B )
| ( in @ D @ C )
| E
| ( A != D )
| ( ( powerset @ A )
!= ( binunion @ B @ C ) ) ),
inference(simp,[status(thm)],[185]) ).
thf(238,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( in @ C @ A )
| ( in @ C @ B )
| D
| ( ( powerset @ C )
!= ( binunion @ A @ B ) ) ),
inference(simp,[status(thm)],[215]) ).
thf(25068,plain,
! [A: $i] :
( ( ( powerset @ A )
!= ( binunion @ sk3 @ sk3 ) )
| ( ( in @ A @ sk2 )
!= ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[22961,1277]) ).
thf(25161,plain,
! [A: $i] :
( ( ( powerset @ A )
!= ( binunion @ sk3 @ sk3 ) )
| ( A
!= ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[25068]) ).
thf(25240,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( binunion @ sk3 @ sk3 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[25161]) ).
thf(11812,plain,
! [A: $i] :
( ( ( powerset @ ( powerset @ A ) )
!= ( powerset @ sk4 ) )
| ( ( in @ A @ sk2 )
!= ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[7492,1277]) ).
thf(11878,plain,
! [A: $i] :
( ( ( powerset @ ( powerset @ A ) )
!= ( powerset @ sk4 ) )
| ( A
!= ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[11812]) ).
thf(12041,plain,
( ( ( powerset @ ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) ) )
!= ( powerset @ sk4 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[11878]) ).
thf(14913,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ sk3 ) )
| ( in @ C @ sk2 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[92,159]) ).
thf(14914,plain,
! [A: $i] :
( ~ ( in @ ( powerset @ A ) @ ( powerset @ sk3 ) )
| ( in @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[14913:[bind(A,$thf( D )),bind(B,$thf( powerset @ D )),bind(C,$thf( D ))]]) ).
thf(15290,plain,
! [A: $i] :
( ~ ( in @ ( powerset @ A ) @ ( powerset @ sk3 ) )
| ( in @ A @ sk2 ) ),
inference(simp,[status(thm)],[14914]) ).
thf(24772,plain,
! [B: $i,A: $i] :
( ( in @ B @ sk2 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ B ) @ ( powerset @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,15290]) ).
thf(24872,plain,
! [B: $i,A: $i] :
( ( in @ B @ sk2 )
| ( A
!= ( powerset @ B ) )
| ( ( powerset @ A )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[24772]) ).
thf(24965,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( powerset @ ( powerset @ A ) )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[24872]) ).
thf(25524,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( powerset @ A ) )
!= ( powerset @ sk3 ) )
| ~ ( in @ B @ ( powerset @ ( powerset @ sk2 ) ) )
| ( ( in @ A @ sk2 )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[24965,46]) ).
thf(25525,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk3 ) )
| ~ ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[25524:[bind(A,$thf( binunion @ sk3 @ sk4 )),bind(B,$thf( sk2 ))]]) ).
thf(26457,plain,
! [A: $i] :
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk3 ) )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,25525]) ).
thf(26629,plain,
! [A: $i] :
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk3 ) )
| ( A != sk2 )
| ( ( powerset @ A )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[26457]) ).
thf(26853,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk3 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[26629]) ).
thf(26909,plain,
( ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) )
| ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk2 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk3 ) ) ),
inference(eqfactor_ordered,[status(thm)],[26853]) ).
thf(26916,plain,
( ( ( powerset @ sk2 )
!= sk2 )
| ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk2 )
| ( ( powerset @ sk2 )
!= sk3 ) ),
inference(simp,[status(thm)],[26909]) ).
thf(29965,plain,
! [A: $i] :
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
| ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29915,46]) ).
thf(29966,plain,
~ ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk3 ) ),
inference(pattern_uni,[status(thm)],[29965:[bind(A,$thf( powerset @ sk3 ))]]) ).
thf(44243,plain,
! [B: $i,A: $i] :
( ( ( powerset @ A )
!= sk3 )
| ~ ( in @ sk2 @ ( powerset @ B ) )
| ( ( in @ A @ B )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[293,29966]) ).
thf(44244,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 )
| ~ ( in @ sk2 @ ( powerset @ ( powerset @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[44243:[bind(A,$thf( binunion @ sk3 @ sk4 )),bind(B,$thf( powerset @ sk3 ))]]) ).
thf(44766,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ B @ A ) )
!= A )
| ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 )
| ( ( in @ B @ ( powerset @ A ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ sk3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,44244]) ).
thf(44767,plain,
( ( ( powerset @ ( sk1 @ sk2 @ ( powerset @ sk3 ) ) )
!= ( powerset @ sk3 ) )
| ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[44766:[bind(A,$thf( powerset @ sk3 )),bind(B,$thf( sk2 ))]]) ).
thf(46040,plain,
( ( ( sk1 @ sk2 @ ( powerset @ sk3 ) )
!= sk3 )
| ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[44767]) ).
thf(47309,plain,
( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk4 ) )
!= ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[47023,47049]) ).
thf(47613,plain,
( ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk4 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[47309]) ).
thf(29998,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk3 ) )
| ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29915,25525]) ).
thf(30088,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 )
| ( ( powerset @ sk3 )
!= sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[29998]) ).
thf(30154,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 )
| ( ( powerset @ sk3 )
!= sk2 ) ),
inference(simp,[status(thm)],[30088]) ).
thf(1300,plain,
! [B: $i,A: $i] :
( ( ( powerset @ A )
!= sk4 )
| ~ ( in @ B @ ( powerset @ ( powerset @ sk2 ) ) )
| ( ( in @ A @ sk2 )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[110,46]) ).
thf(1301,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk4 )
| ~ ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[1300:[bind(A,$thf( binunion @ sk3 @ sk4 )),bind(B,$thf( sk2 ))]]) ).
thf(8891,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ B @ A ) )
!= A )
| ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk4 )
| ( ( in @ B @ ( powerset @ A ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,1301]) ).
thf(8892,plain,
( ( ( powerset @ ( sk1 @ sk2 @ ( powerset @ sk2 ) ) )
!= ( powerset @ sk2 ) )
| ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk4 ) ),
inference(pattern_uni,[status(thm)],[8891:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(146,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ sk4 @ ( powerset @ sk2 ) )
!= ( in @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[11,45]) ).
thf(157,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( sk4 != A )
| ( ( powerset @ sk2 )
!= sk3 ) ),
inference(simp,[status(thm)],[146]) ).
thf(165,plain,
( ( in @ sk4 @ sk2 )
| ( ( powerset @ sk2 )
!= sk3 ) ),
inference(simp,[status(thm)],[157]) ).
thf(251,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( ( powerset @ sk2 )
!= sk3 )
| ( in @ C @ A )
| ( in @ C @ B )
| D
| ( ( in @ sk4 @ sk2 )
!= ( in @ C @ ( binunion @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[165,18]) ).
thf(260,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( in @ C @ A )
| ( in @ C @ B )
| D
| ( ( powerset @ sk2 )
!= sk3 )
| ( sk4 != C )
| ( ( binunion @ A @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[251]) ).
thf(265,plain,
! [C: $o,B: $i,A: $i] :
( ( in @ sk4 @ A )
| ( in @ sk4 @ B )
| C
| ( ( powerset @ sk2 )
!= sk3 )
| ( ( binunion @ A @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[260]) ).
thf(15156,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk3 ) )
| ( in @ B @ sk2 )
| ( ( in @ B @ A )
!= ( in @ A @ ( powerset @ sk3 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[159]) ).
thf(15197,plain,
( ~ ( in @ ( powerset @ sk3 ) @ ( powerset @ sk3 ) )
| ( in @ ( powerset @ sk3 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[15156:[bind(A,$thf( powerset @ sk3 )),bind(B,$thf( powerset @ sk3 ))]]) ).
thf(125,plain,
! [A: $i] :
( ( in @ sk4 @ ( powerset @ A ) )
| ( ( in @ ( sk1 @ sk4 @ A ) @ sk2 )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[71,13]) ).
thf(133,plain,
! [A: $i] :
( ( in @ sk4 @ ( powerset @ A ) )
| ( ( sk1 @ sk4 @ A )
!= ( binunion @ sk3 @ sk4 ) )
| ( ( powerset @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[125]) ).
thf(115,plain,
! [C: $i,B: $i,A: $i] :
( ( ( powerset @ sk2 )
!= sk4 )
| ~ ( in @ B @ ( powerset @ A ) )
| ( in @ C @ A )
| ( ( in @ sk4 @ sk2 )
!= ( in @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[70,19]) ).
thf(116,plain,
! [A: $i] :
( ( ( powerset @ sk2 )
!= sk4 )
| ~ ( in @ sk2 @ ( powerset @ A ) )
| ( in @ sk4 @ A ) ),
inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk4 ))]]) ).
thf(184,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( ( powerset @ sk2 )
!= sk4 )
| ( in @ C @ A )
| ( in @ C @ B )
| D
| ( ( in @ sk4 @ sk2 )
!= ( in @ C @ ( binunion @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[70,18]) ).
thf(220,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( in @ C @ A )
| ( in @ C @ B )
| D
| ( ( powerset @ sk2 )
!= sk4 )
| ( sk4 != C )
| ( ( binunion @ A @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[184]) ).
thf(243,plain,
! [C: $o,B: $i,A: $i] :
( ( in @ sk4 @ A )
| ( in @ sk4 @ B )
| C
| ( ( powerset @ sk2 )
!= sk4 )
| ( ( binunion @ A @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[220]) ).
thf(209,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( binunion @ A @ B ) )
| ( in @ C @ A )
| ( in @ C @ B )
| ( D
!= ( in @ C @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[18]) ).
thf(223,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( binunion @ A @ C ) )
| ( in @ B @ A )
| ( in @ B @ C ) ),
inference(pattern_uni,[status(thm)],[209:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( in @ E @ F ))]]) ).
thf(248,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( binunion @ A @ C ) )
| ( in @ B @ A )
| ( in @ B @ C ) ),
inference(simp,[status(thm)],[223]) ).
thf(25526,plain,
! [A: $i] :
( ( ( powerset @ ( powerset @ A ) )
!= ( powerset @ sk3 ) )
| ( ( in @ A @ sk2 )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[24965,1815]) ).
thf(25668,plain,
! [A: $i] :
( ( ( powerset @ ( powerset @ A ) )
!= ( powerset @ sk3 ) )
| ( A
!= ( binunion @ sk3 @ sk4 ) )
| ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[25526]) ).
thf(25884,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk3 ) )
| ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[25668]) ).
thf(5957,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( in @ sk4 @ ( powerset @ A ) )
| ~ ( in @ C @ ( powerset @ B ) )
| ( in @ D @ ( powerset @ B ) )
| ( ( in @ ( sk1 @ sk4 @ A ) @ sk2 )
!= ( in @ ( sk1 @ D @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[71,93]) ).
thf(5958,plain,
! [A: $i] :
( ( in @ sk4 @ ( powerset @ A ) )
| ~ ( in @ sk2 @ ( powerset @ A ) )
| ( in @ sk4 @ ( powerset @ A ) ) ),
inference(pattern_uni,[status(thm)],[5957:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 )),bind(D,$thf( sk4 ))]]) ).
thf(6139,plain,
! [A: $i] :
( ( in @ sk4 @ ( powerset @ A ) )
| ~ ( in @ sk2 @ ( powerset @ A ) ) ),
inference(simp,[status(thm)],[5958]) ).
thf(1632,plain,
! [C: $i,B: $i,A: $o] :
( ( in @ ( binunion @ B @ B ) @ ( powerset @ B ) )
| ( in @ sk3 @ C )
| ( A
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[948,29]) ).
thf(1633,plain,
! [B: $i,A: $i] :
( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
| ( in @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[1632:[bind(A,$thf( in @ ( powerset @ sk2 ) @ ( powerset @ G ) )),bind(B,$thf( B )),bind(C,$thf( G ))]]) ).
thf(1725,plain,
! [B: $i,A: $i] :
( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
| ( in @ sk3 @ B ) ),
inference(simp,[status(thm)],[1633]) ).
thf(7004,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
| ( in @ C @ sk2 )
| ( ( in @ sk3 @ B )
!= ( in @ C @ ( binunion @ sk4 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1725,3794]) ).
thf(7005,plain,
! [A: $i] :
( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
| ( in @ sk3 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[7004:[bind(A,$thf( A )),bind(B,$thf( binunion @ sk4 @ sk4 )),bind(C,$thf( sk3 ))]]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ( in @ C @ A )
| ( ( in @ sk4 @ ( powerset @ sk2 ) )
!= ( in @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11,19]) ).
thf(35,plain,
! [A: $i] :
( ~ ( in @ ( powerset @ sk2 ) @ ( powerset @ A ) )
| ( in @ sk4 @ A ) ),
inference(pattern_uni,[status(thm)],[34:[bind(A,$thf( A )),bind(B,$thf( powerset @ sk2 )),bind(C,$thf( sk4 ))]]) ).
thf(1655,plain,
! [C: $i,B: $i,A: $o] :
( ( in @ ( binunion @ B @ B ) @ ( powerset @ B ) )
| ( in @ sk4 @ C )
| ( A
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[948,35]) ).
thf(1656,plain,
! [B: $i,A: $i] :
( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
| ( in @ sk4 @ B ) ),
inference(pattern_uni,[status(thm)],[1655:[bind(A,$thf( in @ ( powerset @ sk2 ) @ ( powerset @ G ) )),bind(B,$thf( B )),bind(C,$thf( G ))]]) ).
thf(1736,plain,
! [B: $i,A: $i] :
( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
| ( in @ sk4 @ B ) ),
inference(simp,[status(thm)],[1656]) ).
thf(3734,plain,
( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[3587,13]) ).
thf(3762,plain,
( ( ( binunion @ sk4 @ sk4 )
!= ( binunion @ sk3 @ sk4 ) )
| ( ( powerset @ sk2 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[3734]) ).
thf(3795,plain,
( ( binunion @ sk4 @ sk4 )
!= ( binunion @ sk3 @ sk4 ) ),
inference(simp,[status(thm)],[3762]) ).
thf(47143,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk4 ) )
| ( in @ B @ sk2 )
| ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47023,68]) ).
thf(47144,plain,
( ~ ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk4 ) )
| ( in @ ( powerset @ sk4 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[47143:[bind(A,$thf( powerset @ ( powerset @ sk2 ) )),bind(B,$thf( powerset @ sk4 ))]]) ).
thf(47083,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[47023,45]) ).
thf(47202,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( powerset @ sk4 )
!= A )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[47083]) ).
thf(47279,plain,
( ( in @ ( powerset @ sk4 ) @ sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[47202]) ).
thf(29947,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ A @ ( binunion @ sk3 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29915,13955]) ).
thf(30112,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( powerset @ sk3 )
!= A )
| ( ( binunion @ sk3 @ sk3 )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[29947]) ).
thf(30167,plain,
( ( in @ ( powerset @ sk3 ) @ sk2 )
| ( ( binunion @ sk3 @ sk3 )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[30112]) ).
thf(4510,plain,
! [A: $i] :
( ( ( powerset @ A )
!= sk4 )
| ( in @ sk3 @ sk2 )
| ( ( in @ A @ sk2 )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[110,3847]) ).
thf(4587,plain,
! [A: $i] :
( ( in @ sk3 @ sk2 )
| ( ( powerset @ A )
!= sk4 )
| ( A
!= ( powerset @ sk2 ) )
| ( ( powerset @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[4510]) ).
thf(4609,plain,
( ( in @ sk3 @ sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk4 )
| ( ( powerset @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[4587]) ).
thf(47103,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk4 ) )
| ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[47023,11775]) ).
thf(47171,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk4 ) )
| ( ( powerset @ sk4 )
!= sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[47103]) ).
thf(47264,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk4 ) )
| ( ( powerset @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[47171]) ).
thf(47088,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk3 ) )
| ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[47023,25525]) ).
thf(47207,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk3 ) )
| ( ( powerset @ sk4 )
!= sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[47088]) ).
thf(47282,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk3 ) )
| ( ( powerset @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[47207]) ).
thf(8197,plain,
! [B: $i,A: $i] :
( ~ ( in @ sk2 @ ( powerset @ A ) )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ B )
| ( ( in @ sk4 @ ( powerset @ A ) )
!= ( in @ B @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6139,46]) ).
thf(8198,plain,
( ~ ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 ) ),
inference(pattern_uni,[status(thm)],[8197:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(8905,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ B @ A ) )
!= A )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 )
| ( ( in @ B @ ( powerset @ A ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,8198]) ).
thf(8906,plain,
( ( ( powerset @ ( sk1 @ sk2 @ ( powerset @ sk2 ) ) )
!= ( powerset @ sk2 ) )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 ) ),
inference(pattern_uni,[status(thm)],[8905:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(9993,plain,
( ( ( sk1 @ sk2 @ ( powerset @ sk2 ) )
!= sk2 )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 ) ),
inference(simp,[status(thm)],[8906]) ).
thf(25544,plain,
! [A: $i] :
( ( ( powerset @ ( powerset @ A ) )
!= ( powerset @ sk3 ) )
| ( ( in @ A @ sk2 )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[24965,13]) ).
thf(25712,plain,
! [A: $i] :
( ( ( powerset @ ( powerset @ A ) )
!= ( powerset @ sk3 ) )
| ( A
!= ( binunion @ sk3 @ sk4 ) )
| ( ( powerset @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[25544]) ).
thf(25912,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk3 ) )
| ( ( powerset @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[25712]) ).
thf(1450,plain,
! [A: $i] :
( ( ( powerset @ A )
!= sk3 )
| ( ( in @ A @ sk2 )
!= ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[162,1277]) ).
thf(1463,plain,
! [A: $i] :
( ( ( powerset @ A )
!= sk3 )
| ( A
!= ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1450]) ).
thf(1487,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= sk3 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1463]) ).
thf(11781,plain,
! [A: $i] :
( ( ( powerset @ ( powerset @ A ) )
!= ( powerset @ sk4 ) )
| ( ( in @ A @ sk2 )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[7492,1815]) ).
thf(11943,plain,
! [A: $i] :
( ( ( powerset @ ( powerset @ A ) )
!= ( powerset @ sk4 ) )
| ( A
!= ( binunion @ sk3 @ sk4 ) )
| ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[11781]) ).
thf(12083,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk4 ) )
| ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[11943]) ).
thf(199,plain,
! [G: $o,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ~ ( in @ C @ B )
| ( in @ F @ D )
| ( in @ F @ E )
| G
| ( ( in @ C @ A )
!= ( in @ F @ ( binunion @ D @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,18]) ).
thf(200,plain,
! [E: $i,D: $i,C: $o,B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ ( binunion @ D @ E ) ) )
| ~ ( in @ B @ A )
| ( in @ B @ D )
| ( in @ B @ E )
| C ),
inference(pattern_uni,[status(thm)],[199:[bind(A,$thf( binunion @ H @ I )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( H )),bind(E,$thf( I )),bind(F,$thf( C ))]]) ).
thf(229,plain,
! [E: $i,D: $i,C: $o,B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ ( binunion @ D @ E ) ) )
| ~ ( in @ B @ A )
| ( in @ B @ D )
| ( in @ B @ E )
| C ),
inference(simp,[status(thm)],[200]) ).
thf(8919,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ B @ A ) )
!= A )
| ( in @ sk3 @ sk2 )
| ( ( in @ B @ ( powerset @ A ) )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,3847]) ).
thf(8920,plain,
( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk4 ) )
!= sk4 )
| ( in @ sk3 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8919:[bind(A,$thf( sk4 )),bind(B,$thf( powerset @ sk2 ))]]) ).
thf(3727,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
!= ( in @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[3587,42]) ).
thf(3773,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( binunion @ sk4 @ sk4 )
!= A )
| ( ( powerset @ sk2 )
!= sk4 ) ),
inference(simp,[status(thm)],[3727]) ).
thf(3799,plain,
( ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
| ( ( powerset @ sk2 )
!= sk4 ) ),
inference(simp,[status(thm)],[3773]) ).
thf(312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( in @ sk3 @ ( powerset @ A ) )
| ~ ( in @ C @ ( powerset @ B ) )
| ( in @ D @ B )
| ( ( in @ ( sk1 @ sk3 @ A ) @ sk2 )
!= ( in @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[158,19]) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( in @ sk3 @ ( powerset @ B ) )
| ~ ( in @ sk2 @ ( powerset @ A ) )
| ( in @ ( sk1 @ sk3 @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[312:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( sk2 )),bind(D,$thf( sk1 @ sk3 @ F ))]]) ).
thf(329,plain,
! [B: $i,A: $i] :
( ( in @ sk3 @ ( powerset @ B ) )
| ~ ( in @ sk2 @ ( powerset @ A ) )
| ( in @ ( sk1 @ sk3 @ B ) @ A ) ),
inference(simp,[status(thm)],[313]) ).
thf(8915,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ B @ A ) )
!= A )
| ( ( in @ B @ ( powerset @ A ) )
!= ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,1277]) ).
thf(8916,plain,
( ( powerset @ ( sk1 @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ sk2 ) ) )
!= ( powerset @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8915:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( powerset @ ( binunion @ sk3 @ sk4 ) ))]]) ).
thf(29989,plain,
( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) )
!= ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29915,13]) ).
thf(30099,plain,
( ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk3 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[29989]) ).
thf(3728,plain,
! [A: $i] :
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
| ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
!= ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3587,46]) ).
thf(3776,plain,
! [A: $i] :
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
| ( ( binunion @ sk4 @ sk4 )
!= A )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[3728]) ).
thf(3784,plain,
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ sk4 @ sk4 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[3776]) ).
thf(30011,plain,
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 )
| ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29915,8198]) ).
thf(30105,plain,
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 )
| ( ( powerset @ sk3 )
!= sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[30011]) ).
thf(30163,plain,
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 )
| ( ( powerset @ sk3 )
!= sk2 ) ),
inference(simp,[status(thm)],[30105]) ).
thf(47039,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ sk2 ) )
| ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ A @ ( powerset @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[47023,28398]) ).
thf(47243,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ sk2 ) )
| ( ( powerset @ sk4 )
!= A )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[47039]) ).
thf(47289,plain,
( ( in @ ( powerset @ sk4 ) @ ( powerset @ sk2 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[47243]) ).
thf(56249,plain,
( ( in @ ( powerset @ sk4 ) @ ( powerset @ sk2 ) )
| ( ( powerset @ sk2 )
!= sk3 ) ),
inference(simp,[status(thm)],[47289]) ).
thf(18401,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ B @ A ) )
!= A )
| ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
| ( ( in @ B @ ( powerset @ A ) )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,14963]) ).
thf(18402,plain,
( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk3 ) )
!= sk3 )
| ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[18401:[bind(A,$thf( sk3 )),bind(B,$thf( powerset @ sk2 ))]]) ).
thf(47372,plain,
! [A: $i] :
( ( ( powerset @ A )
!= ( binunion @ sk4 @ sk4 ) )
| ( ( in @ A @ sk2 )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[7109,47049]) ).
thf(47494,plain,
! [A: $i] :
( ( ( powerset @ A )
!= ( binunion @ sk4 @ sk4 ) )
| ( A
!= ( binunion @ sk3 @ sk4 ) )
| ( ( powerset @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[47372]) ).
thf(47636,plain,
( ( ( binunion @ sk4 @ sk4 )
!= ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
| ( ( powerset @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[47494]) ).
thf(126,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( in @ sk4 @ ( powerset @ A ) )
| ~ ( in @ D @ C )
| ( in @ D @ B )
| ( ( in @ ( sk1 @ sk4 @ A ) @ sk2 )
!= ( in @ C @ ( powerset @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[71,19]) ).
thf(137,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( in @ sk4 @ ( powerset @ A ) )
| ( in @ D @ B )
| ~ ( in @ D @ C )
| ( ( sk1 @ sk4 @ A )
!= C )
| ( ( powerset @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[126]) ).
thf(141,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ sk4 @ ( powerset @ A ) )
| ( in @ C @ B )
| ~ ( in @ C @ ( sk1 @ sk4 @ A ) )
| ( ( powerset @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[137]) ).
thf(272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( powerset @ A )
!= sk4 )
| ~ ( in @ C @ ( powerset @ B ) )
| ( in @ D @ B )
| ( ( in @ A @ sk2 )
!= ( in @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[110,19]) ).
thf(273,plain,
! [B: $i,A: $i] :
( ( ( powerset @ A )
!= sk4 )
| ~ ( in @ sk2 @ ( powerset @ B ) )
| ( in @ A @ B ) ),
inference(pattern_uni,[status(thm)],[272:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk2 )),bind(D,$thf( A ))]]) ).
thf(47449,plain,
! [B: $i,A: $i] :
( ( ( powerset @ A )
!= sk4 )
| ~ ( in @ sk2 @ ( powerset @ B ) )
| ( ( in @ A @ B )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[273,47049]) ).
thf(47450,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk4 )
| ~ ( in @ sk2 @ ( powerset @ ( powerset @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[47449:[bind(A,$thf( binunion @ sk3 @ sk4 )),bind(B,$thf( powerset @ sk4 ))]]) ).
thf(40692,plain,
! [B: $i,A: $i] :
( ( ( powerset @ A )
!= sk4 )
| ~ ( in @ sk2 @ ( powerset @ B ) )
| ( ( in @ A @ B )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[273,29966]) ).
thf(40693,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk4 )
| ~ ( in @ sk2 @ ( powerset @ ( powerset @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[40692:[bind(A,$thf( binunion @ sk3 @ sk4 )),bind(B,$thf( powerset @ sk3 ))]]) ).
thf(42872,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ B @ A ) )
!= A )
| ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk4 )
| ( ( in @ B @ ( powerset @ A ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ sk3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,40693]) ).
thf(42873,plain,
( ( ( powerset @ ( sk1 @ sk2 @ ( powerset @ sk3 ) ) )
!= ( powerset @ sk3 ) )
| ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk4 ) ),
inference(pattern_uni,[status(thm)],[42872:[bind(A,$thf( powerset @ sk3 )),bind(B,$thf( sk2 ))]]) ).
thf(1893,plain,
! [A: $i] :
( ( ( powerset @ A )
!= sk3 )
| ( ( in @ A @ sk2 )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[162,1815]) ).
thf(1917,plain,
! [A: $i] :
( ( ( powerset @ A )
!= sk3 )
| ( A
!= ( binunion @ sk3 @ sk4 ) )
| ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1893]) ).
thf(1937,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 )
| ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1917]) ).
thf(12146,plain,
! [A: $i] :
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk4 ) )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,11775]) ).
thf(12314,plain,
! [A: $i] :
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk4 ) )
| ( A != sk2 )
| ( ( powerset @ A )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[12146]) ).
thf(12396,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk4 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[12314]) ).
thf(12593,plain,
( ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) )
| ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk2 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk4 ) ) ),
inference(eqfactor_ordered,[status(thm)],[12396]) ).
thf(12600,plain,
( ( ( powerset @ sk2 )
!= sk2 )
| ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk2 )
| ( ( powerset @ sk2 )
!= sk4 ) ),
inference(simp,[status(thm)],[12593]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( ( in @ ( sk1 @ B @ A ) @ A )
!= ( in @ sk3 @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,12]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( ( sk1 @ B @ A )
!= sk3 )
| ( A
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[83]) ).
thf(96,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) )
| ( ( sk1 @ A @ ( powerset @ sk2 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[91]) ).
thf(114,plain,
! [C: $i,B: $i,A: $i] :
( ( ( powerset @ sk2 )
!= sk4 )
| ~ ( in @ C @ B )
| ( in @ C @ A )
| ( ( in @ sk4 @ sk2 )
!= ( in @ B @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[70,19]) ).
thf(121,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ C @ A )
| ( ( powerset @ sk2 )
!= sk4 )
| ~ ( in @ C @ B )
| ( sk4 != B )
| ( ( powerset @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[114]) ).
thf(124,plain,
! [B: $i,A: $i] :
( ( in @ B @ A )
| ( ( powerset @ sk2 )
!= sk4 )
| ~ ( in @ B @ sk4 )
| ( ( powerset @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[121]) ).
thf(47078,plain,
( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) )
!= ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[47023,13]) ).
thf(47204,plain,
( ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk4 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[47078]) ).
thf(50231,plain,
( ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk4 ) )
| ( ( powerset @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[47204]) ).
thf(207,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( binunion @ A @ B ) )
| ( in @ C @ A )
| ( in @ C @ B )
| ( D
!= ( ~ ( in @ C @ ( binunion @ A @ B ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[18]) ).
thf(224,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ ( binunion @ B @ C ) )
| ( in @ A @ B )
| ( in @ A @ C ) ),
inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( F )),bind(D,$thf( ~ ( in @ F @ ( binunion @ H @ I ) ) ))]]) ).
thf(225,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ ( binunion @ B @ C ) )
| ( in @ A @ B )
| ( in @ A @ C ) ),
inference(simp,[status(thm)],[224]) ).
thf(25573,plain,
! [A: $i] :
( ( ( powerset @ ( powerset @ A ) )
!= ( powerset @ sk3 ) )
| ( ( in @ A @ sk2 )
!= ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[24965,1277]) ).
thf(25706,plain,
! [A: $i] :
( ( ( powerset @ ( powerset @ A ) )
!= ( powerset @ sk3 ) )
| ( A
!= ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[25573]) ).
thf(25908,plain,
( ( ( powerset @ ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) ) )
!= ( powerset @ sk3 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[25706]) ).
thf(1441,plain,
( ( ( powerset @ sk2 )
!= sk3 )
| ( ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ sk4 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[165,1277]) ).
thf(1461,plain,
( ( ( powerset @ sk2 )
!= sk3 )
| ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk4 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1441]) ).
thf(13014,plain,
! [A: $i] :
( ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ ( powerset @ sk2 ) ) )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,1426]) ).
thf(13112,plain,
! [A: $i] :
( ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ ( powerset @ sk2 ) ) )
| ( A
!= ( binunion @ sk3 @ sk4 ) )
| ( ( powerset @ A )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[13014]) ).
thf(13154,plain,
( ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ ( powerset @ sk2 ) ) )
| ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[13112]) ).
thf(30070,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk4 )
| ( ( powerset @ sk3 )
!= sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[30013]) ).
thf(30150,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk4 )
| ( ( powerset @ sk3 )
!= sk2 ) ),
inference(simp,[status(thm)],[30070]) ).
thf(1867,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,1815]) ).
thf(1904,plain,
! [A: $i] :
( ( A
!= ( binunion @ sk3 @ sk4 ) )
| ( ( powerset @ A )
!= ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[1867]) ).
thf(1932,plain,
( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
!= ( powerset @ ( binunion @ sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[1904]) ).
thf(30087,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk3 ) )
| ( ( powerset @ sk3 )
!= sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[29998]) ).
thf(30153,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk3 ) )
| ( ( powerset @ sk3 )
!= sk2 ) ),
inference(simp,[status(thm)],[30087]) ).
thf(1686,plain,
! [C: $o,B: $o,A: $i] :
( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
| B
| C ),
inference(prim_subst,[status(thm)],[948:[bind(A,$thf( C | D ))]]) ).
thf(1714,plain,
! [C: $o,B: $o,A: $i] :
( B
| C
| ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) ) ),
inference(cnf,[status(esa)],[1686]) ).
thf(1715,plain,
! [C: $o,B: $o,A: $i] :
( B
| C
| ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) ) ),
inference(simp,[status(thm)],[1714]) ).
thf(14985,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk3 ) )
| ( in @ B @ sk2 )
| ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
!= ( in @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13531,159]) ).
thf(14986,plain,
( ~ ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) )
| ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[14985:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( binunion @ sk3 @ sk3 ))]]) ).
thf(40282,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ sk2 ) )
| ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ A @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29915,29675]) ).
thf(40343,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ sk2 ) )
| ( ( powerset @ sk3 )
!= A )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[40282]) ).
thf(40479,plain,
( ( in @ ( powerset @ sk3 ) @ ( powerset @ sk2 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[40343]) ).
thf(132,plain,
! [A: $i] :
( ( in @ sk4 @ ( powerset @ A ) )
| ( ( in @ ( sk1 @ sk4 @ A ) @ sk2 )
!= ( in @ sk4 @ ( powerset @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[71]) ).
thf(134,plain,
! [A: $i] :
( ( in @ sk4 @ ( powerset @ A ) )
| ( ( in @ ( sk1 @ sk4 @ A ) @ sk2 )
!= ( in @ sk4 @ ( powerset @ A ) ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(10918,plain,
! [A: $i] :
( ( ( powerset @ ( sk1 @ sk2 @ ( powerset @ sk2 ) ) )
!= ( powerset @ sk2 ) )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[92,8912]) ).
thf(11043,plain,
! [A: $i] :
( ( ( sk1 @ sk2 @ ( powerset @ sk2 ) )
!= sk2 )
| ( A
!= ( binunion @ sk3 @ sk4 ) )
| ( ( powerset @ A )
!= sk3 ) ),
inference(simp,[status(thm)],[10918]) ).
thf(11153,plain,
( ( ( sk1 @ sk2 @ ( powerset @ sk2 ) )
!= sk2 )
| ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[11043]) ).
thf(804,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ A @ sk2 ) )
!= sk3 )
| ( in @ sk3 @ B )
| ( ( in @ A @ ( powerset @ sk2 ) )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[302,29]) ).
thf(805,plain,
( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk2 ) )
!= sk3 )
| ( in @ sk3 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[804:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(9008,plain,
( ( sk1 @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ sk2 ) )
!= sk2 ),
inference(simp,[status(thm)],[8916]) ).
thf(13819,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
!= ( in @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[13531,42]) ).
thf(13942,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( binunion @ sk3 @ sk3 )
!= A )
| ( ( powerset @ sk2 )
!= sk4 ) ),
inference(simp,[status(thm)],[13819]) ).
thf(13968,plain,
( ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
| ( ( powerset @ sk2 )
!= sk4 ) ),
inference(simp,[status(thm)],[13942]) ).
thf(3988,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk4 ) )
| ( in @ B @ sk2 )
| ( ( in @ B @ A )
!= ( in @ A @ ( powerset @ sk4 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[68]) ).
thf(4020,plain,
( ~ ( in @ ( powerset @ sk4 ) @ ( powerset @ sk4 ) )
| ( in @ ( powerset @ sk4 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3988:[bind(A,$thf( powerset @ sk4 )),bind(B,$thf( powerset @ sk4 ))]]) ).
thf(47116,plain,
( ( in @ ( powerset @ sk4 ) @ sk2 )
| ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ ( powerset @ sk4 ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[47023,4020]) ).
thf(47178,plain,
( ( in @ ( powerset @ sk4 ) @ sk2 )
| ( ( powerset @ sk4 )
!= ( powerset @ sk4 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[47116]) ).
thf(47269,plain,
( ( in @ ( powerset @ sk4 ) @ sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[47178]) ).
thf(49708,plain,
( ( in @ ( powerset @ sk4 ) @ sk2 )
| ( ( powerset @ sk2 )
!= sk4 ) ),
inference(simp,[status(thm)],[47269]) ).
thf(29975,plain,
( ( in @ ( powerset @ sk3 ) @ sk2 )
| ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ ( powerset @ sk3 ) @ ( powerset @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29915,15197]) ).
thf(30065,plain,
( ( in @ ( powerset @ sk3 ) @ sk2 )
| ( ( powerset @ sk3 )
!= ( powerset @ sk3 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[29975]) ).
thf(30148,plain,
( ( in @ ( powerset @ sk3 ) @ sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[30065]) ).
thf(32391,plain,
( ( in @ ( powerset @ sk3 ) @ sk2 )
| ( ( powerset @ sk2 )
!= sk3 ) ),
inference(simp,[status(thm)],[30148]) ).
thf(275,plain,
! [C: $i,B: $i,A: $i] :
( ( ( powerset @ A )
!= sk4 )
| ( in @ C @ ( powerset @ B ) )
| ( ( in @ A @ sk2 )
!= ( in @ ( sk1 @ C @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[110,12]) ).
thf(276,plain,
! [A: $i] :
( ( ( powerset @ ( sk1 @ A @ sk2 ) )
!= sk4 )
| ( in @ A @ ( powerset @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[275:[bind(A,$thf( sk1 @ D @ sk2 )),bind(B,$thf( sk2 )),bind(C,$thf( D ))]]) ).
thf(282,plain,
! [A: $i] :
( ( ( powerset @ ( sk1 @ A @ sk2 ) )
!= sk4 )
| ( in @ A @ ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[276]) ).
thf(411,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ A @ sk2 ) )
!= sk4 )
| ( in @ sk3 @ B )
| ( ( in @ A @ ( powerset @ sk2 ) )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[282,29]) ).
thf(412,plain,
( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk2 ) )
!= sk4 )
| ( in @ sk3 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[411:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(4130,plain,
( ( sk4 != sk3 )
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[3795]) ).
thf(4131,plain,
sk4 != sk3,
inference(simp,[status(thm)],[4130]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ( in @ C @ A )
| ( ( in @ C @ B )
!= ( in @ B @ ( powerset @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[19]) ).
thf(41,plain,
! [A: $i] :
( ~ ( in @ ( powerset @ A ) @ ( powerset @ A ) )
| ( in @ ( powerset @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( D )),bind(B,$thf( powerset @ D )),bind(C,$thf( powerset @ D ))]]) ).
thf(44,plain,
! [A: $i] :
( ~ ( in @ ( powerset @ A ) @ ( powerset @ A ) )
| ( in @ ( powerset @ A ) @ A ) ),
inference(simp,[status(thm)],[41]) ).
thf(1753,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ A @ sk2 ) )
!= sk3 )
| ( in @ ( powerset @ B ) @ B )
| ( ( in @ A @ ( powerset @ sk2 ) )
!= ( in @ ( powerset @ B ) @ ( powerset @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[302,44]) ).
thf(1754,plain,
( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk2 ) )
!= sk3 )
| ( in @ ( powerset @ sk2 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1753:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ( ( powerset @ sk2 )
!= sk3 )
| ( in @ B @ ( powerset @ A ) )
| ( ( in @ ( sk1 @ B @ A ) @ A )
!= ( in @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[163,12]) ).
thf(174,plain,
! [B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( ( powerset @ sk2 )
!= sk3 )
| ( ( sk1 @ B @ A )
!= sk3 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[172]) ).
thf(180,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ sk2 ) )
| ( ( powerset @ sk2 )
!= sk3 )
| ( ( sk1 @ A @ sk2 )
!= sk3 ) ),
inference(simp,[status(thm)],[174]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ( ( powerset @ sk2 )
!= sk3 )
| ( in @ B @ ( powerset @ A ) )
| ( ( in @ ( sk1 @ B @ A ) @ A )
!= ( in @ sk4 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[165,12]) ).
thf(259,plain,
! [B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( ( powerset @ sk2 )
!= sk3 )
| ( ( sk1 @ B @ A )
!= sk4 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[256]) ).
thf(264,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ sk2 ) )
| ( ( powerset @ sk2 )
!= sk3 )
| ( ( sk1 @ A @ sk2 )
!= sk4 ) ),
inference(simp,[status(thm)],[259]) ).
thf(1880,plain,
! [A: $i] :
( ( ( powerset @ A )
!= sk4 )
| ( ( in @ A @ sk2 )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[110,1815]) ).
thf(1924,plain,
! [A: $i] :
( ( ( powerset @ A )
!= sk4 )
| ( A
!= ( binunion @ sk3 @ sk4 ) )
| ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1880]) ).
thf(1927,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk4 )
| ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1924]) ).
thf(3748,plain,
( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
!= ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3587,1277]) ).
thf(3783,plain,
( ( ( binunion @ sk4 @ sk4 )
!= ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[3748]) ).
thf(6422,plain,
( ( ( binunion @ sk4 @ sk4 )
!= ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
| ( ( powerset @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[3783]) ).
thf(30042,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk4 ) )
| ( in @ B @ sk2 )
| ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29915,68]) ).
thf(30043,plain,
( ~ ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk4 ) )
| ( in @ ( powerset @ sk3 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[30042:[bind(A,$thf( powerset @ ( powerset @ sk2 ) )),bind(B,$thf( powerset @ sk3 ))]]) ).
thf(47087,plain,
( ( in @ ( powerset @ sk3 ) @ sk2 )
| ( ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk4 ) )
!= ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[47023,30043]) ).
thf(47194,plain,
( ( in @ ( powerset @ sk3 ) @ sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk4 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[47087]) ).
thf(47275,plain,
( ( in @ ( powerset @ sk3 ) @ sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[47194]) ).
thf(401,plain,
! [A: $i] :
( ( ( powerset @ ( sk1 @ A @ sk2 ) )
!= sk4 )
| ( ( in @ A @ ( powerset @ sk2 ) )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[282,13]) ).
thf(402,plain,
( ( powerset @ ( sk1 @ ( binunion @ sk3 @ sk4 ) @ sk2 ) )
!= sk4 ),
inference(pattern_uni,[status(thm)],[401:[bind(A,$thf( binunion @ sk3 @ sk4 ))]]) ).
thf(47113,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ sk2 ) )
| ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ A @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[47023,29675]) ).
thf(47165,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ sk2 ) )
| ( ( powerset @ sk4 )
!= A )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[47113]) ).
thf(47262,plain,
( ( in @ ( powerset @ sk4 ) @ ( powerset @ sk2 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[47165]) ).
thf(54559,plain,
( ( in @ ( powerset @ sk4 ) @ ( powerset @ sk2 ) )
| ( ( powerset @ sk2 )
!= sk4 ) ),
inference(simp,[status(thm)],[47262]) ).
thf(29953,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ A @ ( binunion @ sk4 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29915,3794]) ).
thf(30078,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( powerset @ sk3 )
!= A )
| ( ( binunion @ sk4 @ sk4 )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[29953]) ).
thf(30151,plain,
( ( in @ ( powerset @ sk3 ) @ sk2 )
| ( ( binunion @ sk4 @ sk4 )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[30078]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( ( in @ ( sk1 @ B @ A ) @ B )
!= ( in @ B @ ( powerset @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[8]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( ( sk1 @ B @ A )
!= B )
| ( B
!= ( powerset @ A ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(59,plain,
! [A: $i] :
( ( in @ ( powerset @ A ) @ ( powerset @ A ) )
| ( ( sk1 @ ( powerset @ A ) @ A )
!= ( powerset @ A ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(1438,plain,
! [A: $i] :
( ( ( powerset @ A )
!= sk4 )
| ( ( in @ A @ sk2 )
!= ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[110,1277]) ).
thf(1464,plain,
! [A: $i] :
( ( ( powerset @ A )
!= sk4 )
| ( A
!= ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1438]) ).
thf(1488,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= sk4 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1464]) ).
thf(16507,plain,
! [A: $i] :
( ( in @ ( powerset @ sk3 ) @ sk2 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ sk3 ) @ ( powerset @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,15197]) ).
thf(16643,plain,
! [A: $i] :
( ( in @ ( powerset @ sk3 ) @ sk2 )
| ( A
!= ( powerset @ sk3 ) )
| ( ( powerset @ A )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[16507]) ).
thf(16653,plain,
( ( in @ ( powerset @ sk3 ) @ sk2 )
| ( ( powerset @ ( powerset @ sk3 ) )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[16643]) ).
thf(17020,plain,
( ( in @ ( powerset @ sk3 ) @ sk2 )
| ( ( powerset @ sk3 )
!= sk3 ) ),
inference(simp,[status(thm)],[16653]) ).
thf(30276,plain,
( ( ( powerset @ sk3 )
!= sk3 )
| ( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk3 ) )
!= ( in @ ( powerset @ sk3 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[17020,29966]) ).
thf(30313,plain,
( ( ( powerset @ sk3 )
!= sk3 )
| ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk3 ) )
| ( ( powerset @ sk3 )
!= sk2 ) ),
inference(simp,[status(thm)],[30276]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( ( in @ ( sk1 @ B @ A ) @ B )
!= ( in @ B @ ( powerset @ A ) ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(34197,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ B @ A ) )
!= A )
| ( in @ ( powerset @ sk3 ) @ sk2 )
| ( ( in @ B @ ( powerset @ A ) )
!= ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,30043]) ).
thf(34198,plain,
( ( ( powerset @ ( sk1 @ ( powerset @ ( powerset @ sk2 ) ) @ sk4 ) )
!= sk4 )
| ( in @ ( powerset @ sk3 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[34197:[bind(A,$thf( sk4 )),bind(B,$thf( powerset @ ( powerset @ sk2 ) ))]]) ).
thf(3735,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
!= ( in @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[3587,45]) ).
thf(3766,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( binunion @ sk4 @ sk4 )
!= A )
| ( ( powerset @ sk2 )
!= sk3 ) ),
inference(simp,[status(thm)],[3735]) ).
thf(3796,plain,
( ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
| ( ( powerset @ sk2 )
!= sk3 ) ),
inference(simp,[status(thm)],[3766]) ).
thf(15469,plain,
! [A: $i] :
( ( in @ sk3 @ sk2 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,14847]) ).
thf(15589,plain,
! [A: $i] :
( ( in @ sk3 @ sk2 )
| ( A
!= ( powerset @ sk2 ) )
| ( ( powerset @ A )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[15469]) ).
thf(15630,plain,
( ( in @ sk3 @ sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[15589]) ).
thf(41193,plain,
( ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk4 ) )
| ( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) )
!= ( in @ ( powerset @ sk3 ) @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[40479,13]) ).
thf(41526,plain,
( ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk4 ) )
| ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk3 ) )
| ( ( powerset @ sk2 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[41193]) ).
thf(41555,plain,
( ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk4 ) )
| ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[41526]) ).
thf(25022,plain,
! [A: $i] :
( ( ( powerset @ A )
!= ( binunion @ sk3 @ sk3 ) )
| ( ( in @ A @ sk2 )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[22961,1815]) ).
thf(25114,plain,
! [A: $i] :
( ( ( powerset @ A )
!= ( binunion @ sk3 @ sk3 ) )
| ( A
!= ( binunion @ sk3 @ sk4 ) )
| ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[25022]) ).
thf(25194,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= ( binunion @ sk3 @ sk3 ) )
| ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[25114]) ).
thf(16514,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ B @ A ) )
!= A )
| ( in @ ( powerset @ sk3 ) @ sk2 )
| ( ( in @ B @ ( powerset @ A ) )
!= ( in @ ( powerset @ sk3 ) @ ( powerset @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,15197]) ).
thf(16515,plain,
( ( ( powerset @ ( sk1 @ ( powerset @ sk3 ) @ sk3 ) )
!= sk3 )
| ( in @ ( powerset @ sk3 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[16514:[bind(A,$thf( sk3 )),bind(B,$thf( powerset @ sk3 ))]]) ).
thf(3487,plain,
! [A: $i] :
( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ A ) )
| $false
| ( in @ ( sk1 @ ( binunion @ sk4 @ sk4 ) @ A ) @ sk2 ) ),
inference(prim_subst,[status(thm)],[943:[bind(A,$thf( $false ))]]) ).
thf(3532,plain,
! [A: $i] :
( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ A ) )
| ( in @ ( sk1 @ ( binunion @ sk4 @ sk4 ) @ A ) @ sk2 ) ),
inference(simp,[status(thm)],[3487]) ).
thf(47124,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 )
| ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[47023,1289]) ).
thf(47167,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 )
| ( ( powerset @ sk4 )
!= sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[47124]) ).
thf(47263,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 )
| ( ( powerset @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[47167]) ).
thf(4627,plain,
! [A: $i] :
( ( in @ sk4 @ sk2 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,3951]) ).
thf(4701,plain,
! [A: $i] :
( ( in @ sk4 @ sk2 )
| ( A
!= ( powerset @ sk2 ) )
| ( ( powerset @ A )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[4627]) ).
thf(4716,plain,
( ( in @ sk4 @ sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[4701]) ).
thf(186,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( binunion @ A @ B ) )
| ( in @ C @ A )
| ( in @ C @ B )
| ( D
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,13]) ).
thf(187,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( binunion @ A @ B ) )
| ( in @ C @ A )
| ( in @ C @ B ) ),
inference(pattern_uni,[status(thm)],[186:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ))]]) ).
thf(26924,plain,
( ( ( powerset @ ( sk1 @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ sk2 ) )
!= sk3 )
| ( ( powerset @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[1489]) ).
thf(29968,plain,
( ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) )
!= ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29915,1815]) ).
thf(30115,plain,
( ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk3 ) )
| ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[29968]) ).
thf(29952,plain,
( ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ ( powerset @ sk2 ) ) )
| ( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29915,1426]) ).
thf(30060,plain,
( ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ ( powerset @ sk2 ) ) )
| ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk3 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[29952]) ).
thf(30147,plain,
( ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ ( powerset @ sk2 ) ) )
| ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[30060]) ).
thf(204,plain,
! [E: $o,D: $i,C: $i,B: $i,A: $i] :
( ( in @ sk4 @ ( powerset @ A ) )
| ( in @ D @ B )
| ( in @ D @ C )
| E
| ( ( in @ ( sk1 @ sk4 @ A ) @ sk2 )
!= ( in @ D @ ( binunion @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[71,18]) ).
thf(221,plain,
! [E: $o,D: $i,C: $i,B: $i,A: $i] :
( ( in @ sk4 @ ( powerset @ A ) )
| ( in @ D @ B )
| ( in @ D @ C )
| E
| ( ( sk1 @ sk4 @ A )
!= D )
| ( ( binunion @ B @ C )
!= sk2 ) ),
inference(simp,[status(thm)],[204]) ).
thf(245,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( in @ sk4 @ ( powerset @ A ) )
| ( in @ ( sk1 @ sk4 @ A ) @ B )
| ( in @ ( sk1 @ sk4 @ A ) @ C )
| D
| ( ( binunion @ B @ C )
!= sk2 ) ),
inference(simp,[status(thm)],[221]) ).
thf(308,plain,
! [A: $i] :
( ( in @ sk3 @ ( powerset @ A ) )
| ( ( in @ ( sk1 @ sk3 @ A ) @ sk2 )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[158,13]) ).
thf(318,plain,
! [A: $i] :
( ( in @ sk3 @ ( powerset @ A ) )
| ( ( sk1 @ sk3 @ A )
!= ( binunion @ sk3 @ sk4 ) )
| ( ( powerset @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[308]) ).
thf(38,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ~ ( in @ C @ B )
| ~ ( in @ E @ ( powerset @ D ) )
| ( in @ F @ D )
| ( ( in @ C @ A )
!= ( in @ F @ E ) ) ),
inference(paramod_ordered,[status(thm)],[19,19]) ).
thf(39,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ~ ( in @ C @ B )
| ~ ( in @ A @ ( powerset @ D ) )
| ( in @ C @ D ) ),
inference(pattern_uni,[status(thm)],[38:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( C ))]]) ).
thf(288,plain,
! [A: $i] :
( ( ( powerset @ A )
!= sk3 )
| ( ( in @ A @ sk2 )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[162,13]) ).
thf(297,plain,
! [A: $i] :
( ( ( powerset @ A )
!= sk3 )
| ( A
!= ( binunion @ sk3 @ sk4 ) )
| ( ( powerset @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[288]) ).
thf(303,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 )
| ( ( powerset @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[297]) ).
thf(30236,plain,
! [A: $i] :
( ( ( powerset @ A )
!= ( binunion @ sk4 @ sk4 ) )
| ( ( in @ A @ sk2 )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[7109,29966]) ).
thf(30314,plain,
! [A: $i] :
( ( ( powerset @ A )
!= ( binunion @ sk4 @ sk4 ) )
| ( A
!= ( binunion @ sk3 @ sk4 ) )
| ( ( powerset @ sk3 )
!= sk2 ) ),
inference(simp,[status(thm)],[30236]) ).
thf(30423,plain,
( ( ( binunion @ sk4 @ sk4 )
!= ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
| ( ( powerset @ sk3 )
!= sk2 ) ),
inference(simp,[status(thm)],[30314]) ).
thf(11790,plain,
! [A: $i] :
( ( ( powerset @ ( powerset @ A ) )
!= ( powerset @ sk4 ) )
| ( ( in @ A @ sk2 )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[7492,13]) ).
thf(11838,plain,
! [A: $i] :
( ( ( powerset @ ( powerset @ A ) )
!= ( powerset @ sk4 ) )
| ( A
!= ( binunion @ sk3 @ sk4 ) )
| ( ( powerset @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[11790]) ).
thf(12015,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= ( powerset @ sk4 ) )
| ( ( powerset @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[11838]) ).
thf(18789,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ B @ A ) )
!= A )
| ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
| ( ( in @ B @ ( powerset @ A ) )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,14986]) ).
thf(18790,plain,
( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk3 ) )
!= sk3 )
| ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[18789:[bind(A,$thf( sk3 )),bind(B,$thf( powerset @ sk2 ))]]) ).
thf(55512,plain,
! [C: $o,B: $o,A: $i] :
( B
| ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
| ( C
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1715,1815]) ).
thf(55513,plain,
! [B: $o,A: $i] :
( B
| ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) ) ),
inference(pattern_uni,[status(thm)],[55512:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ))]]) ).
thf(815,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ A @ sk2 ) )
!= sk3 )
| ( in @ sk4 @ B )
| ( ( in @ A @ ( powerset @ sk2 ) )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[302,35]) ).
thf(816,plain,
( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk2 ) )
!= sk3 )
| ( in @ sk4 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[815:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(53234,plain,
! [A: $i] :
( ( in @ ( powerset @ sk4 ) @ sk2 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,47144]) ).
thf(53514,plain,
! [A: $i] :
( ( in @ ( powerset @ sk4 ) @ sk2 )
| ( A
!= ( powerset @ ( powerset @ sk2 ) ) )
| ( ( powerset @ A )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[53234]) ).
thf(53533,plain,
( ( in @ ( powerset @ sk4 ) @ sk2 )
| ( ( powerset @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[53514]) ).
thf(47029,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ A @ ( binunion @ sk3 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[47023,13955]) ).
thf(47201,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( powerset @ sk4 )
!= A )
| ( ( binunion @ sk3 @ sk3 )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[47029]) ).
thf(47278,plain,
( ( in @ ( powerset @ sk4 ) @ sk2 )
| ( ( binunion @ sk3 @ sk3 )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[47201]) ).
thf(192,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( in @ C @ A )
| ( in @ C @ B )
| D
| ( ( in @ sk4 @ ( powerset @ sk2 ) )
!= ( in @ C @ ( binunion @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,18]) ).
thf(217,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( in @ C @ A )
| ( in @ C @ B )
| D
| ( sk4 != C )
| ( ( binunion @ A @ B )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[192]) ).
thf(240,plain,
! [C: $o,B: $i,A: $i] :
( ( in @ sk4 @ A )
| ( in @ sk4 @ B )
| C
| ( ( binunion @ A @ B )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[217]) ).
thf(33904,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ B @ A ) )
!= A )
| ( in @ ( powerset @ sk3 ) @ sk2 )
| ( ( in @ B @ ( powerset @ A ) )
!= ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,30003]) ).
thf(33905,plain,
( ( ( powerset @ ( sk1 @ ( powerset @ ( powerset @ sk2 ) ) @ sk3 ) )
!= sk3 )
| ( in @ ( powerset @ sk3 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[33904:[bind(A,$thf( sk3 )),bind(B,$thf( powerset @ ( powerset @ sk2 ) ))]]) ).
thf(1454,plain,
( ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ sk4 @ ( powerset @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[11,1277]) ).
thf(1460,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk4 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[1454]) ).
thf(42858,plain,
! [A: $i] :
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk4 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ sk3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,40693]) ).
thf(43119,plain,
! [A: $i] :
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk4 )
| ( A != sk2 )
| ( ( powerset @ A )
!= ( powerset @ ( powerset @ sk3 ) ) ) ),
inference(simp,[status(thm)],[42858]) ).
thf(43141,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk4 )
| ( ( powerset @ ( powerset @ sk3 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[43119]) ).
thf(97,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[92,13]) ).
thf(104,plain,
! [A: $i] :
( ( A
!= ( binunion @ sk3 @ sk4 ) )
| ( ( powerset @ A )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(108,plain,
( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= ( powerset @ sk2 ) ),
inference(simp,[status(thm)],[104]) ).
thf(35312,plain,
( ( in @ ( powerset @ sk3 ) @ ( powerset @ sk2 ) )
| ( ( powerset @ sk2 )
!= sk3 ) ),
inference(simp,[status(thm)],[30162]) ).
thf(47036,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ A @ ( binunion @ sk4 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[47023,3794]) ).
thf(47176,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( powerset @ sk4 )
!= A )
| ( ( binunion @ sk4 @ sk4 )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[47036]) ).
thf(47268,plain,
( ( in @ ( powerset @ sk4 ) @ sk2 )
| ( ( binunion @ sk4 @ sk4 )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[47176]) ).
thf(4645,plain,
! [A: $i] :
( ( ( powerset @ A )
!= sk3 )
| ( in @ sk4 @ sk2 )
| ( ( in @ A @ sk2 )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[162,3951]) ).
thf(4668,plain,
! [A: $i] :
( ( in @ sk4 @ sk2 )
| ( ( powerset @ A )
!= sk3 )
| ( A
!= ( powerset @ sk2 ) )
| ( ( powerset @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[4645]) ).
thf(4720,plain,
( ( in @ sk4 @ sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk3 )
| ( ( powerset @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[4668]) ).
thf(290,plain,
! [E: $o,D: $i,C: $i,B: $i,A: $i] :
( ( ( powerset @ A )
!= sk3 )
| ( in @ D @ B )
| ( in @ D @ C )
| E
| ( ( in @ A @ sk2 )
!= ( in @ D @ ( binunion @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[162,18]) ).
thf(300,plain,
! [E: $o,D: $i,C: $i,B: $i,A: $i] :
( ( in @ D @ B )
| ( in @ D @ C )
| E
| ( ( powerset @ A )
!= sk3 )
| ( A != D )
| ( ( binunion @ B @ C )
!= sk2 ) ),
inference(simp,[status(thm)],[290]) ).
thf(306,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( in @ C @ A )
| ( in @ C @ B )
| D
| ( ( powerset @ C )
!= sk3 )
| ( ( binunion @ A @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[300]) ).
thf(135,plain,
! [A: $i] :
( ( in @ sk4 @ ( powerset @ A ) )
| ( ( sk1 @ sk4 @ A )
!= sk4 )
| ( ( powerset @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[132]) ).
thf(30016,plain,
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 )
| ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29915,7526]) ).
thf(30098,plain,
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 )
| ( ( powerset @ sk3 )
!= sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[30016]) ).
thf(30159,plain,
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 )
| ( ( powerset @ sk3 )
!= sk2 ) ),
inference(simp,[status(thm)],[30098]) ).
thf(8921,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ B @ A ) )
!= A )
| ( in @ ( powerset @ sk4 ) @ sk2 )
| ( ( in @ B @ ( powerset @ A ) )
!= ( in @ ( powerset @ sk4 ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,4020]) ).
thf(8922,plain,
( ( ( powerset @ ( sk1 @ ( powerset @ sk4 ) @ sk4 ) )
!= sk4 )
| ( in @ ( powerset @ sk4 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8921:[bind(A,$thf( sk4 )),bind(B,$thf( powerset @ sk4 ))]]) ).
thf(182,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( ( powerset @ sk2 )
!= sk4 )
| ( in @ C @ A )
| ( in @ C @ B )
| D
| ( ( in @ sk3 @ sk2 )
!= ( in @ C @ ( binunion @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[69,18]) ).
thf(218,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( in @ C @ A )
| ( in @ C @ B )
| D
| ( ( powerset @ sk2 )
!= sk4 )
| ( sk3 != C )
| ( ( binunion @ A @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[182]) ).
thf(241,plain,
! [C: $o,B: $i,A: $i] :
( ( in @ sk3 @ A )
| ( in @ sk3 @ B )
| C
| ( ( powerset @ sk2 )
!= sk4 )
| ( ( binunion @ A @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[218]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ( ( powerset @ sk2 )
!= sk4 )
| ~ ( in @ C @ B )
| ( in @ C @ A )
| ( ( in @ sk3 @ sk2 )
!= ( in @ B @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[69,19]) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ C @ A )
| ( ( powerset @ sk2 )
!= sk4 )
| ~ ( in @ C @ B )
| ( sk3 != B )
| ( ( powerset @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[73]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ( in @ B @ A )
| ( ( powerset @ sk2 )
!= sk4 )
| ~ ( in @ B @ sk3 )
| ( ( powerset @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[78]) ).
thf(27578,plain,
( ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ ( powerset @ sk2 ) ) )
| ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[13154]) ).
thf(1990,plain,
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 )
| ( ( powerset @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[1411]) ).
thf(13345,plain,
! [A: $i] :
( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ A ) )
| $false
| ( in @ ( sk1 @ ( binunion @ sk3 @ sk3 ) @ A ) @ sk2 ) ),
inference(prim_subst,[status(thm)],[946:[bind(A,$thf( $false ))]]) ).
thf(13431,plain,
! [A: $i] :
( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ A ) )
| ( in @ ( sk1 @ ( binunion @ sk3 @ sk3 ) @ A ) @ sk2 ) ),
inference(simp,[status(thm)],[13345]) ).
thf(22750,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
!= ( in @ A @ ( binunion @ sk3 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[13531,13955]) ).
thf(22877,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( binunion @ sk3 @ sk3 )
!= A )
| ( ( binunion @ sk3 @ sk3 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[22750]) ).
thf(22964,plain,
( ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
| ( ( binunion @ sk3 @ sk3 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[22877]) ).
thf(44369,plain,
! [B: $i,A: $i] :
( ( ( powerset @ A )
!= sk3 )
| ~ ( in @ sk2 @ ( powerset @ B ) )
| ( ( in @ A @ B )
!= ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[293,1277]) ).
thf(44370,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= sk3 )
| ~ ( in @ sk2 @ ( powerset @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[44369:[bind(A,$thf( powerset @ ( binunion @ sk3 @ sk4 ) )),bind(B,$thf( powerset @ ( powerset @ sk2 ) ))]]) ).
thf(30222,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ B @ A ) )
!= A )
| ( ( in @ B @ ( powerset @ A ) )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,29966]) ).
thf(30223,plain,
( ( powerset @ ( sk1 @ ( binunion @ sk3 @ sk4 ) @ sk3 ) )
!= sk3 ),
inference(pattern_uni,[status(thm)],[30222:[bind(A,$thf( sk3 )),bind(B,$thf( binunion @ sk3 @ sk4 ))]]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( ( powerset @ sk2 )
!= sk4 )
| ( in @ B @ ( powerset @ A ) )
| ( ( in @ ( sk1 @ B @ A ) @ A )
!= ( in @ sk4 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[70,12]) ).
thf(119,plain,
! [B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( ( powerset @ sk2 )
!= sk4 )
| ( ( sk1 @ B @ A )
!= sk4 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[113]) ).
thf(123,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ sk2 ) )
| ( ( powerset @ sk2 )
!= sk4 )
| ( ( sk1 @ A @ sk2 )
!= sk4 ) ),
inference(simp,[status(thm)],[119]) ).
thf(1437,plain,
( ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ sk3 @ ( powerset @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[14,1277]) ).
thf(1472,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[1437]) ).
thf(1769,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ A @ sk2 ) )
!= sk4 )
| ( in @ ( powerset @ B ) @ B )
| ( ( in @ A @ ( powerset @ sk2 ) )
!= ( in @ ( powerset @ B ) @ ( powerset @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[282,44]) ).
thf(1770,plain,
( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk2 ) )
!= sk4 )
| ( in @ ( powerset @ sk2 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1769:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(13816,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
!= ( in @ A @ ( binunion @ sk4 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[13531,3794]) ).
thf(13940,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( binunion @ sk3 @ sk3 )
!= A )
| ( ( binunion @ sk4 @ sk4 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[13816]) ).
thf(13967,plain,
( ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
| ( ( binunion @ sk4 @ sk4 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[13940]) ).
thf(29994,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[29915,45]) ).
thf(30091,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( powerset @ sk3 )
!= A )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[29994]) ).
thf(30156,plain,
( ( in @ ( powerset @ sk3 ) @ sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[30091]) ).
thf(44125,plain,
( ( ( sk1 @ sk2 @ ( powerset @ sk3 ) )
!= sk3 )
| ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk4 ) ),
inference(simp,[status(thm)],[42873]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ( ( powerset @ sk2 )
!= sk4 )
| ( in @ B @ ( powerset @ A ) )
| ( ( in @ ( sk1 @ B @ A ) @ A )
!= ( in @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[69,12]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( ( powerset @ sk2 )
!= sk4 )
| ( ( sk1 @ B @ A )
!= sk3 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[82]) ).
thf(95,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ sk2 ) )
| ( ( powerset @ sk2 )
!= sk4 )
| ( ( sk1 @ A @ sk2 )
!= sk3 ) ),
inference(simp,[status(thm)],[90]) ).
thf(47070,plain,
( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk3 ) )
!= ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[47023,29966]) ).
thf(47240,plain,
( ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk4 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[47070]) ).
thf(1453,plain,
! [A: $i] :
( ( ( powerset @ ( sk1 @ A @ sk2 ) )
!= sk4 )
| ( ( in @ A @ ( powerset @ sk2 ) )
!= ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[282,1277]) ).
thf(1478,plain,
! [A: $i] :
( ( ( powerset @ ( sk1 @ A @ sk2 ) )
!= sk4 )
| ( A
!= ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[1453]) ).
thf(1484,plain,
( ( ( powerset @ ( sk1 @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ sk2 ) )
!= sk4 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[1478]) ).
thf(252,plain,
! [C: $i,B: $i,A: $i] :
( ( ( powerset @ sk2 )
!= sk3 )
| ~ ( in @ C @ B )
| ( in @ C @ A )
| ( ( in @ sk4 @ sk2 )
!= ( in @ B @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[165,19]) ).
thf(258,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ C @ A )
| ( ( powerset @ sk2 )
!= sk3 )
| ~ ( in @ C @ B )
| ( sk4 != B )
| ( ( powerset @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[252]) ).
thf(263,plain,
! [B: $i,A: $i] :
( ( in @ B @ A )
| ( ( powerset @ sk2 )
!= sk3 )
| ~ ( in @ B @ sk4 )
| ( ( powerset @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[258]) ).
thf(5303,plain,
! [A: $i] :
( ( in @ ( powerset @ sk4 ) @ sk2 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ sk4 ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,4020]) ).
thf(5377,plain,
! [A: $i] :
( ( in @ ( powerset @ sk4 ) @ sk2 )
| ( A
!= ( powerset @ sk4 ) )
| ( ( powerset @ A )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[5303]) ).
thf(5388,plain,
( ( in @ ( powerset @ sk4 ) @ sk2 )
| ( ( powerset @ ( powerset @ sk4 ) )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[5377]) ).
thf(1622,plain,
! [C: $i,B: $i,A: $o] :
( ( in @ ( binunion @ B @ B ) @ ( powerset @ B ) )
| ( in @ C @ sk2 )
| ( A
!= ( in @ C @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[948,42]) ).
thf(1623,plain,
! [B: $i,A: $i] :
( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
| ( in @ B @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1622:[bind(A,$thf( in @ D @ sk4 )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(1716,plain,
! [B: $i,A: $i] :
( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
| ( in @ B @ sk2 ) ),
inference(simp,[status(thm)],[1623]) ).
thf(29959,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[29915,42]) ).
thf(30119,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( powerset @ sk3 )
!= A )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk4 ) ),
inference(simp,[status(thm)],[29959]) ).
thf(30171,plain,
( ( in @ ( powerset @ sk3 ) @ sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk4 ) ),
inference(simp,[status(thm)],[30119]) ).
thf(30273,plain,
( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk3 ) )
!= ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29915,29966]) ).
thf(30402,plain,
( ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk3 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[30273]) ).
thf(6968,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
!= ( in @ A @ ( binunion @ sk4 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3587,3794]) ).
thf(7033,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( binunion @ sk4 @ sk4 )
!= A )
| ( ( binunion @ sk4 @ sk4 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[6968]) ).
thf(7105,plain,
( ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
| ( ( binunion @ sk4 @ sk4 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[7033]) ).
thf(53575,plain,
( ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk4 ) )
| ( ( powerset @ sk2 )
!= sk3 ) ),
inference(simp,[status(thm)],[47240]) ).
thf(47112,plain,
( ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[47023,1277]) ).
thf(47184,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= ( powerset @ sk4 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[47112]) ).
thf(47270,plain,
( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= ( powerset @ sk4 ) ),
inference(simp,[status(thm)],[47184]) ).
thf(27579,plain,
( ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk2 ) )
| ( ( binunion @ sk3 @ sk4 )
!= ( binunion @ sk3 @ sk4 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) ) ),
inference(eqfactor_ordered,[status(thm)],[27578]) ).
thf(27581,plain,
( ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk2 ) )
| ( ( powerset @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[27579]) ).
thf(45736,plain,
! [A: $i] :
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= sk3 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ ( powerset @ sk2 ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,44370]) ).
thf(45869,plain,
! [A: $i] :
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= sk3 )
| ( A != sk2 )
| ( ( powerset @ A )
!= ( powerset @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(simp,[status(thm)],[45736]) ).
thf(46012,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= sk3 )
| ( ( powerset @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[45869]) ).
thf(47172,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk4 )
| ( ( powerset @ sk4 )
!= sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[47103]) ).
thf(47265,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk4 )
| ( ( powerset @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[47172]) ).
thf(36,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ~ ( in @ C @ B )
| ~ ( in @ F @ E )
| ( in @ F @ D )
| ( ( in @ C @ A )
!= ( in @ E @ ( powerset @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,19]) ).
thf(37,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ ( powerset @ D ) ) )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ( in @ C @ D ) ),
inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( powerset @ G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( C ))]]) ).
thf(43,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ ( powerset @ D ) ) )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ( in @ C @ D ) ),
inference(simp,[status(thm)],[37]) ).
thf(27580,plain,
( ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk2 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[27579]) ).
thf(52053,plain,
! [A: $i] :
( ( in @ ( powerset @ sk4 ) @ sk2 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,47093]) ).
thf(52220,plain,
! [A: $i] :
( ( in @ ( powerset @ sk4 ) @ sk2 )
| ( A
!= ( powerset @ ( powerset @ sk2 ) ) )
| ( ( powerset @ A )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[52053]) ).
thf(52383,plain,
( ( in @ ( powerset @ sk4 ) @ sk2 )
| ( ( powerset @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[52220]) ).
thf(41161,plain,
! [A: $i] :
( ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk4 ) )
| ( in @ A @ sk2 )
| ( ( in @ ( powerset @ sk3 ) @ ( powerset @ sk2 ) )
!= ( in @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[40479,42]) ).
thf(41500,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( powerset @ sk2 )
!= sk4 )
| ( ( powerset @ sk3 )
!= A )
| ( ( powerset @ sk2 )
!= sk4 ) ),
inference(simp,[status(thm)],[41161]) ).
thf(41546,plain,
( ( in @ ( powerset @ sk3 ) @ sk2 )
| ( ( powerset @ sk2 )
!= sk4 ) ),
inference(simp,[status(thm)],[41500]) ).
thf(1272,plain,
! [A: $i] :
( ( ( powerset @ sk2 )
!= sk4 )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
| ( ( in @ sk3 @ sk2 )
!= ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[69,46]) ).
thf(1375,plain,
! [A: $i] :
( ( ( powerset @ sk2 )
!= sk4 )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
| ( sk3 != A )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1272]) ).
thf(1421,plain,
( ( ( powerset @ sk2 )
!= sk4 )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1375]) ).
thf(6947,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ sk3 @ ( powerset @ sk2 ) )
!= ( in @ A @ ( binunion @ sk4 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,3794]) ).
thf(7015,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( sk3 != A )
| ( ( binunion @ sk4 @ sk4 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[6947]) ).
thf(7089,plain,
( ( in @ sk3 @ sk2 )
| ( ( binunion @ sk4 @ sk4 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[7015]) ).
thf(44752,plain,
! [A: $i] :
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ sk3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,44244]) ).
thf(44999,plain,
! [A: $i] :
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 )
| ( A != sk2 )
| ( ( powerset @ A )
!= ( powerset @ ( powerset @ sk3 ) ) ) ),
inference(simp,[status(thm)],[44752]) ).
thf(45047,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk3 )
| ( ( powerset @ ( powerset @ sk3 ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[44999]) ).
thf(6952,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
| ( in @ C @ sk2 )
| ( ( in @ sk4 @ B )
!= ( in @ C @ ( binunion @ sk4 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1736,3794]) ).
thf(6953,plain,
! [A: $i] :
( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
| ( in @ sk4 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[6952:[bind(A,$thf( A )),bind(B,$thf( binunion @ sk4 @ sk4 )),bind(C,$thf( sk4 ))]]) ).
thf(47101,plain,
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 )
| ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[47023,8198]) ).
thf(47209,plain,
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 )
| ( ( powerset @ sk4 )
!= sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[47101]) ).
thf(47284,plain,
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 )
| ( ( powerset @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[47209]) ).
thf(13837,plain,
( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) )
!= ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[13531,13]) ).
thf(13945,plain,
( ( ( binunion @ sk3 @ sk4 )
!= ( binunion @ sk3 @ sk3 ) )
| ( ( powerset @ sk2 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[13837]) ).
thf(13969,plain,
( ( binunion @ sk3 @ sk4 )
!= ( binunion @ sk3 @ sk3 ) ),
inference(simp,[status(thm)],[13945]) ).
thf(2407,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
| ( in @ D @ ( powerset @ C ) )
| ( ( in @ B @ sk2 )
!= ( in @ ( sk1 @ D @ C ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1716,12]) ).
thf(2408,plain,
! [B: $i,A: $i] :
( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
| ( in @ B @ ( powerset @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[2407:[bind(A,$thf( A )),bind(B,$thf( sk1 @ E @ sk2 )),bind(C,$thf( sk2 )),bind(D,$thf( E ))]]) ).
thf(2534,plain,
! [B: $i,A: $i] :
( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
| ( in @ B @ ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[2408]) ).
thf(32009,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
| ( in @ D @ ( powerset @ C ) )
| ( ( in @ B @ ( powerset @ sk2 ) )
!= ( in @ ( sk1 @ D @ C ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2534,12]) ).
thf(32010,plain,
! [B: $i,A: $i] :
( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
| ( in @ B @ ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[32009:[bind(A,$thf( A )),bind(B,$thf( sk1 @ E @ ( powerset @ sk2 ) )),bind(C,$thf( powerset @ sk2 )),bind(D,$thf( E ))]]) ).
thf(32296,plain,
! [B: $i,A: $i] :
( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
| ( in @ B @ ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[32010]) ).
thf(319,plain,
! [A: $i] :
( ( in @ sk3 @ ( powerset @ A ) )
| ( ( in @ ( sk1 @ sk3 @ A ) @ sk2 )
!= ( in @ sk3 @ ( powerset @ A ) ) ) ),
inference(simp,[status(thm)],[317]) ).
thf(343,plain,
! [A: $i] :
( ( in @ sk3 @ A )
| ( ( in @ ( powerset @ sk2 ) @ ( powerset @ A ) )
!= ( in @ sk3 @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,29]) ).
thf(351,plain,
! [A: $i] :
( ( in @ sk3 @ A )
| ( ( powerset @ sk2 )
!= sk3 )
| ( ( powerset @ A )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[343]) ).
thf(18780,plain,
! [A: $i] :
( ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,14986]) ).
thf(19012,plain,
! [A: $i] :
( ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
| ( A
!= ( powerset @ sk2 ) )
| ( ( powerset @ A )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[18780]) ).
thf(19087,plain,
( ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[19012]) ).
thf(41146,plain,
( ( in @ ( powerset @ sk3 ) @ ( powerset @ sk2 ) )
| ( ( powerset @ sk2 )
!= sk4 ) ),
inference(simp,[status(thm)],[40479]) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ( ( powerset @ sk2 )
!= sk4 )
| ~ ( in @ B @ ( powerset @ A ) )
| ( in @ C @ A )
| ( ( in @ sk3 @ sk2 )
!= ( in @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[69,19]) ).
thf(75,plain,
! [A: $i] :
( ( ( powerset @ sk2 )
!= sk4 )
| ~ ( in @ sk2 @ ( powerset @ A ) )
| ( in @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[74:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( ( in @ ( sk1 @ B @ A ) @ B )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,13]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( ( sk1 @ B @ A )
!= ( binunion @ sk3 @ sk4 ) )
| ( B
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(58,plain,
! [A: $i] :
( ( in @ ( powerset @ sk2 ) @ ( powerset @ A ) )
| ( ( sk1 @ ( powerset @ sk2 ) @ A )
!= ( binunion @ sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[53]) ).
thf(208,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( binunion @ A @ B ) )
| ( in @ C @ A )
| ( in @ C @ B )
| ( D
!= ( in @ C @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[18]) ).
thf(222,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( binunion @ C @ A ) )
| ( in @ B @ C )
| ( in @ B @ A ) ),
inference(pattern_uni,[status(thm)],[208:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( in @ E @ F ))]]) ).
thf(246,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( binunion @ C @ A ) )
| ( in @ B @ C )
| ( in @ B @ A ) ),
inference(simp,[status(thm)],[222]) ).
thf(29967,plain,
! [A: $i] :
( ~ ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) )
| ( ( in @ ( binunion @ sk3 @ sk4 ) @ A )
!= ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29915,46]) ).
thf(30131,plain,
! [A: $i] :
( ~ ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) )
| ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk3 ) )
| ( A
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[29967]) ).
thf(30173,plain,
( ~ ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ ( powerset @ sk2 ) ) )
| ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[30131]) ).
thf(39607,plain,
! [A: $i] :
( ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk3 ) )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,30173]) ).
thf(39781,plain,
! [A: $i] :
( ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk3 ) )
| ( A
!= ( powerset @ ( powerset @ sk2 ) ) )
| ( ( powerset @ A )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[39607]) ).
thf(39874,plain,
( ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk3 ) )
| ( ( powerset @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[39781]) ).
thf(47357,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ B @ A ) )
!= A )
| ( ( in @ B @ ( powerset @ A ) )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,47049]) ).
thf(47358,plain,
( ( powerset @ ( sk1 @ ( binunion @ sk3 @ sk4 ) @ sk4 ) )
!= sk4 ),
inference(pattern_uni,[status(thm)],[47357:[bind(A,$thf( sk4 )),bind(B,$thf( binunion @ sk3 @ sk4 ))]]) ).
thf(271,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( powerset @ A )
!= sk4 )
| ~ ( in @ D @ C )
| ( in @ D @ B )
| ( ( in @ A @ sk2 )
!= ( in @ C @ ( powerset @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[110,19]) ).
thf(281,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( in @ D @ B )
| ( ( powerset @ A )
!= sk4 )
| ~ ( in @ D @ C )
| ( A != C )
| ( ( powerset @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[271]) ).
thf(287,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ C @ A )
| ( ( powerset @ B )
!= sk4 )
| ~ ( in @ C @ B )
| ( ( powerset @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[281]) ).
thf(34183,plain,
! [A: $i] :
( ( in @ ( powerset @ sk3 ) @ sk2 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,30043]) ).
thf(34377,plain,
! [A: $i] :
( ( in @ ( powerset @ sk3 ) @ sk2 )
| ( A
!= ( powerset @ ( powerset @ sk2 ) ) )
| ( ( powerset @ A )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[34183]) ).
thf(34424,plain,
( ( in @ ( powerset @ sk3 ) @ sk2 )
| ( ( powerset @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[34377]) ).
thf(54613,plain,
( ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk4 ) )
| ( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) )
!= ( in @ ( powerset @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[47262,13]) ).
thf(54824,plain,
( ( ( powerset @ sk2 )
!= sk4 )
| ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk4 ) )
| ( ( powerset @ sk2 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[54613]) ).
thf(55013,plain,
( ( ( powerset @ sk2 )
!= sk4 )
| ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[54824]) ).
thf(7551,plain,
! [C: $i,B: $i,A: $o] :
( ( in @ ( binunion @ B @ B ) @ ( powerset @ B ) )
| ( in @ sk3 @ ( powerset @ C ) )
| ( A
!= ( in @ sk2 @ ( powerset @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[948,6122]) ).
thf(7552,plain,
! [B: $i,A: $i] :
( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
| ( in @ sk3 @ ( powerset @ B ) ) ),
inference(pattern_uni,[status(thm)],[7551:[bind(A,$thf( in @ sk2 @ ( powerset @ F ) )),bind(B,$thf( B )),bind(C,$thf( F ))]]) ).
thf(7744,plain,
! [B: $i,A: $i] :
( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
| ( in @ sk3 @ ( powerset @ B ) ) ),
inference(simp,[status(thm)],[7552]) ).
thf(8225,plain,
! [C: $i,B: $i,A: $o] :
( ( in @ ( binunion @ B @ B ) @ ( powerset @ B ) )
| ( in @ sk4 @ ( powerset @ C ) )
| ( A
!= ( in @ sk2 @ ( powerset @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[948,6139]) ).
thf(8226,plain,
! [B: $i,A: $i] :
( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
| ( in @ sk4 @ ( powerset @ B ) ) ),
inference(pattern_uni,[status(thm)],[8225:[bind(A,$thf( in @ sk2 @ ( powerset @ F ) )),bind(B,$thf( B )),bind(C,$thf( F ))]]) ).
thf(8412,plain,
! [B: $i,A: $i] :
( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
| ( in @ sk4 @ ( powerset @ B ) ) ),
inference(simp,[status(thm)],[8226]) ).
thf(404,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ A @ sk2 ) )
!= sk4 )
| ( in @ sk4 @ B )
| ( ( in @ A @ ( powerset @ sk2 ) )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[282,35]) ).
thf(405,plain,
( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk2 ) )
!= sk4 )
| ( in @ sk4 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[404:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(4517,plain,
! [A: $i] :
( ( in @ sk3 @ sk2 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,3847]) ).
thf(4565,plain,
! [A: $i] :
( ( in @ sk3 @ sk2 )
| ( A
!= ( powerset @ sk2 ) )
| ( ( powerset @ A )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[4517]) ).
thf(4597,plain,
( ( in @ sk3 @ sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[4565]) ).
thf(33051,plain,
( ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk3 ) )
| ( ( powerset @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[30099]) ).
thf(4620,plain,
! [A: $i] :
( ( ( powerset @ A )
!= sk4 )
| ( in @ sk4 @ sk2 )
| ( ( in @ A @ sk2 )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[110,3951]) ).
thf(4685,plain,
! [A: $i] :
( ( in @ sk4 @ sk2 )
| ( ( powerset @ A )
!= sk4 )
| ( A
!= ( powerset @ sk2 ) )
| ( ( powerset @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[4620]) ).
thf(4706,plain,
( ( in @ sk4 @ sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk4 )
| ( ( powerset @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[4685]) ).
thf(8885,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ B @ A ) )
!= A )
| ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
| ( ( in @ B @ ( powerset @ A ) )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,3884]) ).
thf(8886,plain,
( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk4 ) )
!= sk4 )
| ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8885:[bind(A,$thf( sk4 )),bind(B,$thf( powerset @ sk2 ))]]) ).
thf(30019,plain,
( ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29915,1277]) ).
thf(30107,plain,
( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= ( powerset @ sk3 ) )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[30019]) ).
thf(30165,plain,
( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= ( powerset @ sk3 ) ),
inference(simp,[status(thm)],[30107]) ).
thf(291,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( powerset @ A )
!= sk3 )
| ~ ( in @ D @ C )
| ( in @ D @ B )
| ( ( in @ A @ sk2 )
!= ( in @ C @ ( powerset @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[162,19]) ).
thf(299,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( in @ D @ B )
| ( ( powerset @ A )
!= sk3 )
| ~ ( in @ D @ C )
| ( A != C )
| ( ( powerset @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[291]) ).
thf(305,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ C @ A )
| ( ( powerset @ B )
!= sk3 )
| ~ ( in @ C @ B )
| ( ( powerset @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[299]) ).
thf(5404,plain,
( ( in @ ( powerset @ sk4 ) @ sk2 )
| ( ( powerset @ sk4 )
!= sk4 ) ),
inference(simp,[status(thm)],[5388]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( ( in @ ( sk1 @ B @ A ) @ A )
!= ( in @ sk4 @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,12]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( ( sk1 @ B @ A )
!= sk4 )
| ( A
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[84]) ).
thf(94,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) )
| ( ( sk1 @ A @ ( powerset @ sk2 ) )
!= sk4 ) ),
inference(simp,[status(thm)],[89]) ).
thf(270,plain,
! [E: $o,D: $i,C: $i,B: $i,A: $i] :
( ( ( powerset @ A )
!= sk4 )
| ( in @ D @ B )
| ( in @ D @ C )
| E
| ( ( in @ A @ sk2 )
!= ( in @ D @ ( binunion @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[110,18]) ).
thf(277,plain,
! [E: $o,D: $i,C: $i,B: $i,A: $i] :
( ( in @ D @ B )
| ( in @ D @ C )
| E
| ( ( powerset @ A )
!= sk4 )
| ( A != D )
| ( ( binunion @ B @ C )
!= sk2 ) ),
inference(simp,[status(thm)],[270]) ).
thf(283,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( in @ C @ A )
| ( in @ C @ B )
| D
| ( ( powerset @ C )
!= sk4 )
| ( ( binunion @ A @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[277]) ).
thf(40816,plain,
! [B: $i,A: $i] :
( ( ( powerset @ A )
!= sk4 )
| ~ ( in @ sk2 @ ( powerset @ B ) )
| ( ( in @ A @ B )
!= ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[273,1277]) ).
thf(40817,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= sk4 )
| ~ ( in @ sk2 @ ( powerset @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[40816:[bind(A,$thf( powerset @ ( binunion @ sk3 @ sk4 ) )),bind(B,$thf( powerset @ ( powerset @ sk2 ) ))]]) ).
thf(310,plain,
! [E: $o,D: $i,C: $i,B: $i,A: $i] :
( ( in @ sk3 @ ( powerset @ A ) )
| ( in @ D @ B )
| ( in @ D @ C )
| E
| ( ( in @ ( sk1 @ sk3 @ A ) @ sk2 )
!= ( in @ D @ ( binunion @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[158,18]) ).
thf(322,plain,
! [E: $o,D: $i,C: $i,B: $i,A: $i] :
( ( in @ sk3 @ ( powerset @ A ) )
| ( in @ D @ B )
| ( in @ D @ C )
| E
| ( ( sk1 @ sk3 @ A )
!= D )
| ( ( binunion @ B @ C )
!= sk2 ) ),
inference(simp,[status(thm)],[310]) ).
thf(326,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( in @ sk3 @ ( powerset @ A ) )
| ( in @ ( sk1 @ sk3 @ A ) @ B )
| ( in @ ( sk1 @ sk3 @ A ) @ C )
| D
| ( ( binunion @ B @ C )
!= sk2 ) ),
inference(simp,[status(thm)],[322]) ).
thf(101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( powerset @ B ) )
| ( in @ D @ B )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[92,19]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( powerset @ B ) @ ( powerset @ A ) )
| ( in @ B @ A ) ),
inference(pattern_uni,[status(thm)],[101:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( powerset @ E )),bind(D,$thf( E ))]]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( powerset @ B ) @ ( powerset @ A ) )
| ( in @ B @ A ) ),
inference(simp,[status(thm)],[102]) ).
thf(201,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( ( powerset @ sk2 )
!= sk3 )
| ( in @ C @ A )
| ( in @ C @ B )
| D
| ( ( in @ sk3 @ sk2 )
!= ( in @ C @ ( binunion @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[163,18]) ).
thf(216,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( in @ C @ A )
| ( in @ C @ B )
| D
| ( ( powerset @ sk2 )
!= sk3 )
| ( sk3 != C )
| ( ( binunion @ A @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[201]) ).
thf(239,plain,
! [C: $o,B: $i,A: $i] :
( ( in @ sk3 @ A )
| ( in @ sk3 @ B )
| C
| ( ( powerset @ sk2 )
!= sk3 )
| ( ( binunion @ A @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[216]) ).
thf(183,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( in @ C @ A )
| ( in @ C @ B )
| D
| ( ( in @ sk3 @ ( powerset @ sk2 ) )
!= ( in @ C @ ( binunion @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,18]) ).
thf(219,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( in @ C @ A )
| ( in @ C @ B )
| D
| ( sk3 != C )
| ( ( binunion @ A @ B )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[183]) ).
thf(242,plain,
! [C: $o,B: $i,A: $i] :
( ( in @ sk3 @ A )
| ( in @ sk3 @ B )
| C
| ( ( binunion @ A @ B )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[219]) ).
thf(15661,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ B @ A ) )
!= A )
| ( in @ sk4 @ sk2 )
| ( ( in @ B @ ( powerset @ A ) )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,15073]) ).
thf(15662,plain,
( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk3 ) )
!= sk3 )
| ( in @ sk4 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[15661:[bind(A,$thf( sk3 )),bind(B,$thf( powerset @ sk2 ))]]) ).
thf(8888,plain,
! [B: $i,A: $i] :
( ( ( powerset @ ( sk1 @ B @ A ) )
!= A )
| ( ( in @ B @ ( powerset @ A ) )
!= ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,13]) ).
thf(8889,plain,
( ( powerset @ ( sk1 @ ( binunion @ sk3 @ sk4 ) @ sk2 ) )
!= sk2 ),
inference(pattern_uni,[status(thm)],[8888:[bind(A,$thf( sk2 )),bind(B,$thf( binunion @ sk3 @ sk4 ))]]) ).
thf(22704,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ sk3 @ ( powerset @ sk2 ) )
!= ( in @ A @ ( binunion @ sk3 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,13955]) ).
thf(22825,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( sk3 != A )
| ( ( binunion @ sk3 @ sk3 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[22704]) ).
thf(22918,plain,
( ( in @ sk3 @ sk2 )
| ( ( binunion @ sk3 @ sk3 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[22825]) ).
thf(13161,plain,
( ( ( powerset @ ( sk1 @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ sk2 ) )
!= sk4 )
| ( ( powerset @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[1484]) ).
thf(1295,plain,
! [A: $i] :
( ( ( powerset @ sk2 )
!= sk3 )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
| ( ( in @ sk3 @ sk2 )
!= ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[163,46]) ).
thf(1353,plain,
! [A: $i] :
( ( ( powerset @ sk2 )
!= sk3 )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
| ( sk3 != A )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1295]) ).
thf(1399,plain,
( ( ( powerset @ sk2 )
!= sk3 )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1353]) ).
thf(6424,plain,
( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ sk4 @ sk4 ) )
| ( ( powerset @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[3784]) ).
thf(9992,plain,
( ( ( sk1 @ sk2 @ ( powerset @ sk2 ) )
!= sk2 )
| ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
!= sk4 ) ),
inference(simp,[status(thm)],[8892]) ).
thf(253,plain,
! [C: $i,B: $i,A: $i] :
( ( ( powerset @ sk2 )
!= sk3 )
| ~ ( in @ B @ ( powerset @ A ) )
| ( in @ C @ A )
| ( ( in @ sk4 @ sk2 )
!= ( in @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[165,19]) ).
thf(254,plain,
! [A: $i] :
( ( ( powerset @ sk2 )
!= sk3 )
| ~ ( in @ sk2 @ ( powerset @ A ) )
| ( in @ sk4 @ A ) ),
inference(pattern_uni,[status(thm)],[253:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk4 ))]]) ).
thf(35358,plain,
( ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk3 ) )
| ( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) )
!= ( in @ ( powerset @ sk3 ) @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[30162,13]) ).
thf(35511,plain,
( ( ( powerset @ sk2 )
!= sk3 )
| ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk3 ) )
| ( ( powerset @ sk2 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[35358]) ).
thf(35722,plain,
( ( ( powerset @ sk2 )
!= sk3 )
| ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[35511]) ).
thf(41527,plain,
( ( ( powerset @ sk2 )
!= sk4 )
| ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk3 ) )
| ( ( powerset @ sk2 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[41193]) ).
thf(41556,plain,
( ( ( powerset @ sk2 )
!= sk4 )
| ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[41527]) ).
thf(13839,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
!= ( in @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[13531,45]) ).
thf(13923,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( binunion @ sk3 @ sk3 )
!= A )
| ( ( powerset @ sk2 )
!= sk3 ) ),
inference(simp,[status(thm)],[13839]) ).
thf(13962,plain,
( ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
| ( ( powerset @ sk2 )
!= sk3 ) ),
inference(simp,[status(thm)],[13923]) ).
thf(1307,plain,
! [A: $i] :
( ( ( powerset @ sk2 )
!= sk3 )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
| ( ( in @ sk4 @ sk2 )
!= ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[165,46]) ).
thf(1371,plain,
! [A: $i] :
( ( ( powerset @ sk2 )
!= sk3 )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
| ( sk4 != A )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1307]) ).
thf(1417,plain,
( ( ( powerset @ sk2 )
!= sk3 )
| ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1371]) ).
thf(111,plain,
( ( binunion @ sk3 @ sk4 )
!= sk2 ),
inference(simp,[status(thm)],[108]) ).
thf(43824,plain,
! [A: $i] :
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= sk4 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ sk2 @ ( powerset @ ( powerset @ ( powerset @ sk2 ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,40817]) ).
thf(44039,plain,
! [A: $i] :
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= sk4 )
| ( A != sk2 )
| ( ( powerset @ A )
!= ( powerset @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
inference(simp,[status(thm)],[43824]) ).
thf(44091,plain,
( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
!= sk4 )
| ( ( powerset @ ( powerset @ ( powerset @ sk2 ) ) )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[44039]) ).
thf(30291,plain,
( ( ( powerset @ sk4 )
!= sk4 )
| ( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk3 ) )
!= ( in @ ( powerset @ sk4 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[5404,29966]) ).
thf(30373,plain,
( ( ( powerset @ sk4 )
!= sk4 )
| ( ( binunion @ sk3 @ sk4 )
!= ( powerset @ sk4 ) )
| ( ( powerset @ sk3 )
!= sk2 ) ),
inference(simp,[status(thm)],[30291]) ).
thf(346,plain,
! [A: $i] :
( ( ( powerset @ sk2 )
!= sk3 )
| ( in @ sk3 @ A )
| ( ( in @ ( powerset @ sk2 ) @ ( powerset @ A ) )
!= ( in @ sk4 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[165,29]) ).
thf(354,plain,
! [A: $i] :
( ( in @ sk3 @ A )
| ( ( powerset @ sk2 )
!= sk3 )
| ( ( powerset @ sk2 )
!= sk4 )
| ( ( powerset @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[346]) ).
thf(15654,plain,
! [A: $i] :
( ( in @ sk4 @ sk2 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,15073]) ).
thf(15770,plain,
! [A: $i] :
( ( in @ sk4 @ sk2 )
| ( A
!= ( powerset @ sk2 ) )
| ( ( powerset @ A )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[15654]) ).
thf(15800,plain,
( ( in @ sk4 @ sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk3 ) ) ),
inference(simp,[status(thm)],[15770]) ).
thf(18008,plain,
! [A: $i] :
( ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,13881]) ).
thf(18130,plain,
! [A: $i] :
( ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
| ( A
!= ( powerset @ sk2 ) )
| ( ( powerset @ A )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[18008]) ).
thf(18334,plain,
( ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
| ( ( powerset @ ( powerset @ sk2 ) )
!= ( powerset @ sk4 ) ) ),
inference(simp,[status(thm)],[18130]) ).
thf(72875,plain,
$false,
inference(e,[status(thm)],[69,8930,47281,1411,13955,1469,138,5857,22012,30003,10901,52387,11504,18691,170,18018,1401,1486,1426,3794,56,22970,2184,28398,47261,57185,13960,22016,34139,22925,42,1475,320,25,47023,24,30162,30149,14,8875,110,802,47259,15477,11510,93,284,325,3951,15073,1479,46,1815,57,29,4595,1489,7492,179,30144,7104,238,25240,12041,14847,26916,46040,47613,30154,293,8892,265,15197,133,44244,116,243,248,25884,6139,7005,1736,3795,47144,47279,6124,6122,30167,302,4609,47264,47282,3884,165,9993,25912,1487,70,12083,92,229,8920,3799,29966,329,25021,8916,30099,3784,948,30163,56249,47093,18402,47636,141,109,47450,42873,526,1937,12600,96,124,50231,225,25908,1461,13154,30150,1932,30153,1715,14986,40479,13,40693,134,11153,6160,805,3587,9008,13968,49708,32391,44767,15290,28903,412,4131,1754,13896,45,1301,180,264,1927,8906,6422,47275,402,54559,52350,30151,59,47204,1488,30313,44,30043,25525,12,54,7109,3783,34198,40459,13531,71,3796,15630,41555,25194,16515,3532,47263,159,4716,187,26924,30115,30147,245,318,39,303,30423,12015,18790,55513,816,53533,47278,240,33905,1460,43141,108,8198,35312,47268,4720,11775,306,135,47289,30159,8922,35,226,3,241,80,162,1420,27578,1990,13431,22964,7526,44370,1277,30223,123,1472,1770,16653,13967,30156,44125,95,47240,29675,1484,263,282,5388,1716,12396,30171,3847,30402,4020,7105,53575,47270,27581,11,46012,47265,43,27580,24965,52383,41546,1421,7089,1289,45047,47049,6953,47284,13969,30148,32296,319,29915,158,17020,351,19087,8912,41146,8,75,58,246,39874,47326,47358,287,34424,14963,55013,26853,1725,47262,7744,8412,405,19,273,4597,33051,4706,8886,30165,2534,305,5404,1710,94,283,40817,326,107,239,242,15662,8889,4118,22918,163,68,13161,47269,1399,6424,9992,30173,254,13881,35722,41556,13962,1417,111,44091,30373,354,22961,15800,18334]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU711^2 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n017.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 15:25:24 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.98/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.96 % [INFO] Parsing done (101ms).
% 1.29/0.97 % [INFO] Running in sequential loop mode.
% 1.59/1.17 % [INFO] eprover registered as external prover.
% 1.59/1.17 % [INFO] cvc4 registered as external prover.
% 1.59/1.18 % [INFO] Scanning for conjecture ...
% 1.88/1.24 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.92/1.26 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.92/1.26 % [INFO] Problem is higher-order (TPTP THF).
% 1.92/1.27 % [INFO] Type checking passed.
% 1.92/1.27 % [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 ...
% 111.64/20.16 % External prover 'e' found a proof!
% 111.64/20.16 % [INFO] Killing All external provers ...
% 111.64/20.16 % Time passed: 19642ms (effective reasoning time: 19184ms)
% 111.64/20.16 % 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)>
% 111.64/20.16 % Axioms used in derivation (0):
% 111.64/20.16 % No. of inferences in proof: 865
% 111.64/20.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 19642 ms resp. 19184 ms w/o parsing
% 112.51/20.40 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 112.51/20.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------