%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU164+3 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:37:51 AM UTC 2026
% Result : Theorem 92.27s 24.50s
% Output : Refutation 89.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 23
% Syntax : Number of formulae : 634 ( 224 unt; 0 typ; 12 def)
% Number of atoms : 1730 ( 749 equ; 0 cnn)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 6460 ( 981 ~; 607 |; 56 &;4745 @)
% ( 9 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 5 con; 0-3 aty)
% Number of variables : 874 ( 19 ^; 828 !; 15 ?; 874 :)
% ( 0 !>; 0 ?*; 0 @-; 12 @+)
% Comments :
%------------------------------------------------------------------------------
thf(union_decl,type,
union: $i > $i ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i > $o ).
thf(sk9_decl,type,
sk9: $i > $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i > $i ).
thf(sk12_decl,type,
sk12: $i ).
thf(sk13_decl,type,
sk13: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
( ( A @ powerset @ union )
!= A ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ in ) )
=> ( C = B ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C = B )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ in ) )
=> ( B @ ( C @ subset ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ subset ) )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
( ( C @ ( D @ in ) )
& ( D @ ( A @ in ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ in ) )
=> ? [D: $i] :
( ( B @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ? [D: $i] :
( ( B @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( B @ ( C @ in ) )
& ( C @ ( B @ ( A @ sk10 ) @ in ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(9,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(101,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) )
=> ( B
= ( A @ singleton ) ) )
& ( ( B
= ( A @ singleton ) )
=> ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,plain,
( ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C = A )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( C = A ) ) )
=> ( B
= ( A @ singleton ) ) )
& ! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
=> ( ! [C: $i] :
( ( C = A )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( C = A ) ) ) ) ),
inference(miniscope,[status(thm)],[18]) ).
thf(20,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( E @ singleton ) )
| ~ ( F @ ( E @ ( F @ sk3 ) @ in ) )
| ( ( E @ ( F @ sk2 ) )
!= E ) )
& ( ( F
= ( E @ singleton ) )
| ( ( E @ ( F @ sk3 ) )
= E )
| ( ( E @ ( F @ sk2 ) )
!= E ) )
& ( ( F
= ( E @ singleton ) )
| ~ ( F @ ( E @ ( F @ sk3 ) @ in ) )
| ( F @ ( E @ ( F @ sk2 ) @ in ) ) )
& ( ( F
= ( E @ singleton ) )
| ( ( E @ ( F @ sk3 ) )
= E )
| ( F @ ( E @ ( F @ sk2 ) @ in ) ) )
& ( ( B @ ( D @ in ) )
| ( D != A )
| ( B
!= ( A @ singleton ) ) )
& ( ( C = A )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ singleton ) ) ) ),
inference(cnf,[status(esa)],[19]) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ( C != A )
| ( B
!= ( A @ singleton ) ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ( C != A )
| ( B
!= ( A @ singleton ) ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(28,plain,
! [A: $i] : ( A @ singleton @ ( A @ in ) ),
inference(simp,[status(thm)],[27]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ singleton ) ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ in ) )
| ( C = A )
| ( B
!= ( A @ singleton ) ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ~ ( A @ singleton @ ( B @ in ) )
| ( B = A ) ),
inference(simp,[status(thm)],[37]) ).
thf(102,plain,
sk12 @ empty,
inference(cnf,[status(esa)],[101]) ).
thf(10,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(103,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(104,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[103]) ).
thf(105,plain,
~ ( sk13 @ empty ),
inference(cnf,[status(esa)],[104]) ).
thf(119,plain,
( ( ( sk13 @ empty )
!= ( sk12 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[102,105]) ).
thf(120,plain,
( ( sk13 @ empty )
!= ( sk12 @ empty ) ),
inference(simp,[status(thm)],[119]) ).
thf(121,plain,
sk13 != sk12,
inference(simp,[status(thm)],[120]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ( B != sk13 )
| ( A != sk12 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,121]) ).
thf(143,plain,
! [A: $i] :
( ( A != sk12 )
| ~ ( A @ singleton @ ( sk13 @ in ) ) ),
inference(pattern_uni,[status(thm)],[142:[bind(A,$thf( A )),bind(B,$thf( sk13 ))]]) ).
thf(200,plain,
~ ( sk12 @ singleton @ ( sk13 @ in ) ),
inference(simp,[status(thm)],[143]) ).
thf(219,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk12 @ singleton @ ( sk13 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,200]) ).
thf(220,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk12 @ singleton @ ( sk13 @ in ) ) ),
inference(simp,[status(thm)],[219]) ).
thf(233,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk12 @ singleton ) )
| ( A != sk13 ) ),
inference(simp,[status(thm)],[220]) ).
thf(237,plain,
( ( sk13 @ singleton )
!= ( sk12 @ singleton ) ),
inference(simp,[status(thm)],[233]) ).
thf(466,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk13 @ singleton ) )
| ( B
!= ( sk12 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,237]) ).
thf(467,plain,
! [A: $i] :
( ( A
!= ( sk12 @ singleton ) )
| ~ ( sk13 @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[466:[bind(A,$thf( sk13 @ singleton )),bind(B,$thf( B ))]]) ).
thf(475,plain,
~ ( sk13 @ singleton @ singleton @ ( sk12 @ singleton @ in ) ),
inference(simp,[status(thm)],[467]) ).
thf(509,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk13 @ singleton @ singleton @ ( sk12 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,475]) ).
thf(510,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk13 @ singleton @ singleton @ ( sk12 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[509]) ).
thf(547,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk13 @ singleton @ singleton ) )
| ( A
!= ( sk12 @ singleton ) ) ),
inference(simp,[status(thm)],[510]) ).
thf(550,plain,
( ( sk13 @ singleton @ singleton )
!= ( sk12 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[547]) ).
thf(783,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk13 @ singleton @ singleton ) )
| ( A
!= ( sk12 @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,550]) ).
thf(784,plain,
! [A: $i] :
( ( A
!= ( sk12 @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( sk13 @ singleton @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[783:[bind(A,$thf( A )),bind(B,$thf( sk13 @ singleton @ singleton ))]]) ).
thf(804,plain,
~ ( sk12 @ singleton @ singleton @ singleton @ ( sk13 @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[784]) ).
thf(850,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk12 @ singleton @ singleton @ singleton @ ( sk13 @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,804]) ).
thf(851,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk12 @ singleton @ singleton @ singleton @ ( sk13 @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[850]) ).
thf(904,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk12 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk13 @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[851]) ).
thf(909,plain,
( ( sk13 @ singleton @ singleton @ singleton )
!= ( sk12 @ singleton @ singleton @ singleton ) ),
inference(simp,[status(thm)],[904]) ).
thf(11,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(106,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(107,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(cnf,[status(esa)],[106]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ powerset ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( A @ ( C @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(39,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( A @ ( C @ subset ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( A @ ( C @ subset ) ) ) )
=> ( B
= ( A @ powerset ) ) )
& ( ( B
= ( A @ powerset ) )
=> ! [C: $i] :
( ( ( A @ ( C @ subset ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( A @ ( C @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(40,plain,
( ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ subset ) )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ subset ) ) ) )
=> ( B
= ( A @ powerset ) ) )
& ! [A: $i,B: $i] :
( ( B
= ( A @ powerset ) )
=> ( ! [C: $i] :
( ( A @ ( C @ subset ) )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ subset ) ) ) ) ) ),
inference(miniscope,[status(thm)],[39]) ).
thf(41,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( E @ powerset ) )
| ~ ( F @ ( E @ ( F @ sk5 ) @ in ) )
| ~ ( E @ ( E @ ( F @ sk4 ) @ subset ) ) )
& ( ( F
= ( E @ powerset ) )
| ( E @ ( E @ ( F @ sk5 ) @ subset ) )
| ~ ( E @ ( E @ ( F @ sk4 ) @ subset ) ) )
& ( ( F
= ( E @ powerset ) )
| ~ ( F @ ( E @ ( F @ sk5 ) @ in ) )
| ( F @ ( E @ ( F @ sk4 ) @ in ) ) )
& ( ( F
= ( E @ powerset ) )
| ( E @ ( E @ ( F @ sk5 ) @ subset ) )
| ( F @ ( E @ ( F @ sk4 ) @ in ) ) )
& ( ( B @ ( D @ in ) )
| ~ ( A @ ( D @ subset ) )
| ( B
!= ( A @ powerset ) ) )
& ( ( A @ ( C @ subset ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ powerset ) ) ) ),
inference(cnf,[status(esa)],[40]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ~ ( A @ ( C @ subset ) )
| ( B
!= ( A @ powerset ) ) ),
inference(cnfConj,[status(thm)],[41]) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ~ ( A @ ( C @ subset ) )
| ( B
!= ( A @ powerset ) ) ),
inference(lifteq,[status(thm)],[46]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( A @ powerset @ ( B @ in ) )
| ~ ( A @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(2489,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( B @ ( C @ subset ) ) )
| ( B @ powerset @ ( C @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[107,51]) ).
thf(2490,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( B @ ( C @ subset ) ) )
| ( B @ powerset @ ( C @ in ) ) ),
inference(simp,[status(thm)],[2489]) ).
thf(2491,plain,
! [A: $i] : ( A @ powerset @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[2490:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ powerset @ union )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ powerset @ union )
= A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [A: $i] :
( ( A @ powerset @ union )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,plain,
( ( sk1 @ powerset @ union )
!= sk1 ),
inference(cnf,[status(esa)],[13]) ).
thf(15,plain,
( ( sk1 @ powerset @ union )
!= sk1 ),
inference(lifteq,[status(thm)],[14]) ).
thf(168,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ powerset @ union ) )
| ( B != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,15]) ).
thf(169,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( sk1 @ powerset @ union @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[168:[bind(A,$thf( sk1 @ powerset @ union )),bind(B,$thf( B ))]]) ).
thf(210,plain,
~ ( sk1 @ powerset @ union @ singleton @ ( sk1 @ in ) ),
inference(simp,[status(thm)],[169]) ).
thf(2551,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ powerset @ union @ singleton @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,210]) ).
thf(2552,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ powerset @ union @ singleton @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[2551]) ).
thf(2573,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk1 @ powerset @ union @ singleton ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[2552]) ).
thf(2595,plain,
( ( sk1 @ powerset @ union @ singleton )
!= ( sk1 @ powerset ) ),
inference(simp,[status(thm)],[2573]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ union ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(68,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) )
=> ( B
= ( A @ union ) ) )
& ( ( B
= ( A @ union ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(69,plain,
( ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) )
=> ( B
= ( A @ union ) ) )
& ! [A: $i,B: $i] :
( ( B
= ( A @ union ) )
=> ( ! [C: $i] :
( ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[68]) ).
thf(70,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G
= ( F @ union ) )
| ~ ( G @ ( F @ ( G @ sk10 ) @ in ) )
| ( G @ ( F @ sk8 ) ) )
& ( ( G
= ( F @ union ) )
| ( F @ ( F @ ( G @ sk11 ) @ in ) )
| ( G @ ( F @ sk8 ) ) )
& ( ( G
= ( F @ union ) )
| ( F @ ( G @ sk11 ) @ ( F @ ( G @ sk10 ) @ in ) )
| ( G @ ( F @ sk8 ) ) )
& ( ( G
= ( F @ union ) )
| ~ ( G @ ( F @ sk8 ) )
| ~ ( F @ ( H @ in ) )
| ~ ( H @ ( F @ ( G @ sk9 ) @ in ) ) )
& ( ( G
= ( F @ union ) )
| ~ ( G @ ( F @ sk8 ) )
| ( G @ ( F @ ( G @ sk9 ) @ in ) ) )
& ( ( B @ ( D @ in ) )
| ~ ( A @ ( E @ in ) )
| ~ ( E @ ( D @ in ) )
| ( B
!= ( A @ union ) ) )
& ( ( A @ ( A @ ( B @ ( C @ sk7 ) ) @ in ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ union ) ) )
& ( ( A @ ( B @ ( C @ sk7 ) ) @ ( C @ in ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ union ) ) ) ),
inference(cnf,[status(esa)],[69]) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ sk7 ) ) @ in ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ union ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(87,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ sk7 ) ) @ in ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ union ) ) ),
inference(lifteq,[status(thm)],[71]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ union @ ( B @ sk7 ) ) @ in ) )
| ~ ( A @ union @ ( B @ in ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(2555,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ singleton @ ( sk13 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,200]) ).
thf(2556,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ singleton @ ( sk13 @ in ) ) ),
inference(simp,[status(thm)],[2555]) ).
thf(2562,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk12 @ singleton ) )
| ( A != sk13 ) ),
inference(simp,[status(thm)],[2556]) ).
thf(2583,plain,
( ( sk12 @ singleton )
!= ( sk13 @ powerset ) ),
inference(simp,[status(thm)],[2562]) ).
thf(2614,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk12 @ singleton ) )
| ( A
!= ( sk13 @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,2583]) ).
thf(2615,plain,
! [A: $i] :
( ( A
!= ( sk13 @ powerset ) )
| ~ ( A @ singleton @ ( sk12 @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[2614:[bind(A,$thf( A )),bind(B,$thf( sk12 @ singleton ))]]) ).
thf(2628,plain,
~ ( sk13 @ powerset @ singleton @ ( sk12 @ singleton @ in ) ),
inference(simp,[status(thm)],[2615]) ).
thf(3531,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ powerset @ singleton @ ( sk12 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,2628]) ).
thf(3532,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ powerset @ singleton @ ( sk12 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[3531]) ).
thf(3595,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk13 @ powerset @ singleton ) )
| ( A
!= ( sk12 @ singleton ) ) ),
inference(simp,[status(thm)],[3532]) ).
thf(3602,plain,
( ( sk13 @ powerset @ singleton )
!= ( sk12 @ singleton @ powerset ) ),
inference(simp,[status(thm)],[3595]) ).
thf(3856,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk13 @ powerset @ singleton ) )
| ( A
!= ( sk12 @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,3602]) ).
thf(3857,plain,
! [A: $i] :
( ( A
!= ( sk12 @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( sk13 @ powerset @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[3856:[bind(A,$thf( A )),bind(B,$thf( sk13 @ powerset @ singleton ))]]) ).
thf(3883,plain,
~ ( sk12 @ singleton @ powerset @ singleton @ ( sk13 @ powerset @ singleton @ in ) ),
inference(simp,[status(thm)],[3857]) ).
thf(8025,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ singleton @ powerset @ singleton @ ( sk13 @ powerset @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,3883]) ).
thf(8026,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ singleton @ powerset @ singleton @ ( sk13 @ powerset @ singleton @ in ) ) ),
inference(simp,[status(thm)],[8025]) ).
thf(8163,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk12 @ singleton @ powerset @ singleton ) )
| ( A
!= ( sk13 @ powerset @ singleton ) ) ),
inference(simp,[status(thm)],[8026]) ).
thf(8186,plain,
( ( sk12 @ singleton @ powerset @ singleton )
!= ( sk13 @ powerset @ singleton @ powerset ) ),
inference(simp,[status(thm)],[8163]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(16,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ in ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(122,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ ( A @ in ) ) ),
inference(eqfactor_ordered,[status(thm)],[17]) ).
thf(123,plain,
! [A: $i] :
~ ( A @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[122:[bind(A,$thf( B ))]]) ).
thf(124,plain,
! [A: $i] :
~ ( A @ ( A @ in ) ),
inference(simp,[status(thm)],[123]) ).
thf(2518,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( B @ ( B @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,124]) ).
thf(2519,plain,
! [B: $i,A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( B @ ( B @ in ) ) ),
inference(simp,[status(thm)],[2518]) ).
thf(2576,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset )
!= B )
| ( A != B ) ),
inference(simp,[status(thm)],[2519]) ).
thf(2598,plain,
! [A: $i] :
( ( A @ powerset )
!= A ),
inference(simp,[status(thm)],[2576]) ).
thf(6050,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ powerset ) )
| ( B != C )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,2598]) ).
thf(6051,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ powerset @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[6050:[bind(A,$thf( D @ powerset )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(6063,plain,
! [A: $i] :
~ ( A @ powerset @ singleton @ ( A @ in ) ),
inference(simp,[status(thm)],[6051]) ).
thf(1108,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk13 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk12 @ singleton @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,909]) ).
thf(1109,plain,
! [A: $i] :
( ( A
!= ( sk12 @ singleton @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( sk13 @ singleton @ singleton @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[1108:[bind(A,$thf( A )),bind(B,$thf( sk13 @ singleton @ singleton @ singleton ))]]) ).
thf(1142,plain,
~ ( sk12 @ singleton @ singleton @ singleton @ singleton @ ( sk13 @ singleton @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[1109]) ).
thf(144,plain,
! [B: $i,A: $i] :
( ( A != sk13 )
| ( B != sk12 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,121]) ).
thf(145,plain,
! [A: $i] :
( ( A != sk12 )
| ~ ( sk13 @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[144:[bind(A,$thf( sk13 ))]]) ).
thf(201,plain,
~ ( sk13 @ singleton @ ( sk12 @ in ) ),
inference(simp,[status(thm)],[145]) ).
thf(2506,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ singleton @ ( sk12 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,201]) ).
thf(2507,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ singleton @ ( sk12 @ in ) ) ),
inference(simp,[status(thm)],[2506]) ).
thf(2569,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk13 @ singleton ) )
| ( A != sk12 ) ),
inference(simp,[status(thm)],[2507]) ).
thf(2591,plain,
( ( sk13 @ singleton )
!= ( sk12 @ powerset ) ),
inference(simp,[status(thm)],[2569]) ).
thf(2634,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk13 @ singleton ) )
| ( A
!= ( sk12 @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,2591]) ).
thf(2635,plain,
! [A: $i] :
( ( A
!= ( sk12 @ powerset ) )
| ~ ( A @ singleton @ ( sk13 @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[2634:[bind(A,$thf( A )),bind(B,$thf( sk13 @ singleton ))]]) ).
thf(2649,plain,
~ ( sk12 @ powerset @ singleton @ ( sk13 @ singleton @ in ) ),
inference(simp,[status(thm)],[2635]) ).
thf(3707,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk12 @ powerset @ singleton @ ( sk13 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,2649]) ).
thf(3708,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk12 @ powerset @ singleton @ ( sk13 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[3707]) ).
thf(3756,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk12 @ powerset @ singleton ) )
| ( A
!= ( sk13 @ singleton ) ) ),
inference(simp,[status(thm)],[3708]) ).
thf(3769,plain,
( ( sk13 @ singleton @ singleton )
!= ( sk12 @ powerset @ singleton ) ),
inference(simp,[status(thm)],[3756]) ).
thf(4940,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk13 @ singleton @ singleton ) )
| ( A
!= ( sk12 @ powerset @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,3769]) ).
thf(4941,plain,
! [A: $i] :
( ( A
!= ( sk12 @ powerset @ singleton ) )
| ~ ( A @ singleton @ ( sk13 @ singleton @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[4940:[bind(A,$thf( A )),bind(B,$thf( sk13 @ singleton @ singleton ))]]) ).
thf(4973,plain,
~ ( sk12 @ powerset @ singleton @ singleton @ ( sk13 @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[4941]) ).
thf(10966,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk12 @ powerset @ singleton @ singleton @ ( sk13 @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,4973]) ).
thf(10967,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk12 @ powerset @ singleton @ singleton @ ( sk13 @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[10966]) ).
thf(11065,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk12 @ powerset @ singleton @ singleton ) )
| ( A
!= ( sk13 @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[10967]) ).
thf(11080,plain,
( ( sk13 @ singleton @ singleton @ singleton )
!= ( sk12 @ powerset @ singleton @ singleton ) ),
inference(simp,[status(thm)],[11065]) ).
thf(162,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ powerset @ union ) )
| ( A != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,15]) ).
thf(163,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( A @ singleton @ ( sk1 @ powerset @ union @ in ) ) ),
inference(pattern_uni,[status(thm)],[162:[bind(A,$thf( A )),bind(B,$thf( sk1 @ powerset @ union ))]]) ).
thf(209,plain,
~ ( sk1 @ singleton @ ( sk1 @ powerset @ union @ in ) ),
inference(simp,[status(thm)],[163]) ).
thf(2494,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk1 @ powerset @ union @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,209]) ).
thf(2495,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk1 @ powerset @ union @ in ) ) ),
inference(simp,[status(thm)],[2494]) ).
thf(2557,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk1 @ singleton ) )
| ( A
!= ( sk1 @ powerset @ union ) ) ),
inference(simp,[status(thm)],[2495]) ).
thf(2608,plain,
( ( sk1 @ singleton )
!= ( sk1 @ powerset @ union @ powerset ) ),
inference(simp,[status(thm)],[2557]) ).
thf(2729,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ( B
!= ( sk1 @ powerset @ union @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,2608]) ).
thf(2730,plain,
! [A: $i] :
( ( A
!= ( sk1 @ powerset @ union @ powerset ) )
| ~ ( sk1 @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[2729:[bind(A,$thf( sk1 @ singleton )),bind(B,$thf( B ))]]) ).
thf(2740,plain,
~ ( sk1 @ singleton @ singleton @ ( sk1 @ powerset @ union @ powerset @ in ) ),
inference(simp,[status(thm)],[2730]) ).
thf(2700,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ powerset @ union @ singleton ) )
| ( B
!= ( sk1 @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,2595]) ).
thf(2701,plain,
! [A: $i] :
( ( A
!= ( sk1 @ powerset ) )
| ~ ( sk1 @ powerset @ union @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[2700:[bind(A,$thf( sk1 @ powerset @ union @ singleton )),bind(B,$thf( B ))]]) ).
thf(2717,plain,
~ ( sk1 @ powerset @ union @ singleton @ singleton @ ( sk1 @ powerset @ in ) ),
inference(simp,[status(thm)],[2701]) ).
thf(4040,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ powerset @ union @ singleton @ singleton @ ( sk1 @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,2717]) ).
thf(4041,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ powerset @ union @ singleton @ singleton @ ( sk1 @ powerset @ in ) ) ),
inference(simp,[status(thm)],[4040]) ).
thf(4127,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk1 @ powerset @ union @ singleton @ singleton ) )
| ( A
!= ( sk1 @ powerset ) ) ),
inference(simp,[status(thm)],[4041]) ).
thf(4137,plain,
( ( sk1 @ powerset @ union @ singleton @ singleton )
!= ( sk1 @ powerset @ powerset ) ),
inference(simp,[status(thm)],[4127]) ).
thf(2638,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk13 @ singleton ) )
| ( B
!= ( sk12 @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,2591]) ).
thf(2639,plain,
! [A: $i] :
( ( A
!= ( sk12 @ powerset ) )
| ~ ( sk13 @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[2638:[bind(A,$thf( sk13 @ singleton )),bind(B,$thf( B ))]]) ).
thf(2650,plain,
~ ( sk13 @ singleton @ singleton @ ( sk12 @ powerset @ in ) ),
inference(simp,[status(thm)],[2639]) ).
thf(3771,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ singleton @ singleton @ ( sk12 @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,2650]) ).
thf(3772,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ singleton @ singleton @ ( sk12 @ powerset @ in ) ) ),
inference(simp,[status(thm)],[3771]) ).
thf(3834,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk13 @ singleton @ singleton ) )
| ( A
!= ( sk12 @ powerset ) ) ),
inference(simp,[status(thm)],[3772]) ).
thf(3847,plain,
( ( sk13 @ singleton @ singleton )
!= ( sk12 @ powerset @ powerset ) ),
inference(simp,[status(thm)],[3834]) ).
thf(6005,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk13 @ singleton @ singleton ) )
| ( A
!= ( sk12 @ powerset @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,3847]) ).
thf(6006,plain,
! [A: $i] :
( ( A
!= ( sk12 @ powerset @ powerset ) )
| ~ ( A @ singleton @ ( sk13 @ singleton @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[6005:[bind(A,$thf( A )),bind(B,$thf( sk13 @ singleton @ singleton ))]]) ).
thf(6039,plain,
~ ( sk12 @ powerset @ powerset @ singleton @ ( sk13 @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[6006]) ).
thf(3691,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ powerset @ singleton @ ( sk13 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,2649]) ).
thf(3692,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ powerset @ singleton @ ( sk13 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[3691]) ).
thf(3753,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk12 @ powerset @ singleton ) )
| ( A
!= ( sk13 @ singleton ) ) ),
inference(simp,[status(thm)],[3692]) ).
thf(3767,plain,
( ( sk12 @ powerset @ singleton )
!= ( sk13 @ singleton @ powerset ) ),
inference(simp,[status(thm)],[3753]) ).
thf(4901,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk12 @ powerset @ singleton ) )
| ( B
!= ( sk13 @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,3767]) ).
thf(4902,plain,
! [A: $i] :
( ( A
!= ( sk13 @ singleton @ powerset ) )
| ~ ( sk12 @ powerset @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[4901:[bind(A,$thf( sk12 @ powerset @ singleton )),bind(B,$thf( B ))]]) ).
thf(4928,plain,
~ ( sk12 @ powerset @ singleton @ singleton @ ( sk13 @ singleton @ powerset @ in ) ),
inference(simp,[status(thm)],[4902]) ).
thf(10217,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ powerset @ singleton @ singleton @ ( sk13 @ singleton @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,4928]) ).
thf(10218,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ powerset @ singleton @ singleton @ ( sk13 @ singleton @ powerset @ in ) ) ),
inference(simp,[status(thm)],[10217]) ).
thf(10360,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk12 @ powerset @ singleton @ singleton ) )
| ( A
!= ( sk13 @ singleton @ powerset ) ) ),
inference(simp,[status(thm)],[10218]) ).
thf(10382,plain,
( ( sk12 @ powerset @ singleton @ singleton )
!= ( sk13 @ singleton @ powerset @ powerset ) ),
inference(simp,[status(thm)],[10360]) ).
thf(2692,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ powerset @ union @ singleton ) )
| ( A
!= ( sk1 @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,2595]) ).
thf(2693,plain,
! [A: $i] :
( ( A
!= ( sk1 @ powerset ) )
| ~ ( A @ singleton @ ( sk1 @ powerset @ union @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[2692:[bind(A,$thf( A )),bind(B,$thf( sk1 @ powerset @ union @ singleton ))]]) ).
thf(2716,plain,
~ ( sk1 @ powerset @ singleton @ ( sk1 @ powerset @ union @ singleton @ in ) ),
inference(simp,[status(thm)],[2693]) ).
thf(3956,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ powerset @ singleton @ ( sk1 @ powerset @ union @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,2716]) ).
thf(3957,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ powerset @ singleton @ ( sk1 @ powerset @ union @ singleton @ in ) ) ),
inference(simp,[status(thm)],[3956]) ).
thf(4019,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ powerset @ singleton ) )
| ( A
!= ( sk1 @ powerset @ union @ singleton ) ) ),
inference(simp,[status(thm)],[3957]) ).
thf(4036,plain,
( ( sk1 @ powerset @ union @ singleton @ singleton )
!= ( sk1 @ powerset @ singleton ) ),
inference(simp,[status(thm)],[4019]) ).
thf(6649,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ powerset @ union @ singleton @ singleton ) )
| ( A
!= ( sk1 @ powerset @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,4036]) ).
thf(6650,plain,
! [A: $i] :
( ( A
!= ( sk1 @ powerset @ singleton ) )
| ~ ( A @ singleton @ ( sk1 @ powerset @ union @ singleton @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[6649:[bind(A,$thf( A )),bind(B,$thf( sk1 @ powerset @ union @ singleton @ singleton ))]]) ).
thf(6713,plain,
~ ( sk1 @ powerset @ singleton @ singleton @ ( sk1 @ powerset @ union @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[6650]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(60,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(61,plain,
( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ ( A @ subset ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ) ),
inference(miniscope,[status(thm)],[60]) ).
thf(62,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ subset ) )
| ~ ( E @ ( D @ ( E @ sk6 ) @ in ) ) )
& ( ( E @ ( D @ subset ) )
| ( D @ ( D @ ( E @ sk6 ) @ in ) ) )
& ( ( B @ ( C @ in ) )
| ~ ( A @ ( C @ in ) )
| ~ ( B @ ( A @ subset ) ) ) ),
inference(cnf,[status(esa)],[61]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk6 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[62]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk6 ) @ in ) ) ),
inference(simp,[status(thm)],[64]) ).
thf(2486,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( C @ ( D @ subset ) ) )
| ( C @ powerset @ ( D @ in ) )
| ~ $true
| ( A @ ( A @ ( B @ sk6 ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[66,51]) ).
thf(2487,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( C @ ( D @ subset ) ) )
| ( C @ powerset @ ( D @ in ) )
| ( A @ ( A @ ( B @ sk6 ) @ in ) ) ),
inference(simp,[status(thm)],[2486]) ).
thf(2488,plain,
! [B: $i,A: $i] :
( ( B @ powerset @ ( A @ in ) )
| ( A @ ( A @ ( B @ sk6 ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[2487:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ union ) )
| ( A @ ( A @ ( B @ sk11 ) @ in ) )
| ( B @ ( A @ sk8 ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk11 ) @ in ) )
| ( B @ ( A @ sk8 ) )
| ( B
= ( A @ union ) ) ),
inference(lifteq,[status(thm)],[77]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk11 ) @ in ) )
| ( B @ ( A @ sk8 ) )
| ( B
= ( A @ union ) ) ),
inference(simp,[status(thm)],[83]) ).
thf(1625,plain,
! [B: $i,A: $i] :
( ( ( A @ union )
!= ( sk1 @ powerset @ union ) )
| ( B != sk1 )
| ( A @ ( A @ ( B @ sk11 ) @ in ) )
| ( B @ ( A @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[84,15]) ).
thf(1626,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk1 @ powerset @ ( sk1 @ powerset @ ( A @ sk11 ) @ in ) )
| ( A @ ( sk1 @ powerset @ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[1625:[bind(A,$thf( sk1 @ powerset )),bind(B,$thf( B ))]]) ).
thf(1666,plain,
( ( sk1 @ powerset @ ( sk1 @ powerset @ ( sk1 @ sk11 ) @ in ) )
| ( sk1 @ ( sk1 @ powerset @ sk8 ) ) ),
inference(simp,[status(thm)],[1626]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ subset ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ powerset ) ) ),
inference(cnfConj,[status(thm)],[41]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ subset ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ powerset ) ) ),
inference(lifteq,[status(thm)],[42]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ subset ) )
| ~ ( A @ powerset @ ( B @ in ) ) ),
inference(simp,[status(thm)],[48]) ).
thf(2326,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ powerset @ ( sk1 @ powerset @ ( sk1 @ sk11 ) @ in ) )
!= ( A @ powerset @ ( B @ in ) ) )
| ( A @ ( B @ subset ) )
| ~ $true
| ( sk1 @ ( sk1 @ powerset @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[1666,49]) ).
thf(2327,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ powerset @ ( sk1 @ powerset @ ( sk1 @ sk11 ) @ in ) )
!= ( A @ powerset @ ( B @ in ) ) )
| ( A @ ( B @ subset ) )
| ( sk1 @ ( sk1 @ powerset @ sk8 ) ) ),
inference(simp,[status(thm)],[2326]) ).
thf(2328,plain,
( ( sk1 @ ( sk1 @ powerset @ ( sk1 @ sk11 ) @ subset ) )
| ( sk1 @ ( sk1 @ powerset @ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[2327:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ powerset @ ( sk1 @ sk11 ) ))]]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ union ) )
| ~ ( B @ ( A @ sk8 ) )
| ( B @ ( A @ ( B @ sk9 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ sk8 ) )
| ( B @ ( A @ ( B @ sk9 ) @ in ) )
| ( B
= ( A @ union ) ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ sk8 ) )
| ( B @ ( A @ ( B @ sk9 ) @ in ) )
| ( B
= ( A @ union ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(20993,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ powerset @ sk8 ) )
!= ( B @ ( A @ sk8 ) ) )
| ~ $true
| ( B @ ( A @ ( B @ sk9 ) @ in ) )
| ( B
= ( A @ union ) )
| ( sk1 @ ( sk1 @ powerset @ ( sk1 @ sk11 ) @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[2328,90]) ).
thf(20994,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ powerset @ sk8 ) )
!= ( B @ ( A @ sk8 ) ) )
| ( B @ ( A @ ( B @ sk9 ) @ in ) )
| ( B
= ( A @ union ) )
| ( sk1 @ ( sk1 @ powerset @ ( sk1 @ sk11 ) @ subset ) ) ),
inference(simp,[status(thm)],[20993]) ).
thf(20995,plain,
( ( sk1 @ ( sk1 @ powerset @ ( sk1 @ sk9 ) @ in ) )
| ( ( sk1 @ powerset @ union )
= sk1 )
| ( sk1 @ ( sk1 @ powerset @ ( sk1 @ sk11 ) @ subset ) ) ),
inference(pattern_uni,[status(thm)],[20994:[bind(A,$thf( sk1 @ powerset )),bind(B,$thf( sk1 ))]]) ).
thf(23140,plain,
( ( sk1 @ ( sk1 @ powerset @ ( sk1 @ sk9 ) @ in ) )
| ( sk1 @ ( sk1 @ powerset @ ( sk1 @ sk11 ) @ subset ) ) ),
inference(simplifyReflect,[status(thm)],[20995,15]) ).
thf(2492,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ singleton @ singleton @ singleton @ singleton @ ( sk13 @ singleton @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,1142]) ).
thf(2493,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ singleton @ singleton @ singleton @ singleton @ ( sk13 @ singleton @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[2492]) ).
thf(2579,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk12 @ singleton @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk13 @ singleton @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[2493]) ).
thf(2603,plain,
( ( sk12 @ singleton @ singleton @ singleton @ singleton )
!= ( sk13 @ singleton @ singleton @ singleton @ powerset ) ),
inference(simp,[status(thm)],[2579]) ).
thf(462,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk13 @ singleton ) )
| ( A
!= ( sk12 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,237]) ).
thf(463,plain,
! [A: $i] :
( ( A
!= ( sk12 @ singleton ) )
| ~ ( A @ singleton @ ( sk13 @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[462:[bind(A,$thf( A )),bind(B,$thf( sk13 @ singleton ))]]) ).
thf(478,plain,
~ ( sk12 @ singleton @ singleton @ ( sk13 @ singleton @ in ) ),
inference(simp,[status(thm)],[463]) ).
thf(2498,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ singleton @ singleton @ ( sk13 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,478]) ).
thf(2499,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ singleton @ singleton @ ( sk13 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[2498]) ).
thf(2570,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk12 @ singleton @ singleton ) )
| ( A
!= ( sk13 @ singleton ) ) ),
inference(simp,[status(thm)],[2499]) ).
thf(2592,plain,
( ( sk12 @ singleton @ singleton )
!= ( sk13 @ singleton @ powerset ) ),
inference(simp,[status(thm)],[2570]) ).
thf(2662,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk12 @ singleton @ singleton ) )
| ( B
!= ( sk13 @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,2592]) ).
thf(2663,plain,
! [A: $i] :
( ( A
!= ( sk13 @ singleton @ powerset ) )
| ~ ( sk12 @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[2662:[bind(A,$thf( sk12 @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(2678,plain,
~ ( sk12 @ singleton @ singleton @ singleton @ ( sk13 @ singleton @ powerset @ in ) ),
inference(simp,[status(thm)],[2663]) ).
thf(6341,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ singleton @ singleton @ singleton @ ( sk13 @ singleton @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,2678]) ).
thf(6342,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ singleton @ singleton @ singleton @ ( sk13 @ singleton @ powerset @ in ) ) ),
inference(simp,[status(thm)],[6341]) ).
thf(6455,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk12 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk13 @ singleton @ powerset ) ) ),
inference(simp,[status(thm)],[6342]) ).
thf(6470,plain,
( ( sk12 @ singleton @ singleton @ singleton )
!= ( sk13 @ singleton @ powerset @ powerset ) ),
inference(simp,[status(thm)],[6455]) ).
thf(3547,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk13 @ powerset @ singleton @ ( sk12 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,2628]) ).
thf(3548,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk13 @ powerset @ singleton @ ( sk12 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[3547]) ).
thf(3597,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk13 @ powerset @ singleton ) )
| ( A
!= ( sk12 @ singleton ) ) ),
inference(simp,[status(thm)],[3548]) ).
thf(3604,plain,
( ( sk12 @ singleton @ singleton )
!= ( sk13 @ powerset @ singleton ) ),
inference(simp,[status(thm)],[3597]) ).
thf(4811,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk12 @ singleton @ singleton ) )
| ( A
!= ( sk13 @ powerset @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,3604]) ).
thf(4812,plain,
! [A: $i] :
( ( A
!= ( sk13 @ powerset @ singleton ) )
| ~ ( A @ singleton @ ( sk12 @ singleton @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[4811:[bind(A,$thf( A )),bind(B,$thf( sk12 @ singleton @ singleton ))]]) ).
thf(4844,plain,
~ ( sk13 @ powerset @ singleton @ singleton @ ( sk12 @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[4812]) ).
thf(9382,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ powerset @ singleton @ singleton @ ( sk12 @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,4844]) ).
thf(9383,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ powerset @ singleton @ singleton @ ( sk12 @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[9382]) ).
thf(9515,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk13 @ powerset @ singleton @ singleton ) )
| ( A
!= ( sk12 @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[9383]) ).
thf(9529,plain,
( ( sk13 @ powerset @ singleton @ singleton )
!= ( sk12 @ singleton @ singleton @ powerset ) ),
inference(simp,[status(thm)],[9515]) ).
thf(267,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk6 ) @ in ) )
!= ( C @ singleton @ ( D @ in ) ) )
| ~ $true
| ( D = C )
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[66,38]) ).
thf(268,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk6 ) @ in ) )
!= ( C @ singleton @ ( D @ in ) ) )
| ( D = C )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[267]) ).
thf(269,plain,
! [B: $i,A: $i] :
( ( ( B @ singleton @ ( A @ sk6 ) )
= B )
| ( A @ ( B @ singleton @ subset ) ) ),
inference(pattern_uni,[status(thm)],[268:[bind(A,$thf( G @ singleton )),bind(B,$thf( E )),bind(C,$thf( G )),bind(D,$thf( G @ singleton @ ( E @ sk6 ) ))]]) ).
thf(289,plain,
! [B: $i,A: $i] :
( ( ( B @ singleton @ ( A @ sk6 ) )
= B )
| ( A @ ( B @ singleton @ subset ) ) ),
inference(simp,[status(thm)],[269]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ powerset ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ in ) )
| ( B @ ( A @ ( B @ sk4 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[41]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk5 ) @ in ) )
| ( B @ ( A @ ( B @ sk4 ) @ in ) )
| ( B
= ( A @ powerset ) ) ),
inference(lifteq,[status(thm)],[43]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk5 ) @ in ) )
| ( B @ ( A @ ( B @ sk4 ) @ in ) )
| ( B
= ( A @ powerset ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(11292,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk12 @ powerset @ powerset @ singleton @ ( sk13 @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,6039]) ).
thf(11293,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk12 @ powerset @ powerset @ singleton @ ( sk13 @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[11292]) ).
thf(11395,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk12 @ powerset @ powerset @ singleton ) )
| ( A
!= ( sk13 @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[11293]) ).
thf(11404,plain,
( ( sk13 @ singleton @ singleton @ singleton )
!= ( sk12 @ powerset @ powerset @ singleton ) ),
inference(simp,[status(thm)],[11395]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ powerset ) )
| ( ( B @ union )
!= sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,15]) ).
thf(171,plain,
! [A: $i] :
( ( ( A @ union )
!= sk1 )
| ~ ( sk1 @ powerset @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[170:[bind(A,$thf( sk1 @ powerset )),bind(B,$thf( B ))]]) ).
thf(211,plain,
! [A: $i] :
( ( ( A @ union )
!= sk1 )
| ~ ( sk1 @ powerset @ singleton @ ( A @ in ) ) ),
inference(simp,[status(thm)],[171]) ).
thf(2500,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ singleton @ singleton @ ( sk12 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,475]) ).
thf(2501,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ singleton @ singleton @ ( sk12 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[2500]) ).
thf(2558,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk13 @ singleton @ singleton ) )
| ( A
!= ( sk12 @ singleton ) ) ),
inference(simp,[status(thm)],[2501]) ).
thf(2609,plain,
( ( sk13 @ singleton @ singleton )
!= ( sk12 @ singleton @ powerset ) ),
inference(simp,[status(thm)],[2558]) ).
thf(3499,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk13 @ singleton @ singleton ) )
| ( A
!= ( sk12 @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,2609]) ).
thf(3500,plain,
! [A: $i] :
( ( A
!= ( sk12 @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( sk13 @ singleton @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[3499:[bind(A,$thf( A )),bind(B,$thf( sk13 @ singleton @ singleton ))]]) ).
thf(3527,plain,
~ ( sk12 @ singleton @ powerset @ singleton @ ( sk13 @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[3500]) ).
thf(293,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk1 @ powerset @ union @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,209]) ).
thf(294,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk1 @ powerset @ union @ in ) ) ),
inference(simp,[status(thm)],[293]) ).
thf(316,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ singleton ) )
| ( A
!= ( sk1 @ powerset @ union ) ) ),
inference(simp,[status(thm)],[294]) ).
thf(323,plain,
( ( sk1 @ powerset @ union @ singleton )
!= ( sk1 @ singleton ) ),
inference(simp,[status(thm)],[316]) ).
thf(480,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ powerset @ union @ singleton ) )
| ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,323]) ).
thf(481,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( sk1 @ powerset @ union @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[480:[bind(A,$thf( A )),bind(B,$thf( sk1 @ powerset @ union @ singleton ))]]) ).
thf(503,plain,
~ ( sk1 @ singleton @ singleton @ ( sk1 @ powerset @ union @ singleton @ in ) ),
inference(simp,[status(thm)],[481]) ).
thf(632,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk1 @ powerset @ union @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,503]) ).
thf(633,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk1 @ powerset @ union @ singleton @ in ) ) ),
inference(simp,[status(thm)],[632]) ).
thf(681,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ singleton @ singleton ) )
| ( A
!= ( sk1 @ powerset @ union @ singleton ) ) ),
inference(simp,[status(thm)],[633]) ).
thf(687,plain,
( ( sk1 @ powerset @ union @ singleton @ singleton )
!= ( sk1 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[681]) ).
thf(2300,plain,
! [A: $i] :
( ( ( sk1 @ powerset @ ( sk1 @ powerset @ ( sk1 @ sk11 ) @ in ) )
!= ( A @ ( A @ in ) ) )
| ~ $true
| ( sk1 @ ( sk1 @ powerset @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[1666,124]) ).
thf(2301,plain,
! [A: $i] :
( ( ( sk1 @ powerset @ ( sk1 @ powerset @ ( sk1 @ sk11 ) @ in ) )
!= ( A @ ( A @ in ) ) )
| ( sk1 @ ( sk1 @ powerset @ sk8 ) ) ),
inference(simp,[status(thm)],[2300]) ).
thf(2347,plain,
! [A: $i] :
( ( ( sk1 @ powerset )
!= A )
| ( ( sk1 @ powerset @ ( sk1 @ sk11 ) )
!= A )
| ( sk1 @ ( sk1 @ powerset @ sk8 ) ) ),
inference(simp,[status(thm)],[2301]) ).
thf(2371,plain,
( ( ( sk1 @ powerset @ ( sk1 @ sk11 ) )
!= ( sk1 @ powerset ) )
| ( sk1 @ ( sk1 @ powerset @ sk8 ) ) ),
inference(simp,[status(thm)],[2347]) ).
thf(6659,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ powerset @ union @ singleton @ singleton ) )
| ( B
!= ( sk1 @ powerset @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,4036]) ).
thf(6660,plain,
! [A: $i] :
( ( A
!= ( sk1 @ powerset @ singleton ) )
| ~ ( sk1 @ powerset @ union @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[6659:[bind(A,$thf( sk1 @ powerset @ union @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(6702,plain,
~ ( sk1 @ powerset @ union @ singleton @ singleton @ singleton @ ( sk1 @ powerset @ singleton @ in ) ),
inference(simp,[status(thm)],[6660]) ).
thf(9416,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk13 @ powerset @ singleton @ singleton @ ( sk12 @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,4844]) ).
thf(9417,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk13 @ powerset @ singleton @ singleton @ ( sk12 @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[9416]) ).
thf(9521,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk13 @ powerset @ singleton @ singleton ) )
| ( A
!= ( sk12 @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[9417]) ).
thf(9533,plain,
( ( sk12 @ singleton @ singleton @ singleton )
!= ( sk13 @ powerset @ singleton @ singleton ) ),
inference(simp,[status(thm)],[9521]) ).
thf(2502,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ powerset @ singleton @ ( B @ in ) ) )
| ( ( B @ union )
!= sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,211]) ).
thf(2503,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ powerset @ singleton @ ( B @ in ) ) )
| ( ( B @ union )
!= sk1 ) ),
inference(simp,[status(thm)],[2502]) ).
thf(2565,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset )
!= ( sk1 @ powerset @ singleton ) )
| ( A != B )
| ( ( B @ union )
!= sk1 ) ),
inference(simp,[status(thm)],[2503]) ).
thf(2586,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk1 @ powerset @ singleton ) )
| ( ( A @ union )
!= sk1 ) ),
inference(simp,[status(thm)],[2565]) ).
thf(4946,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk13 @ singleton @ singleton ) )
| ( B
!= ( sk12 @ powerset @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,3769]) ).
thf(4947,plain,
! [A: $i] :
( ( A
!= ( sk12 @ powerset @ singleton ) )
| ~ ( sk13 @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[4946:[bind(A,$thf( sk13 @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(4974,plain,
~ ( sk13 @ singleton @ singleton @ singleton @ ( sk12 @ powerset @ singleton @ in ) ),
inference(simp,[status(thm)],[4947]) ).
thf(11094,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ singleton @ singleton @ singleton @ ( sk12 @ powerset @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,4974]) ).
thf(11095,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ singleton @ singleton @ singleton @ ( sk12 @ powerset @ singleton @ in ) ) ),
inference(simp,[status(thm)],[11094]) ).
thf(11233,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk13 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk12 @ powerset @ singleton ) ) ),
inference(simp,[status(thm)],[11095]) ).
thf(11253,plain,
( ( sk13 @ singleton @ singleton @ singleton )
!= ( sk12 @ powerset @ singleton @ powerset ) ),
inference(simp,[status(thm)],[11233]) ).
thf(2618,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk12 @ singleton ) )
| ( B
!= ( sk13 @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,2583]) ).
thf(2619,plain,
! [A: $i] :
( ( A
!= ( sk13 @ powerset ) )
| ~ ( sk12 @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[2618:[bind(A,$thf( sk12 @ singleton )),bind(B,$thf( B ))]]) ).
thf(2629,plain,
~ ( sk12 @ singleton @ singleton @ ( sk13 @ powerset @ in ) ),
inference(simp,[status(thm)],[2619]) ).
thf(3611,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ singleton @ singleton @ ( sk13 @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,2629]) ).
thf(3612,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ singleton @ singleton @ ( sk13 @ powerset @ in ) ) ),
inference(simp,[status(thm)],[3611]) ).
thf(3676,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk12 @ singleton @ singleton ) )
| ( A
!= ( sk13 @ powerset ) ) ),
inference(simp,[status(thm)],[3612]) ).
thf(3686,plain,
( ( sk12 @ singleton @ singleton )
!= ( sk13 @ powerset @ powerset ) ),
inference(simp,[status(thm)],[3676]) ).
thf(4859,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk12 @ singleton @ singleton ) )
| ( B
!= ( sk13 @ powerset @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,3686]) ).
thf(4860,plain,
! [A: $i] :
( ( A
!= ( sk13 @ powerset @ powerset ) )
| ~ ( sk12 @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[4859:[bind(A,$thf( sk12 @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(4888,plain,
~ ( sk12 @ singleton @ singleton @ singleton @ ( sk13 @ powerset @ powerset @ in ) ),
inference(simp,[status(thm)],[4860]) ).
thf(1116,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk13 @ singleton @ singleton @ singleton ) )
| ( B
!= ( sk12 @ singleton @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,909]) ).
thf(1117,plain,
! [A: $i] :
( ( A
!= ( sk12 @ singleton @ singleton @ singleton ) )
| ~ ( sk13 @ singleton @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[1116:[bind(A,$thf( sk13 @ singleton @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(1143,plain,
~ ( sk13 @ singleton @ singleton @ singleton @ singleton @ ( sk12 @ singleton @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[1117]) ).
thf(2516,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ singleton @ singleton @ singleton @ singleton @ ( sk12 @ singleton @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,1143]) ).
thf(2517,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ singleton @ singleton @ singleton @ singleton @ ( sk12 @ singleton @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[2516]) ).
thf(2568,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk13 @ singleton @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk12 @ singleton @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[2517]) ).
thf(2589,plain,
( ( sk13 @ singleton @ singleton @ singleton @ singleton )
!= ( sk12 @ singleton @ singleton @ singleton @ powerset ) ),
inference(simp,[status(thm)],[2568]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( ( B @ powerset @ union )
!= sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,15]) ).
thf(173,plain,
! [A: $i] :
( ( ( A @ powerset @ union )
!= sk1 )
| ~ ( sk1 @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[172:[bind(A,$thf( sk1 ))]]) ).
thf(212,plain,
! [A: $i] :
( ( ( A @ powerset @ union )
!= sk1 )
| ~ ( sk1 @ singleton @ ( A @ in ) ) ),
inference(simp,[status(thm)],[173]) ).
thf(2520,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ singleton @ ( B @ in ) ) )
| ( ( B @ powerset @ union )
!= sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,212]) ).
thf(2521,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ singleton @ ( B @ in ) ) )
| ( ( B @ powerset @ union )
!= sk1 ) ),
inference(simp,[status(thm)],[2520]) ).
thf(2578,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset )
!= ( sk1 @ singleton ) )
| ( A != B )
| ( ( B @ powerset @ union )
!= sk1 ) ),
inference(simp,[status(thm)],[2521]) ).
thf(2601,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk1 @ singleton ) )
| ( ( A @ powerset @ union )
!= sk1 ) ),
inference(simp,[status(thm)],[2578]) ).
thf(2656,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk12 @ singleton @ singleton ) )
| ( A
!= ( sk13 @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,2592]) ).
thf(2657,plain,
! [A: $i] :
( ( A
!= ( sk13 @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( sk12 @ singleton @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[2656:[bind(A,$thf( A )),bind(B,$thf( sk12 @ singleton @ singleton ))]]) ).
thf(2677,plain,
~ ( sk13 @ singleton @ powerset @ singleton @ ( sk12 @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[2657]) ).
thf(6236,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk13 @ singleton @ powerset @ singleton @ ( sk12 @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,2677]) ).
thf(6237,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk13 @ singleton @ powerset @ singleton @ ( sk12 @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[6236]) ).
thf(6317,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk13 @ singleton @ powerset @ singleton ) )
| ( A
!= ( sk12 @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[6237]) ).
thf(6328,plain,
( ( sk12 @ singleton @ singleton @ singleton )
!= ( sk13 @ singleton @ powerset @ singleton ) ),
inference(simp,[status(thm)],[6317]) ).
thf(3862,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk13 @ powerset @ singleton ) )
| ( B
!= ( sk12 @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,3602]) ).
thf(3863,plain,
! [A: $i] :
( ( A
!= ( sk12 @ singleton @ powerset ) )
| ~ ( sk13 @ powerset @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[3862:[bind(A,$thf( sk13 @ powerset @ singleton )),bind(B,$thf( B ))]]) ).
thf(3884,plain,
~ ( sk13 @ powerset @ singleton @ singleton @ ( sk12 @ singleton @ powerset @ in ) ),
inference(simp,[status(thm)],[3863]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ powerset ) )
| ( ( A @ union )
!= sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,15]) ).
thf(165,plain,
! [A: $i] :
( ( ( A @ union )
!= sk1 )
| ~ ( A @ singleton @ ( sk1 @ powerset @ in ) ) ),
inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( A )),bind(B,$thf( sk1 @ powerset ))]]) ).
thf(125,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( B @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,124]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( B @ in ) ) ),
inference(simp,[status(thm)],[125]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= B )
| ( A != B ) ),
inference(simp,[status(thm)],[126]) ).
thf(136,plain,
! [A: $i] :
( ( A @ singleton )
!= A ),
inference(simp,[status(thm)],[133]) ).
thf(195,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ singleton ) )
| ( B != C )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,136]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[195:[bind(A,$thf( D @ singleton )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(199,plain,
! [A: $i] :
~ ( A @ singleton @ singleton @ ( A @ in ) ),
inference(simp,[status(thm)],[196]) ).
thf(1146,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( B @ singleton @ singleton @ ( B @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,199]) ).
thf(1147,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( B @ singleton @ singleton @ ( B @ in ) ) ),
inference(simp,[status(thm)],[1146]) ).
thf(1166,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= ( B @ singleton @ singleton ) )
| ( A != B ) ),
inference(simp,[status(thm)],[1147]) ).
thf(1174,plain,
! [A: $i] :
( ( A @ singleton @ singleton )
!= ( A @ singleton ) ),
inference(simp,[status(thm)],[1166]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ union ) )
| ( A @ ( B @ sk11 ) @ ( A @ ( B @ sk10 ) @ in ) )
| ( B @ ( A @ sk8 ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk11 ) @ ( A @ ( B @ sk10 ) @ in ) )
| ( B @ ( A @ sk8 ) )
| ( B
= ( A @ union ) ) ),
inference(lifteq,[status(thm)],[72]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk11 ) @ ( A @ ( B @ sk10 ) @ in ) )
| ( B @ ( A @ sk8 ) )
| ( B
= ( A @ union ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(4853,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk12 @ singleton @ singleton ) )
| ( A
!= ( sk13 @ powerset @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,3686]) ).
thf(4854,plain,
! [A: $i] :
( ( A
!= ( sk13 @ powerset @ powerset ) )
| ~ ( A @ singleton @ ( sk12 @ singleton @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[4853:[bind(A,$thf( A )),bind(B,$thf( sk12 @ singleton @ singleton ))]]) ).
thf(4887,plain,
~ ( sk13 @ powerset @ powerset @ singleton @ ( sk12 @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[4854]) ).
thf(9742,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk13 @ powerset @ powerset @ singleton @ ( sk12 @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,4887]) ).
thf(9743,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk13 @ powerset @ powerset @ singleton @ ( sk12 @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[9742]) ).
thf(9844,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk13 @ powerset @ powerset @ singleton ) )
| ( A
!= ( sk12 @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[9743]) ).
thf(9868,plain,
( ( sk12 @ singleton @ singleton @ singleton )
!= ( sk13 @ powerset @ powerset @ singleton ) ),
inference(simp,[status(thm)],[9844]) ).
thf(2522,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk1 @ powerset @ union @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,503]) ).
thf(2523,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk1 @ powerset @ union @ singleton @ in ) ) ),
inference(simp,[status(thm)],[2522]) ).
thf(2560,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk1 @ singleton @ singleton ) )
| ( A
!= ( sk1 @ powerset @ union @ singleton ) ) ),
inference(simp,[status(thm)],[2523]) ).
thf(2581,plain,
( ( sk1 @ singleton @ singleton )
!= ( sk1 @ powerset @ union @ singleton @ powerset ) ),
inference(simp,[status(thm)],[2560]) ).
thf(2880,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ singleton @ singleton ) )
| ( B
!= ( sk1 @ powerset @ union @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,2581]) ).
thf(2881,plain,
! [A: $i] :
( ( A
!= ( sk1 @ powerset @ union @ singleton @ powerset ) )
| ~ ( sk1 @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[2880:[bind(A,$thf( sk1 @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(2895,plain,
~ ( sk1 @ singleton @ singleton @ singleton @ ( sk1 @ powerset @ union @ singleton @ powerset @ in ) ),
inference(simp,[status(thm)],[2881]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ powerset ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ in ) )
| ~ ( A @ ( A @ ( B @ sk4 ) @ subset ) ) ),
inference(cnfConj,[status(thm)],[41]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk5 ) @ in ) )
| ~ ( A @ ( A @ ( B @ sk4 ) @ subset ) )
| ( B
= ( A @ powerset ) ) ),
inference(lifteq,[status(thm)],[45]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk5 ) @ in ) )
| ~ ( A @ ( A @ ( B @ sk4 ) @ subset ) )
| ( B
= ( A @ powerset ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(2526,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( C @ ( B @ in ) ) )
| ~ ( B @ ( C @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,17]) ).
thf(2527,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( C @ ( B @ in ) ) )
| ~ ( B @ ( C @ in ) ) ),
inference(simp,[status(thm)],[2526]) ).
thf(2528,plain,
! [A: $i] :
~ ( A @ ( A @ powerset @ in ) ),
inference(pattern_uni,[status(thm)],[2527:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ powerset ))]]) ).
thf(2605,plain,
! [A: $i] :
~ ( A @ ( A @ powerset @ in ) ),
inference(simp,[status(thm)],[2528]) ).
thf(25853,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( B @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,2605]) ).
thf(25854,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( B @ powerset @ in ) ) ),
inference(simp,[status(thm)],[25853]) ).
thf(25900,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= B )
| ( A
!= ( B @ powerset ) ) ),
inference(simp,[status(thm)],[25854]) ).
thf(25925,plain,
! [A: $i] :
( ( A @ powerset @ singleton )
!= A ),
inference(simp,[status(thm)],[25900]) ).
thf(127,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( C @ ( B @ in ) ) )
| ~ ( B @ ( C @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,17]) ).
thf(128,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( C @ ( B @ in ) ) )
| ~ ( B @ ( C @ in ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(129,plain,
! [A: $i] :
~ ( A @ ( A @ singleton @ in ) ),
inference(pattern_uni,[status(thm)],[128:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ singleton ))]]) ).
thf(134,plain,
! [A: $i] :
~ ( A @ ( A @ singleton @ in ) ),
inference(simp,[status(thm)],[129]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( B @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,134]) ).
thf(139,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( B @ singleton @ in ) ) ),
inference(simp,[status(thm)],[138]) ).
thf(140,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= B )
| ( A
!= ( B @ singleton ) ) ),
inference(simp,[status(thm)],[139]) ).
thf(141,plain,
! [A: $i] :
( ( A @ singleton @ singleton )
!= A ),
inference(simp,[status(thm)],[140]) ).
thf(4895,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk12 @ powerset @ singleton ) )
| ( A
!= ( sk13 @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,3767]) ).
thf(4896,plain,
! [A: $i] :
( ( A
!= ( sk13 @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( sk12 @ powerset @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[4895:[bind(A,$thf( A )),bind(B,$thf( sk12 @ powerset @ singleton ))]]) ).
thf(4927,plain,
~ ( sk13 @ singleton @ powerset @ singleton @ ( sk12 @ powerset @ singleton @ in ) ),
inference(simp,[status(thm)],[4896]) ).
thf(10046,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ singleton @ powerset @ singleton @ ( sk12 @ powerset @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,4927]) ).
thf(10047,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ singleton @ powerset @ singleton @ ( sk12 @ powerset @ singleton @ in ) ) ),
inference(simp,[status(thm)],[10046]) ).
thf(10187,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk13 @ singleton @ powerset @ singleton ) )
| ( A
!= ( sk12 @ powerset @ singleton ) ) ),
inference(simp,[status(thm)],[10047]) ).
thf(10203,plain,
( ( sk13 @ singleton @ powerset @ singleton )
!= ( sk12 @ powerset @ singleton @ powerset ) ),
inference(simp,[status(thm)],[10187]) ).
thf(4817,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk12 @ singleton @ singleton ) )
| ( B
!= ( sk13 @ powerset @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,3604]) ).
thf(4818,plain,
! [A: $i] :
( ( A
!= ( sk13 @ powerset @ singleton ) )
| ~ ( sk12 @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[4817:[bind(A,$thf( sk12 @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(4845,plain,
~ ( sk12 @ singleton @ singleton @ singleton @ ( sk13 @ powerset @ singleton @ in ) ),
inference(simp,[status(thm)],[4818]) ).
thf(3505,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk13 @ singleton @ singleton ) )
| ( B
!= ( sk12 @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,2609]) ).
thf(3506,plain,
! [A: $i] :
( ( A
!= ( sk12 @ singleton @ powerset ) )
| ~ ( sk13 @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[3505:[bind(A,$thf( sk13 @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(3528,plain,
~ ( sk13 @ singleton @ singleton @ singleton @ ( sk12 @ singleton @ powerset @ in ) ),
inference(simp,[status(thm)],[3506]) ).
thf(7867,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ singleton @ singleton @ singleton @ ( sk12 @ singleton @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,3528]) ).
thf(7868,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ singleton @ singleton @ singleton @ ( sk12 @ singleton @ powerset @ in ) ) ),
inference(simp,[status(thm)],[7867]) ).
thf(8003,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk13 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk12 @ singleton @ powerset ) ) ),
inference(simp,[status(thm)],[7868]) ).
thf(8016,plain,
( ( sk13 @ singleton @ singleton @ singleton )
!= ( sk12 @ singleton @ powerset @ powerset ) ),
inference(simp,[status(thm)],[8003]) ).
thf(9706,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ powerset @ powerset @ singleton @ ( sk12 @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,4887]) ).
thf(9707,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ powerset @ powerset @ singleton @ ( sk12 @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[9706]) ).
thf(9849,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk13 @ powerset @ powerset @ singleton ) )
| ( A
!= ( sk12 @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[9707]) ).
thf(9872,plain,
( ( sk12 @ singleton @ singleton @ powerset )
!= ( sk13 @ powerset @ powerset @ singleton ) ),
inference(simp,[status(thm)],[9849]) ).
thf(811,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ powerset @ union @ singleton @ singleton ) )
| ( A
!= ( sk1 @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,687]) ).
thf(812,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( sk1 @ powerset @ union @ singleton @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[811:[bind(A,$thf( A )),bind(B,$thf( sk1 @ powerset @ union @ singleton @ singleton ))]]) ).
thf(844,plain,
~ ( sk1 @ singleton @ singleton @ singleton @ ( sk1 @ powerset @ union @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[812]) ).
thf(1177,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ singleton @ ( sk1 @ powerset @ union @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,844]) ).
thf(1178,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ singleton @ ( sk1 @ powerset @ union @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1177]) ).
thf(1242,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk1 @ powerset @ union @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[1178]) ).
thf(1249,plain,
( ( sk1 @ powerset @ union @ singleton @ singleton @ singleton )
!= ( sk1 @ singleton @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1242]) ).
thf(2874,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ singleton @ singleton ) )
| ( A
!= ( sk1 @ powerset @ union @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,2581]) ).
thf(2875,plain,
! [A: $i] :
( ( A
!= ( sk1 @ powerset @ union @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( sk1 @ singleton @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[2874:[bind(A,$thf( A )),bind(B,$thf( sk1 @ singleton @ singleton ))]]) ).
thf(2900,plain,
~ ( sk1 @ powerset @ union @ singleton @ powerset @ singleton @ ( sk1 @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[2875]) ).
thf(789,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk13 @ singleton @ singleton ) )
| ( B
!= ( sk12 @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,550]) ).
thf(790,plain,
! [A: $i] :
( ( A
!= ( sk12 @ singleton @ singleton ) )
| ~ ( sk13 @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[789:[bind(A,$thf( sk13 @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(807,plain,
~ ( sk13 @ singleton @ singleton @ singleton @ ( sk12 @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[790]) ).
thf(2553,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ singleton @ singleton @ singleton @ ( sk12 @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,807]) ).
thf(2554,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ singleton @ singleton @ singleton @ ( sk12 @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[2553]) ).
thf(2567,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk13 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk12 @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[2554]) ).
thf(2588,plain,
( ( sk13 @ singleton @ singleton @ singleton )
!= ( sk12 @ singleton @ singleton @ powerset ) ),
inference(simp,[status(thm)],[2567]) ).
thf(6086,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk13 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk12 @ singleton @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,2588]) ).
thf(6087,plain,
! [A: $i] :
( ( A
!= ( sk12 @ singleton @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( sk13 @ singleton @ singleton @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[6086:[bind(A,$thf( A )),bind(B,$thf( sk13 @ singleton @ singleton @ singleton ))]]) ).
thf(6129,plain,
~ ( sk12 @ singleton @ singleton @ powerset @ singleton @ ( sk13 @ singleton @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[6087]) ).
thf(1849,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk6 ) @ in ) )
!= ( C @ powerset @ ( D @ in ) ) )
| ( C @ ( D @ subset ) )
| ~ $true
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[66,49]) ).
thf(1850,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk6 ) @ in ) )
!= ( C @ powerset @ ( D @ in ) ) )
| ( C @ ( D @ subset ) )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[1849]) ).
thf(1851,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ powerset @ ( A @ sk6 ) @ subset ) )
| ( A @ ( B @ powerset @ subset ) ) ),
inference(pattern_uni,[status(thm)],[1850:[bind(A,$thf( G @ powerset )),bind(B,$thf( E )),bind(C,$thf( G )),bind(D,$thf( G @ powerset @ ( E @ sk6 ) ))]]) ).
thf(1857,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ powerset @ ( A @ sk6 ) @ subset ) )
| ( A @ ( B @ powerset @ subset ) ) ),
inference(simp,[status(thm)],[1851]) ).
thf(10932,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ powerset @ singleton @ singleton @ ( sk13 @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,4973]) ).
thf(10933,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ powerset @ singleton @ singleton @ ( sk13 @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[10932]) ).
thf(11071,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk12 @ powerset @ singleton @ singleton ) )
| ( A
!= ( sk13 @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[10933]) ).
thf(11084,plain,
( ( sk12 @ powerset @ singleton @ singleton )
!= ( sk13 @ singleton @ singleton @ powerset ) ),
inference(simp,[status(thm)],[11071]) ).
thf(3934,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ powerset @ singleton @ ( sk1 @ powerset @ union @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,2716]) ).
thf(3935,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ powerset @ singleton @ ( sk1 @ powerset @ union @ singleton @ in ) ) ),
inference(simp,[status(thm)],[3934]) ).
thf(4018,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk1 @ powerset @ singleton ) )
| ( A
!= ( sk1 @ powerset @ union @ singleton ) ) ),
inference(simp,[status(thm)],[3935]) ).
thf(4035,plain,
( ( sk1 @ powerset @ union @ singleton @ powerset )
!= ( sk1 @ powerset @ singleton ) ),
inference(simp,[status(thm)],[4018]) ).
thf(6543,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ powerset @ singleton ) )
| ( B
!= ( sk1 @ powerset @ union @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,4035]) ).
thf(6544,plain,
! [A: $i] :
( ( A
!= ( sk1 @ powerset @ union @ singleton @ powerset ) )
| ~ ( sk1 @ powerset @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[6543:[bind(A,$thf( sk1 @ powerset @ singleton )),bind(B,$thf( B ))]]) ).
thf(6610,plain,
~ ( sk1 @ powerset @ singleton @ singleton @ ( sk1 @ powerset @ union @ singleton @ powerset @ in ) ),
inference(simp,[status(thm)],[6544]) ).
thf(27629,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( B @ powerset @ singleton @ ( B @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,6063]) ).
thf(27630,plain,
! [B: $i,A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( B @ powerset @ singleton @ ( B @ in ) ) ),
inference(simp,[status(thm)],[27629]) ).
thf(27734,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset )
!= ( B @ powerset @ singleton ) )
| ( A != B ) ),
inference(simp,[status(thm)],[27630]) ).
thf(27762,plain,
! [A: $i] :
( ( A @ powerset @ singleton )
!= ( A @ powerset ) ),
inference(simp,[status(thm)],[27734]) ).
thf(488,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ powerset @ union @ singleton ) )
| ( B
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,323]) ).
thf(489,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( sk1 @ powerset @ union @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[488:[bind(A,$thf( sk1 @ powerset @ union @ singleton )),bind(B,$thf( B ))]]) ).
thf(505,plain,
~ ( sk1 @ powerset @ union @ singleton @ singleton @ ( sk1 @ singleton @ in ) ),
inference(simp,[status(thm)],[489]) ).
thf(2541,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ powerset @ union @ singleton @ singleton @ ( sk1 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,505]) ).
thf(2542,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ powerset @ union @ singleton @ singleton @ ( sk1 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[2541]) ).
thf(2564,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk1 @ powerset @ union @ singleton @ singleton ) )
| ( A
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[2542]) ).
thf(2585,plain,
( ( sk1 @ powerset @ union @ singleton @ singleton )
!= ( sk1 @ singleton @ powerset ) ),
inference(simp,[status(thm)],[2564]) ).
thf(6048,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ powerset ) )
| ( A != C )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,2598]) ).
thf(6049,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( A @ singleton @ ( B @ powerset @ in ) ) ),
inference(pattern_uni,[status(thm)],[6048:[bind(A,$thf( A )),bind(B,$thf( D @ powerset )),bind(C,$thf( D ))]]) ).
thf(6062,plain,
! [A: $i] :
~ ( A @ singleton @ ( A @ powerset @ in ) ),
inference(simp,[status(thm)],[6049]) ).
thf(27484,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( B @ singleton @ ( B @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,6062]) ).
thf(27485,plain,
! [B: $i,A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( B @ singleton @ ( B @ powerset @ in ) ) ),
inference(simp,[status(thm)],[27484]) ).
thf(27592,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset )
!= ( B @ singleton ) )
| ( A
!= ( B @ powerset ) ) ),
inference(simp,[status(thm)],[27485]) ).
thf(27599,plain,
! [A: $i] :
( ( A @ singleton )
!= ( A @ powerset @ powerset ) ),
inference(simp,[status(thm)],[27592]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ~ ( B @ ( A @ ( B @ sk3 ) @ in ) )
| ( B @ ( A @ ( B @ sk2 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk3 ) @ in ) )
| ( B @ ( A @ ( B @ sk2 ) @ in ) )
| ( B
= ( A @ singleton ) ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk3 ) @ in ) )
| ( B @ ( A @ ( B @ sk2 ) @ in ) )
| ( B
= ( A @ singleton ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk3 ) )
= A )
| ( ( A @ ( B @ sk2 ) )
!= A ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk3 ) )
= A )
| ( ( A @ ( B @ sk2 ) )
!= A ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk3 ) )
= A )
| ( ( A @ ( B @ sk2 ) )
!= A ) ),
inference(simp,[status(thm)],[33]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ powerset ) )
| ( A @ ( A @ ( B @ sk5 ) @ subset ) )
| ( B @ ( A @ ( B @ sk4 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[41]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk5 ) @ subset ) )
| ( B @ ( A @ ( B @ sk4 ) @ in ) )
| ( B
= ( A @ powerset ) ) ),
inference(lifteq,[status(thm)],[47]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk5 ) @ subset ) )
| ( B @ ( A @ ( B @ sk4 ) @ in ) )
| ( B
= ( A @ powerset ) ) ),
inference(simp,[status(thm)],[58]) ).
thf(6202,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ singleton @ powerset @ singleton @ ( sk12 @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,2677]) ).
thf(6203,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ singleton @ powerset @ singleton @ ( sk12 @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[6202]) ).
thf(6318,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk13 @ singleton @ powerset @ singleton ) )
| ( A
!= ( sk12 @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[6203]) ).
thf(6329,plain,
( ( sk12 @ singleton @ singleton @ powerset )
!= ( sk13 @ singleton @ powerset @ singleton ) ),
inference(simp,[status(thm)],[6318]) ).
thf(11787,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset )
!= ( sk12 @ singleton @ singleton @ powerset ) )
| ( B
!= ( sk13 @ singleton @ powerset @ singleton ) )
| ( A @ ( A @ ( B @ sk5 ) @ subset ) )
| ( B @ ( A @ ( B @ sk4 ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[59,6329]) ).
thf(11788,plain,
! [A: $i] :
( ( A
!= ( sk13 @ singleton @ powerset @ singleton ) )
| ( sk12 @ singleton @ singleton @ ( sk12 @ singleton @ singleton @ ( A @ sk5 ) @ subset ) )
| ( A @ ( sk12 @ singleton @ singleton @ ( A @ sk4 ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[11787:[bind(A,$thf( sk12 @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(11809,plain,
( ( sk12 @ singleton @ singleton @ ( sk12 @ singleton @ singleton @ ( sk13 @ singleton @ powerset @ singleton @ sk5 ) @ subset ) )
| ( sk13 @ singleton @ powerset @ singleton @ ( sk12 @ singleton @ singleton @ ( sk13 @ singleton @ powerset @ singleton @ sk4 ) @ in ) ) ),
inference(simp,[status(thm)],[11788]) ).
thf(7306,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset )
!= ( sk1 @ powerset @ union @ singleton @ powerset ) )
| ( B
!= ( sk1 @ powerset @ singleton ) )
| ( A @ ( A @ ( B @ sk5 ) @ subset ) )
| ( B @ ( A @ ( B @ sk4 ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[59,4035]) ).
thf(7307,plain,
! [A: $i] :
( ( A
!= ( sk1 @ powerset @ singleton ) )
| ( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ union @ singleton @ ( A @ sk5 ) @ subset ) )
| ( A @ ( sk1 @ powerset @ union @ singleton @ ( A @ sk4 ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[7306:[bind(A,$thf( sk1 @ powerset @ union @ singleton )),bind(B,$thf( B ))]]) ).
thf(7570,plain,
( ( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ singleton @ sk5 ) @ subset ) )
| ( sk1 @ powerset @ singleton @ ( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ singleton @ sk4 ) @ in ) ) ),
inference(simp,[status(thm)],[7307]) ).
thf(8579,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ powerset @ singleton @ ( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ singleton @ sk4 ) @ in ) )
!= ( A @ singleton @ ( B @ in ) ) )
| ~ $true
| ( B = A )
| ( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ singleton @ sk5 ) @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[7570,38]) ).
thf(8580,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ powerset @ singleton @ ( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ singleton @ sk4 ) @ in ) )
!= ( A @ singleton @ ( B @ in ) ) )
| ( B = A )
| ( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ singleton @ sk5 ) @ subset ) ) ),
inference(simp,[status(thm)],[8579]) ).
thf(8581,plain,
( ( ( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ singleton @ sk4 ) )
= ( sk1 @ powerset ) )
| ( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ singleton @ sk5 ) @ subset ) ) ),
inference(pattern_uni,[status(thm)],[8580:[bind(A,$thf( sk1 @ powerset )),bind(B,$thf( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ singleton @ sk4 ) ))]]) ).
thf(27504,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( B @ singleton @ ( B @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,6062]) ).
thf(27505,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( B @ singleton @ ( B @ powerset @ in ) ) ),
inference(simp,[status(thm)],[27504]) ).
thf(27576,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= ( B @ singleton ) )
| ( A
!= ( B @ powerset ) ) ),
inference(simp,[status(thm)],[27505]) ).
thf(27618,plain,
! [A: $i] :
( ( A @ powerset @ singleton )
!= ( A @ singleton ) ),
inference(simp,[status(thm)],[27576]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk7 ) ) @ ( C @ in ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ union ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(85,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk7 ) ) @ ( C @ in ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ union ) ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(86,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ union @ ( B @ sk7 ) ) @ ( B @ in ) )
| ~ ( A @ union @ ( B @ in ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(2912,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ powerset @ union @ singleton @ singleton ) )
| ( A
!= ( sk1 @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,2585]) ).
thf(2913,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( sk1 @ powerset @ union @ singleton @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[2912:[bind(A,$thf( A )),bind(B,$thf( sk1 @ powerset @ union @ singleton @ singleton ))]]) ).
thf(2943,plain,
~ ( sk1 @ singleton @ powerset @ singleton @ ( sk1 @ powerset @ union @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[2913]) ).
thf(11256,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ powerset @ powerset @ singleton @ ( sk13 @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,6039]) ).
thf(11257,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ powerset @ powerset @ singleton @ ( sk13 @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[11256]) ).
thf(11398,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk12 @ powerset @ powerset @ singleton ) )
| ( A
!= ( sk13 @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[11257]) ).
thf(11406,plain,
( ( sk13 @ singleton @ singleton @ powerset )
!= ( sk12 @ powerset @ powerset @ singleton ) ),
inference(simp,[status(thm)],[11398]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ singleton @ subset ) )
<=> ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(95,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ subset ) ) )
& ( ( B @ ( A @ singleton @ subset ) )
=> ( B @ ( A @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(96,plain,
( ! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ subset ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ singleton @ subset ) )
=> ( B @ ( A @ in ) ) ) ),
inference(miniscope,[status(thm)],[95]) ).
thf(97,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ singleton @ subset ) )
| ~ ( D @ ( C @ in ) ) )
& ( ( B @ ( A @ in ) )
| ~ ( B @ ( A @ singleton @ subset ) ) ) ),
inference(cnf,[status(esa)],[96]) ).
thf(98,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ in ) )
| ~ ( B @ ( A @ singleton @ subset ) ) ),
inference(cnfConj,[status(thm)],[97]) ).
thf(6527,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ powerset @ singleton ) )
| ( A
!= ( sk1 @ powerset @ union @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,4035]) ).
thf(6528,plain,
! [A: $i] :
( ( A
!= ( sk1 @ powerset @ union @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( sk1 @ powerset @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[6527:[bind(A,$thf( A )),bind(B,$thf( sk1 @ powerset @ singleton ))]]) ).
thf(6604,plain,
~ ( sk1 @ powerset @ union @ singleton @ powerset @ singleton @ ( sk1 @ powerset @ singleton @ in ) ),
inference(simp,[status(thm)],[6528]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( ( A @ powerset @ union )
!= sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,15]) ).
thf(167,plain,
! [A: $i] :
( ( ( A @ powerset @ union )
!= sk1 )
| ~ ( A @ singleton @ ( sk1 @ in ) ) ),
inference(pattern_uni,[status(thm)],[166:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(2543,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( B @ singleton @ ( sk1 @ in ) ) )
| ( ( B @ powerset @ union )
!= sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,167]) ).
thf(2544,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( B @ singleton @ ( sk1 @ in ) ) )
| ( ( B @ powerset @ union )
!= sk1 ) ),
inference(simp,[status(thm)],[2543]) ).
thf(2571,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset )
!= ( B @ singleton ) )
| ( A != sk1 )
| ( ( B @ powerset @ union )
!= sk1 ) ),
inference(simp,[status(thm)],[2544]) ).
thf(2593,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ powerset ) )
| ( ( A @ powerset @ union )
!= sk1 ) ),
inference(simp,[status(thm)],[2571]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
<=> ( B @ ( C @ in ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(108,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) )
& ( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(2539,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ singleton @ singleton @ singleton @ ( sk13 @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,804]) ).
thf(2540,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ singleton @ singleton @ singleton @ ( sk13 @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[2539]) ).
thf(2559,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk12 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk13 @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[2540]) ).
thf(2610,plain,
( ( sk12 @ singleton @ singleton @ singleton )
!= ( sk13 @ singleton @ singleton @ powerset ) ),
inference(simp,[status(thm)],[2559]) ).
thf(7743,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk12 @ singleton @ powerset @ singleton @ ( sk13 @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,3527]) ).
thf(7744,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk12 @ singleton @ powerset @ singleton @ ( sk13 @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[7743]) ).
thf(7844,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk12 @ singleton @ powerset @ singleton ) )
| ( A
!= ( sk13 @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[7744]) ).
thf(7852,plain,
( ( sk13 @ singleton @ singleton @ singleton )
!= ( sk12 @ singleton @ powerset @ singleton ) ),
inference(simp,[status(thm)],[7844]) ).
thf(2725,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ singleton ) )
| ( A
!= ( sk1 @ powerset @ union @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,2608]) ).
thf(2726,plain,
! [A: $i] :
( ( A
!= ( sk1 @ powerset @ union @ powerset ) )
| ~ ( A @ singleton @ ( sk1 @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[2725:[bind(A,$thf( A )),bind(B,$thf( sk1 @ singleton ))]]) ).
thf(2739,plain,
~ ( sk1 @ powerset @ union @ powerset @ singleton @ ( sk1 @ singleton @ in ) ),
inference(simp,[status(thm)],[2726]) ).
thf(5050,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ powerset @ union @ powerset @ singleton @ ( sk1 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,2739]) ).
thf(5051,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ powerset @ union @ powerset @ singleton @ ( sk1 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[5050]) ).
thf(5131,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ powerset @ union @ powerset @ singleton ) )
| ( A
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[5051]) ).
thf(5139,plain,
( ( sk1 @ singleton @ singleton )
!= ( sk1 @ powerset @ union @ powerset @ singleton ) ),
inference(simp,[status(thm)],[5131]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ union ) )
| ~ ( B @ ( A @ ( B @ sk10 ) @ in ) )
| ( B @ ( A @ sk8 ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk10 ) @ in ) )
| ( B @ ( A @ sk8 ) )
| ( B
= ( A @ union ) ) ),
inference(lifteq,[status(thm)],[78]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk10 ) @ in ) )
| ( B @ ( A @ sk8 ) )
| ( B
= ( A @ union ) ) ),
inference(simp,[status(thm)],[79]) ).
thf(6011,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk13 @ singleton @ singleton ) )
| ( B
!= ( sk12 @ powerset @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,3847]) ).
thf(6012,plain,
! [A: $i] :
( ( A
!= ( sk12 @ powerset @ powerset ) )
| ~ ( sk13 @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[6011:[bind(A,$thf( sk13 @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(6040,plain,
~ ( sk13 @ singleton @ singleton @ singleton @ ( sk12 @ powerset @ powerset @ in ) ),
inference(simp,[status(thm)],[6012]) ).
thf(11426,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ singleton @ singleton @ singleton @ ( sk12 @ powerset @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,6040]) ).
thf(11427,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ singleton @ singleton @ singleton @ ( sk12 @ powerset @ powerset @ in ) ) ),
inference(simp,[status(thm)],[11426]) ).
thf(11567,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk13 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk12 @ powerset @ powerset ) ) ),
inference(simp,[status(thm)],[11427]) ).
thf(11579,plain,
( ( sk13 @ singleton @ singleton @ singleton )
!= ( sk12 @ powerset @ powerset @ powerset ) ),
inference(simp,[status(thm)],[11567]) ).
thf(2508,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( B @ singleton @ ( sk1 @ powerset @ in ) ) )
| ( ( B @ union )
!= sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,165]) ).
thf(2509,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( B @ singleton @ ( sk1 @ powerset @ in ) ) )
| ( ( B @ union )
!= sk1 ) ),
inference(simp,[status(thm)],[2508]) ).
thf(2575,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset )
!= ( B @ singleton ) )
| ( A
!= ( sk1 @ powerset ) )
| ( ( B @ union )
!= sk1 ) ),
inference(simp,[status(thm)],[2509]) ).
thf(2597,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ powerset @ powerset ) )
| ( ( A @ union )
!= sk1 ) ),
inference(simp,[status(thm)],[2575]) ).
thf(821,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ powerset @ union @ singleton @ singleton ) )
| ( B
!= ( sk1 @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,687]) ).
thf(822,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton @ singleton ) )
| ~ ( sk1 @ powerset @ union @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[821:[bind(A,$thf( sk1 @ powerset @ union @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(845,plain,
~ ( sk1 @ powerset @ union @ singleton @ singleton @ singleton @ ( sk1 @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[822]) ).
thf(2545,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ powerset @ union @ singleton @ singleton @ singleton @ ( sk1 @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,845]) ).
thf(2546,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ powerset @ union @ singleton @ singleton @ singleton @ ( sk1 @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[2545]) ).
thf(2561,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk1 @ powerset @ union @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk1 @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[2546]) ).
thf(2582,plain,
( ( sk1 @ powerset @ union @ singleton @ singleton @ singleton )
!= ( sk1 @ singleton @ singleton @ powerset ) ),
inference(simp,[status(thm)],[2561]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ~ ( A @ ( C @ in ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[62]) ).
thf(25837,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( B @ ( B @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,2605]) ).
thf(25838,plain,
! [B: $i,A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( B @ ( B @ powerset @ in ) ) ),
inference(simp,[status(thm)],[25837]) ).
thf(25906,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset )
!= B )
| ( A
!= ( B @ powerset ) ) ),
inference(simp,[status(thm)],[25838]) ).
thf(25931,plain,
! [A: $i] :
( ( A @ powerset @ powerset )
!= A ),
inference(simp,[status(thm)],[25906]) ).
thf(2763,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk6 ) @ in ) )
!= ( C @ singleton @ ( D @ in ) ) )
| ~ $true
| ( D = C )
| ( B @ powerset @ ( A @ in ) ) ),
inference(paramod_ordered,[status(thm)],[2488,38]) ).
thf(2764,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk6 ) @ in ) )
!= ( C @ singleton @ ( D @ in ) ) )
| ( D = C )
| ( B @ powerset @ ( A @ in ) ) ),
inference(simp,[status(thm)],[2763]) ).
thf(2765,plain,
! [B: $i,A: $i] :
( ( ( B @ singleton @ ( A @ sk6 ) )
= B )
| ( A @ powerset @ ( B @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[2764:[bind(A,$thf( G @ singleton )),bind(B,$thf( E )),bind(C,$thf( G )),bind(D,$thf( G @ singleton @ ( E @ sk6 ) ))]]) ).
thf(2850,plain,
! [B: $i,A: $i] :
( ( ( B @ singleton @ ( A @ sk6 ) )
= B )
| ( A @ powerset @ ( B @ singleton @ in ) ) ),
inference(simp,[status(thm)],[2765]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk6 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[62]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk6 ) @ in ) ) ),
inference(simp,[status(thm)],[65]) ).
thf(9876,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ singleton @ singleton @ singleton @ ( sk13 @ powerset @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,4888]) ).
thf(9877,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ singleton @ singleton @ singleton @ ( sk13 @ powerset @ powerset @ in ) ) ),
inference(simp,[status(thm)],[9876]) ).
thf(10016,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk12 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk13 @ powerset @ powerset ) ) ),
inference(simp,[status(thm)],[9877]) ).
thf(10028,plain,
( ( sk12 @ singleton @ singleton @ singleton )
!= ( sk13 @ powerset @ powerset @ powerset ) ),
inference(simp,[status(thm)],[10016]) ).
thf(23437,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ powerset @ ( sk1 @ sk11 ) @ subset ) )
!= ( A @ ( B @ subset ) ) )
| ( A @ powerset @ ( B @ in ) )
| ~ $true
| ( sk1 @ ( sk1 @ powerset @ ( sk1 @ sk9 ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[23140,51]) ).
thf(23438,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ powerset @ ( sk1 @ sk11 ) @ subset ) )
!= ( A @ ( B @ subset ) ) )
| ( A @ powerset @ ( B @ in ) )
| ( sk1 @ ( sk1 @ powerset @ ( sk1 @ sk9 ) @ in ) ) ),
inference(simp,[status(thm)],[23437]) ).
thf(23439,plain,
( ( sk1 @ powerset @ ( sk1 @ powerset @ ( sk1 @ sk11 ) @ in ) )
| ( sk1 @ ( sk1 @ powerset @ ( sk1 @ sk9 ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[23438:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ powerset @ ( sk1 @ sk11 ) ))]]) ).
thf(2524,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( B @ ( B @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,134]) ).
thf(2525,plain,
! [B: $i,A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( B @ ( B @ singleton @ in ) ) ),
inference(simp,[status(thm)],[2524]) ).
thf(2563,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset )
!= B )
| ( A
!= ( B @ singleton ) ) ),
inference(simp,[status(thm)],[2525]) ).
thf(2584,plain,
! [A: $i] :
( ( A @ singleton @ powerset )
!= A ),
inference(simp,[status(thm)],[2563]) ).
thf(10742,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ singleton @ sk5 ) @ subset ) )
!= ( A @ ( B @ subset ) ) )
| ( A @ powerset @ ( B @ in ) )
| ~ $true
| ( ( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ singleton @ sk4 ) )
= ( sk1 @ powerset ) ) ),
inference(paramod_ordered,[status(thm)],[8581,51]) ).
thf(10743,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ singleton @ sk5 ) @ subset ) )
!= ( A @ ( B @ subset ) ) )
| ( A @ powerset @ ( B @ in ) )
| ( ( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ singleton @ sk4 ) )
= ( sk1 @ powerset ) ) ),
inference(simp,[status(thm)],[10742]) ).
thf(10744,plain,
( ( sk1 @ powerset @ union @ singleton @ powerset @ ( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ singleton @ sk5 ) @ in ) )
| ( ( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ singleton @ sk4 ) )
= ( sk1 @ powerset ) ) ),
inference(pattern_uni,[status(thm)],[10743:[bind(A,$thf( sk1 @ powerset @ union @ singleton )),bind(B,$thf( sk1 @ powerset @ union @ singleton @ ( sk1 @ powerset @ singleton @ sk5 ) ))]]) ).
thf(8061,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk12 @ singleton @ powerset @ singleton @ ( sk13 @ powerset @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,3883]) ).
thf(8062,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk12 @ singleton @ powerset @ singleton @ ( sk13 @ powerset @ singleton @ in ) ) ),
inference(simp,[status(thm)],[8061]) ).
thf(8160,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk12 @ singleton @ powerset @ singleton ) )
| ( A
!= ( sk13 @ powerset @ singleton ) ) ),
inference(simp,[status(thm)],[8062]) ).
thf(8183,plain,
( ( sk13 @ powerset @ singleton @ singleton )
!= ( sk12 @ singleton @ powerset @ singleton ) ),
inference(simp,[status(thm)],[8160]) ).
thf(25452,plain,
! [B: $i,A: $i] :
( ( ( A @ union )
!= ( sk1 @ powerset @ union ) )
| ( B != sk1 )
| ( A @ ( B @ sk11 ) @ ( A @ ( B @ sk10 ) @ in ) )
| ( B @ ( A @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[92,15]) ).
thf(25453,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk1 @ powerset @ ( A @ sk11 ) @ ( sk1 @ powerset @ ( A @ sk10 ) @ in ) )
| ( A @ ( sk1 @ powerset @ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[25452:[bind(A,$thf( sk1 @ powerset )),bind(B,$thf( B ))]]) ).
thf(25711,plain,
( ( sk1 @ powerset @ ( sk1 @ sk11 ) @ ( sk1 @ powerset @ ( sk1 @ sk10 ) @ in ) )
| ( sk1 @ ( sk1 @ powerset @ sk8 ) ) ),
inference(simp,[status(thm)],[25453]) ).
thf(1908,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk12 @ singleton @ singleton @ singleton @ singleton @ ( sk13 @ singleton @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,1142]) ).
thf(1909,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk12 @ singleton @ singleton @ singleton @ singleton @ ( sk13 @ singleton @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1908]) ).
thf(1979,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk12 @ singleton @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk13 @ singleton @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[1909]) ).
thf(1998,plain,
( ( sk13 @ singleton @ singleton @ singleton @ singleton )
!= ( sk12 @ singleton @ singleton @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1979]) ).
thf(8191,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ powerset @ singleton @ singleton @ ( sk12 @ singleton @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,3884]) ).
thf(8192,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk13 @ powerset @ singleton @ singleton @ ( sk12 @ singleton @ powerset @ in ) ) ),
inference(simp,[status(thm)],[8191]) ).
thf(8329,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk13 @ powerset @ singleton @ singleton ) )
| ( A
!= ( sk12 @ singleton @ powerset ) ) ),
inference(simp,[status(thm)],[8192]) ).
thf(8337,plain,
( ( sk13 @ powerset @ singleton @ singleton )
!= ( sk12 @ singleton @ powerset @ powerset ) ),
inference(simp,[status(thm)],[8329]) ).
thf(2547,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ singleton @ ( sk1 @ powerset @ union @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,844]) ).
thf(2548,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ singleton @ ( sk1 @ powerset @ union @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[2547]) ).
thf(2572,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk1 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk1 @ powerset @ union @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[2548]) ).
thf(2594,plain,
( ( sk1 @ singleton @ singleton @ singleton )
!= ( sk1 @ powerset @ union @ singleton @ singleton @ powerset ) ),
inference(simp,[status(thm)],[2572]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ powerset ) )
| ( A @ ( A @ ( B @ sk5 ) @ subset ) )
| ~ ( A @ ( A @ ( B @ sk4 ) @ subset ) ) ),
inference(cnfConj,[status(thm)],[41]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk5 ) @ subset ) )
| ~ ( A @ ( A @ ( B @ sk4 ) @ subset ) )
| ( B
= ( A @ powerset ) ) ),
inference(lifteq,[status(thm)],[44]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk5 ) @ subset ) )
| ~ ( A @ ( A @ ( B @ sk4 ) @ subset ) )
| ( B
= ( A @ powerset ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(17795,plain,
! [B: $i,A: $i] :
( ( ( sk13 @ singleton @ powerset @ singleton @ ( sk12 @ singleton @ singleton @ ( sk13 @ singleton @ powerset @ singleton @ sk4 ) @ in ) )
!= ( A @ singleton @ ( B @ in ) ) )
| ~ $true
| ( B = A )
| ( sk12 @ singleton @ singleton @ ( sk12 @ singleton @ singleton @ ( sk13 @ singleton @ powerset @ singleton @ sk5 ) @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[11809,38]) ).
thf(17796,plain,
! [B: $i,A: $i] :
( ( ( sk13 @ singleton @ powerset @ singleton @ ( sk12 @ singleton @ singleton @ ( sk13 @ singleton @ powerset @ singleton @ sk4 ) @ in ) )
!= ( A @ singleton @ ( B @ in ) ) )
| ( B = A )
| ( sk12 @ singleton @ singleton @ ( sk12 @ singleton @ singleton @ ( sk13 @ singleton @ powerset @ singleton @ sk5 ) @ subset ) ) ),
inference(simp,[status(thm)],[17795]) ).
thf(17797,plain,
( ( ( sk12 @ singleton @ singleton @ ( sk13 @ singleton @ powerset @ singleton @ sk4 ) )
= ( sk13 @ singleton @ powerset ) )
| ( sk12 @ singleton @ singleton @ ( sk12 @ singleton @ singleton @ ( sk13 @ singleton @ powerset @ singleton @ sk5 ) @ subset ) ) ),
inference(pattern_uni,[status(thm)],[17796:[bind(A,$thf( sk13 @ singleton @ powerset )),bind(B,$thf( sk12 @ singleton @ singleton @ ( sk13 @ singleton @ powerset @ singleton @ sk4 ) ))]]) ).
thf(2922,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ powerset @ union @ singleton @ singleton ) )
| ( B
!= ( sk1 @ singleton @ powerset ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[38,2585]) ).
thf(2923,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton @ powerset ) )
| ~ ( sk1 @ powerset @ union @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[2922:[bind(A,$thf( sk1 @ powerset @ union @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(2944,plain,
~ ( sk1 @ powerset @ union @ singleton @ singleton @ singleton @ ( sk1 @ singleton @ powerset @ in ) ),
inference(simp,[status(thm)],[2923]) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ union ) )
| ~ ( B @ ( A @ sk8 ) )
| ~ ( A @ ( C @ in ) )
| ~ ( C @ ( A @ ( B @ sk9 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(81,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ sk8 ) )
| ~ ( A @ ( C @ in ) )
| ~ ( C @ ( A @ ( B @ sk9 ) @ in ) )
| ( B
= ( A @ union ) ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ sk8 ) )
| ~ ( A @ ( C @ in ) )
| ~ ( C @ ( A @ ( B @ sk9 ) @ in ) )
| ( B
= ( A @ union ) ) ),
inference(simp,[status(thm)],[81]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ~ ( B @ ( A @ ( B @ sk3 ) @ in ) )
| ( ( A @ ( B @ sk2 ) )
!= A ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk3 ) @ in ) )
| ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk2 ) )
!= A ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk3 ) @ in ) )
| ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk2 ) )
!= A ) ),
inference(simp,[status(thm)],[35]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk3 ) )
= A )
| ( B @ ( A @ ( B @ sk2 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk2 ) @ in ) )
| ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk3 ) )
= A ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk2 ) @ in ) )
| ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk3 ) )
= A ) ),
inference(simp,[status(thm)],[29]) ).
thf(10082,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk13 @ singleton @ powerset @ singleton @ ( sk12 @ powerset @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,4927]) ).
thf(10083,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk13 @ singleton @ powerset @ singleton @ ( sk12 @ powerset @ singleton @ in ) ) ),
inference(simp,[status(thm)],[10082]) ).
thf(10189,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk13 @ singleton @ powerset @ singleton ) )
| ( A
!= ( sk12 @ powerset @ singleton ) ) ),
inference(simp,[status(thm)],[10083]) ).
thf(10205,plain,
( ( sk12 @ powerset @ singleton @ singleton )
!= ( sk13 @ singleton @ powerset @ singleton ) ),
inference(simp,[status(thm)],[10189]) ).
thf(9544,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ singleton @ singleton @ singleton @ ( sk13 @ powerset @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,4845]) ).
thf(9545,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ singleton @ singleton @ singleton @ ( sk13 @ powerset @ singleton @ in ) ) ),
inference(simp,[status(thm)],[9544]) ).
thf(9679,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk12 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk13 @ powerset @ singleton ) ) ),
inference(simp,[status(thm)],[9545]) ).
thf(9697,plain,
( ( sk12 @ singleton @ singleton @ singleton )
!= ( sk13 @ powerset @ singleton @ powerset ) ),
inference(simp,[status(thm)],[9679]) ).
thf(7709,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ singleton @ powerset @ singleton @ ( sk13 @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,3527]) ).
thf(7710,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk12 @ singleton @ powerset @ singleton @ ( sk13 @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[7709]) ).
thf(7842,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk12 @ singleton @ powerset @ singleton ) )
| ( A
!= ( sk13 @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[7710]) ).
thf(7851,plain,
( ( sk13 @ singleton @ singleton @ powerset )
!= ( sk12 @ singleton @ powerset @ singleton ) ),
inference(simp,[status(thm)],[7842]) ).
thf(75,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ~ ( A @ ( D @ in ) )
| ~ ( D @ ( C @ in ) )
| ( B
!= ( A @ union ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(93,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ~ ( A @ ( D @ in ) )
| ~ ( D @ ( C @ in ) )
| ( B
!= ( A @ union ) ) ),
inference(lifteq,[status(thm)],[75]) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ union @ ( B @ in ) )
| ~ ( A @ ( C @ in ) )
| ~ ( C @ ( B @ in ) ) ),
inference(simp,[status(thm)],[93]) ).
thf(2496,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( B @ singleton @ singleton @ ( B @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,199]) ).
thf(2497,plain,
! [B: $i,A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( B @ singleton @ singleton @ ( B @ in ) ) ),
inference(simp,[status(thm)],[2496]) ).
thf(2577,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset )
!= ( B @ singleton @ singleton ) )
| ( A != B ) ),
inference(simp,[status(thm)],[2497]) ).
thf(2600,plain,
! [A: $i] :
( ( A @ singleton @ singleton )
!= ( A @ powerset ) ),
inference(simp,[status(thm)],[2577]) ).
thf(5028,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ powerset @ union @ powerset @ singleton @ ( sk1 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,2739]) ).
thf(5029,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ powerset @ union @ powerset @ singleton @ ( sk1 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[5028]) ).
thf(5132,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk1 @ powerset @ union @ powerset @ singleton ) )
| ( A
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[5029]) ).
thf(5140,plain,
( ( sk1 @ powerset @ union @ powerset @ singleton )
!= ( sk1 @ singleton @ powerset ) ),
inference(simp,[status(thm)],[5132]) ).
thf(5152,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk1 @ powerset @ union @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2491,2740]) ).
thf(5153,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk1 @ powerset @ union @ powerset @ in ) ) ),
inference(simp,[status(thm)],[5152]) ).
thf(5254,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk1 @ singleton @ singleton ) )
| ( A
!= ( sk1 @ powerset @ union @ powerset ) ) ),
inference(simp,[status(thm)],[5153]) ).
thf(5261,plain,
( ( sk1 @ singleton @ singleton )
!= ( sk1 @ powerset @ union @ powerset @ powerset ) ),
inference(simp,[status(thm)],[5254]) ).
thf(65589,plain,
$false,
inference(e,[status(thm)],[101,909,2595,88,8186,3883,6063,1142,4973,11080,550,2740,2491,4137,6039,10382,6713,2488,23140,2603,2328,6470,4928,9529,289,57,3602,11404,475,2650,106,121,84,211,3527,687,2371,6702,9533,2586,60,11253,4888,201,3767,102,2589,2601,6328,1666,3884,165,1174,28,38,92,2628,2609,9868,1143,4974,2895,53,25925,141,10203,4845,8016,9872,124,2649,212,1249,2598,2900,6129,2581,13,503,134,1857,237,105,11084,6610,4036,2677,27762,2585,2717,27599,32,34,17,3686,11809,59,8581,2716,3604,27618,49,804,4887,86,2943,39,11406,98,6604,103,323,66,2593,108,2605,2610,4844,2592,7852,505,5139,80,167,209,2629,11579,2597,2582,63,4035,18,95,2588,2678,25931,2850,67,199,16,3847,3769,10028,23439,2584,845,10744,8183,25711,1998,844,7570,2591,8337,2594,55,2608,17797,2944,2739,4927,82,478,6062,36,30,51,10205,9697,210,107,7851,136,807,6040,94,6329,2600,5140,2583,15,200,68,90,3528,5261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU164+3 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.39 % Computer : n014.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 08:43:01 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.86/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/1.18 % [INFO] Parsing done (191ms).
% 1.39/1.20 % [INFO] Running in sequential loop mode.
% 2.04/1.61 % [INFO] eprover registered as external prover.
% 2.04/1.62 % [INFO] Scanning for conjecture ...
% 2.23/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 2.23/1.75 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.23/1.78 % [INFO] Problem is first-order (TPTP FOF).
% 2.23/1.79 % [INFO] Type checking passed.
% 2.23/1.79 % [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 ...
% 92.27/24.49 % External prover 'e' found a proof!
% 92.27/24.49 % [INFO] Killing All external provers ...
% 92.27/24.49 % Time passed: 23949ms (effective reasoning time: 23287ms)
% 92.27/24.49 % 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)>
% 92.27/24.50 % Axioms used in derivation (10): d1_tarski, t2_tarski, d4_tarski, l2_zfmisc_1, d1_zfmisc_1, rc1_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden, d3_tarski, reflexivity_r1_tarski
% 92.27/24.50 % No. of inferences in proof: 622
% 92.27/24.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 23949 ms resp. 23287 ms w/o parsing
% 89.89/24.73 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 89.89/24.73 % [INFO] Killing All external provers ...
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