%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU815^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : n004.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 : Wed Sep 30 08:29:24 AM UTC 2026
% Result : Theorem 76.52s 23.04s
% Output : Refutation 69.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 190 ( 54 unt; 0 typ; 10 def)
% Number of atoms : 1176 ( 124 equ; 0 cnn)
% Maximal formula atoms : 68 ( 6 avg)
% Number of connectives : 4502 ( 770 ~; 763 |; 10 &;2886 @)
% ( 0 <=>; 73 =>; 0 <=; 0 <~>)
% Maximal formula depth : 108 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 576 ( 7 ^; 564 !; 0 ?; 576 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(setunion_decl,type,
setunion: $i > $i ).
thf(setunionI_decl,type,
setunionI: $o ).
thf(setunionE_decl,type,
setunionE: $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(subsetI1_decl,type,
subsetI1: $o ).
thf(transitiveset_decl,type,
transitiveset: $i > $o ).
thf(transitivesetOp2_decl,type,
transitivesetOp2: $o ).
thf(sk1_decl,type,
sk1: $o > $i > $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(setunionI_def,definition,
( setunionI
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ B @ C )
=> ( ( in @ C @ A )
=> ( in @ B @ ( setunion @ A ) ) ) ) ) ) ).
thf(setunionE_def,definition,
( setunionE
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ! [C: $o] :
( ! [D: $i] :
( ( in @ B @ D )
=> ( ( in @ D @ A )
=> C ) )
=> C ) ) ) ) ).
thf(subsetI1_def,definition,
( subsetI1
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) ) ) ) ).
thf(transitiveset_def,definition,
( transitiveset
= ( ^ [A: $i] :
! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ) ) ).
thf(transitivesetOp2_def,definition,
( transitivesetOp2
= ( ! [A: $i] :
( ( transitiveset @ A )
=> ! [B: $i,C: $i] :
( ( in @ B @ A )
=> ( ( in @ C @ B )
=> ( in @ C @ A ) ) ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $o,B: $i,C: $i] :
@+[D: $i] :
~ ( ( in @ B @ D )
=> ( ( in @ D @ C )
=> A ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( in @ C @ B )
=> ( in @ C @ A ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( in @ B @ A )
=> ( subset @ B @ A ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ! [B: $i] :
( ( in @ B @ A )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( subset @ C @ B ) ) )
=> ! [B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ( subset @ B @ ( setunion @ A ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( in @ A @ ( setunion @ sk4 ) )
=> ( subset @ A @ ( setunion @ sk4 ) ) ) ) ) ).
thf(1,conjecture,
( setunionI
=> ( setunionE
=> ( subsetI1
=> ( transitivesetOp2
=> ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( transitiveset @ B ) )
=> ( transitiveset @ ( setunion @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionTransitive) ).
thf(2,negated_conjecture,
~ ( setunionI
=> ( setunionE
=> ( subsetI1
=> ( transitivesetOp2
=> ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( transitiveset @ B ) )
=> ( transitiveset @ ( setunion @ A ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( in @ B @ C )
=> ( ( in @ C @ A )
=> ( in @ B @ ( setunion @ A ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ! [C: $o] :
( ! [D: $i] :
( ( in @ B @ D )
=> ( ( in @ D @ A )
=> C ) )
=> C ) )
=> ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) )
=> ! [B: $i,C: $i] :
( ( in @ B @ A )
=> ( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
=> ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( subset @ C @ B ) ) )
=> ! [B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ( subset @ B @ ( setunion @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( in @ B @ C )
=> ( ( in @ C @ A )
=> ( in @ B @ ( setunion @ A ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ! [C: $o] :
( ! [D: $i] :
( ( in @ B @ D )
=> ( ( in @ D @ A )
=> C ) )
=> C ) )
=> ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) )
=> ! [B: $i] :
( ( in @ B @ A )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
=> ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( subset @ C @ B ) ) )
=> ! [B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ( subset @ B @ ( setunion @ A ) ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $o,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( in @ B @ C )
| ~ ( in @ C @ A )
| ( in @ B @ ( setunion @ A ) ) )
& ( ~ ( in @ E @ ( setunion @ D ) )
| ( in @ E @ ( sk1 @ F @ E @ D ) )
| F )
& ( ~ ( in @ E @ ( setunion @ D ) )
| ( in @ ( sk1 @ F @ E @ D ) @ D )
| F )
& ( ~ ( in @ E @ ( setunion @ D ) )
| ~ F
| F )
& ( ( in @ ( sk2 @ H @ G ) @ G )
| ( subset @ G @ H ) )
& ( ~ ( in @ ( sk2 @ H @ G ) @ H )
| ( subset @ G @ H ) )
& ( ( in @ ( sk3 @ I ) @ I )
| ~ ( in @ J @ I )
| ~ ( in @ K @ J )
| ( in @ K @ I ) )
& ( ~ ( subset @ ( sk3 @ I ) @ I )
| ~ ( in @ J @ I )
| ~ ( in @ K @ J )
| ( in @ K @ I ) )
& ( ~ ( in @ L @ sk4 )
| ~ ( in @ M @ L )
| ( subset @ M @ L ) )
& ( in @ sk5 @ ( setunion @ sk4 ) )
& ~ ( subset @ sk5 @ ( setunion @ sk4 ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(9,plain,
in @ sk5 @ ( setunion @ sk4 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(10,plain,
! [C: $o,B: $i,A: $i] :
( ~ ( in @ B @ ( setunion @ A ) )
| ( in @ B @ ( sk1 @ C @ B @ A ) )
| C ),
inference(cnfConj,[status(thm)],[5]) ).
thf(17,plain,
! [C: $o,B: $i,A: $i] :
( ~ ( in @ B @ ( setunion @ A ) )
| ( in @ B @ ( sk1 @ C @ B @ A ) )
| C ),
inference(simp,[status(thm)],[10]) ).
thf(154,plain,
! [C: $o,B: $i,A: $i] :
( ~ $true
| ( in @ B @ ( sk1 @ C @ B @ A ) )
| C
| ( ( in @ sk5 @ ( setunion @ sk4 ) )
!= ( in @ B @ ( setunion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,17]) ).
thf(155,plain,
! [C: $o,B: $i,A: $i] :
( ( in @ B @ ( sk1 @ C @ B @ A ) )
| C
| ( ( in @ sk5 @ ( setunion @ sk4 ) )
!= ( in @ B @ ( setunion @ A ) ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(156,plain,
! [A: $o] :
( ( in @ sk5 @ ( sk1 @ A @ sk5 @ sk4 ) )
| A ),
inference(pattern_uni,[status(thm)],[155:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 ))]]) ).
thf(205,plain,
! [A: $o] :
( ( in @ sk5 @ ( sk1 @ A @ sk5 @ sk4 ) )
| A ),
inference(simp,[status(thm)],[156]) ).
thf(228,plain,
! [A: $o] :
( ( in @ sk5 @ ( sk1 @ ~ A @ sk5 @ sk4 ) )
| ~ A ),
inference(prim_subst,[status(thm)],[205:[bind(A,$thf( ~ ( B ) ))]]) ).
thf(237,plain,
! [A: $o] :
( ( in @ sk5 @ ( sk1 @ ~ A @ sk5 @ sk4 ) )
| ~ A ),
inference(cnf,[status(esa)],[228]) ).
thf(238,plain,
! [A: $o] :
( ( in @ sk5 @ ( sk1 @ ~ A @ sk5 @ sk4 ) )
| ~ A ),
inference(simp,[status(thm)],[237]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( in @ ( sk2 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( in @ ( sk2 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[13]) ).
thf(12,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ C )
| ~ ( in @ C @ A )
| ( in @ B @ ( setunion @ A ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(281,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ C )
| ~ $true
| ( in @ B @ ( setunion @ A ) )
| ( ( in @ sk5 @ ( setunion @ sk4 ) )
!= ( in @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9,12]) ).
thf(282,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ C )
| ( in @ B @ ( setunion @ A ) )
| ( ( in @ sk5 @ ( setunion @ sk4 ) )
!= ( in @ C @ A ) ) ),
inference(simp,[status(thm)],[281]) ).
thf(283,plain,
! [A: $i] :
( ~ ( in @ A @ sk5 )
| ( in @ A @ ( setunion @ ( setunion @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[282:[bind(A,$thf( setunion @ sk4 )),bind(B,$thf( B )),bind(C,$thf( sk5 ))]]) ).
thf(355,plain,
! [A: $i] :
( ~ ( in @ A @ sk5 )
| ( in @ A @ ( setunion @ ( setunion @ sk4 ) ) ) ),
inference(simp,[status(thm)],[283]) ).
thf(1771,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ~ $true
| ( in @ C @ ( setunion @ ( setunion @ sk4 ) ) )
| ( ( in @ ( sk2 @ B @ A ) @ A )
!= ( in @ C @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[20,355]) ).
thf(1772,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ( in @ C @ ( setunion @ ( setunion @ sk4 ) ) )
| ( ( in @ ( sk2 @ B @ A ) @ A )
!= ( in @ C @ sk5 ) ) ),
inference(simp,[status(thm)],[1771]) ).
thf(1773,plain,
! [A: $i] :
( ( subset @ sk5 @ A )
| ( in @ ( sk2 @ A @ sk5 ) @ ( setunion @ ( setunion @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[1772:[bind(A,$thf( sk5 )),bind(B,$thf( D )),bind(C,$thf( sk2 @ D @ sk5 ))]]) ).
thf(1915,plain,
! [A: $i] :
( ( subset @ sk5 @ A )
| ( in @ ( sk2 @ A @ sk5 ) @ ( setunion @ ( setunion @ sk4 ) ) ) ),
inference(simp,[status(thm)],[1773]) ).
thf(16,plain,
! [C: $o,B: $i,A: $i] :
( ~ ( in @ B @ ( setunion @ A ) )
| ( in @ ( sk1 @ C @ B @ A ) @ A )
| C ),
inference(cnfConj,[status(thm)],[5]) ).
thf(22,plain,
! [C: $o,B: $i,A: $i] :
( ~ ( in @ B @ ( setunion @ A ) )
| ( in @ ( sk1 @ C @ B @ A ) @ A )
| C ),
inference(simp,[status(thm)],[16]) ).
thf(13181,plain,
! [C: $o,B: $i,A: $i] :
( ~ $true
| ( in @ ( sk1 @ C @ B @ A ) @ A )
| C
| ( ( in @ sk5 @ ( setunion @ sk4 ) )
!= ( in @ B @ ( setunion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,22]) ).
thf(13182,plain,
! [C: $o,B: $i,A: $i] :
( ( in @ ( sk1 @ C @ B @ A ) @ A )
| C
| ( ( in @ sk5 @ ( setunion @ sk4 ) )
!= ( in @ B @ ( setunion @ A ) ) ) ),
inference(simp,[status(thm)],[13181]) ).
thf(13183,plain,
! [A: $o] :
( ( in @ ( sk1 @ A @ sk5 @ sk4 ) @ sk4 )
| A ),
inference(pattern_uni,[status(thm)],[13182:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 ))]]) ).
thf(13334,plain,
! [A: $o] :
( ( in @ ( sk1 @ A @ sk5 @ sk4 ) @ sk4 )
| A ),
inference(simp,[status(thm)],[13183]) ).
thf(13642,plain,
( ( in @ ( sk1 @ $false @ sk5 @ sk4 ) @ sk4 )
| $false ),
inference(prim_subst,[status(thm)],[13334:[bind(A,$thf( $false ))]]) ).
thf(13702,plain,
in @ ( sk1 @ $false @ sk5 @ sk4 ) @ sk4,
inference(simp,[status(thm)],[13642]) ).
thf(8,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk4 )
| ~ ( in @ B @ A )
| ( subset @ B @ A ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk4 )
| ~ ( in @ B @ A )
| ( subset @ B @ A ) ),
inference(simp,[status(thm)],[8]) ).
thf(14679,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk4 )
| ~ $true
| ( subset @ B @ A )
| ( ( in @ ( sk1 @ $false @ sk5 @ sk4 ) @ sk4 )
!= ( in @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13702,24]) ).
thf(14680,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk4 )
| ( subset @ B @ A )
| ( ( in @ ( sk1 @ $false @ sk5 @ sk4 ) @ sk4 )
!= ( in @ B @ A ) ) ),
inference(simp,[status(thm)],[14679]) ).
thf(14681,plain,
( ~ ( in @ sk4 @ sk4 )
| ( subset @ ( sk1 @ $false @ sk5 @ sk4 ) @ sk4 ) ),
inference(pattern_uni,[status(thm)],[14680:[bind(A,$thf( sk4 )),bind(B,$thf( sk1 @ $false @ sk5 @ sk4 ))]]) ).
thf(15,plain,
~ ( subset @ sk5 @ ( setunion @ sk4 ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( in @ ( sk2 @ B @ A ) @ A )
| ~ $true
| ( ( subset @ A @ B )
!= ( subset @ sk5 @ ( setunion @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,15]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( in @ ( sk2 @ B @ A ) @ A )
| ( ( subset @ A @ B )
!= ( subset @ sk5 @ ( setunion @ sk4 ) ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(27,plain,
in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ sk5,
inference(pattern_uni,[status(thm)],[26:[bind(A,$thf( sk5 )),bind(B,$thf( setunion @ sk4 ))]]) ).
thf(1788,plain,
! [A: $i] :
( ~ $true
| ( in @ A @ ( setunion @ ( setunion @ sk4 ) ) )
| ( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ sk5 )
!= ( in @ A @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[27,355]) ).
thf(1789,plain,
! [A: $i] :
( ( in @ A @ ( setunion @ ( setunion @ sk4 ) ) )
| ( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ sk5 )
!= ( in @ A @ sk5 ) ) ),
inference(simp,[status(thm)],[1788]) ).
thf(1790,plain,
in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ ( setunion @ sk4 ) ),
inference(pattern_uni,[status(thm)],[1789:[bind(A,$thf( sk2 @ ( setunion @ sk4 ) @ sk5 ))]]) ).
thf(14449,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk4 )
| ~ ( in @ B @ A )
| ~ $true
| ( ( subset @ B @ A )
!= ( subset @ sk5 @ ( setunion @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,15]) ).
thf(14450,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk4 )
| ~ ( in @ B @ A )
| ( ( subset @ B @ A )
!= ( subset @ sk5 @ ( setunion @ sk4 ) ) ) ),
inference(simp,[status(thm)],[14449]) ).
thf(14451,plain,
( ~ ( in @ ( setunion @ sk4 ) @ sk4 )
| ~ ( in @ sk5 @ ( setunion @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[14450:[bind(A,$thf( setunion @ sk4 )),bind(B,$thf( sk5 ))]]) ).
thf(14841,plain,
( ~ ( in @ ( setunion @ sk4 ) @ sk4 )
| ~ $true ),
inference(rewrite,[status(thm)],[14451,9]) ).
thf(14842,plain,
~ ( in @ ( setunion @ sk4 ) @ sk4 ),
inference(simp,[status(thm)],[14841]) ).
thf(14855,plain,
( ~ $true
| ( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ ( setunion @ sk4 ) ) )
!= ( in @ ( setunion @ sk4 ) @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[1790,14842]) ).
thf(14856,plain,
( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ ( setunion @ sk4 ) ) )
!= ( in @ ( setunion @ sk4 ) @ sk4 ) ),
inference(simp,[status(thm)],[14855]) ).
thf(14893,plain,
( ( ( sk2 @ ( setunion @ sk4 ) @ sk5 )
!= ( setunion @ sk4 ) )
| ( ( setunion @ ( setunion @ sk4 ) )
!= sk4 ) ),
inference(simp,[status(thm)],[14856]) ).
thf(278,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ~ ( in @ C @ A )
| ( in @ B @ ( setunion @ A ) )
| ( ( in @ sk5 @ ( setunion @ sk4 ) )
!= ( in @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[9,12]) ).
thf(279,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( in @ B @ ( setunion @ A ) )
| ( ( in @ sk5 @ ( setunion @ sk4 ) )
!= ( in @ B @ C ) ) ),
inference(simp,[status(thm)],[278]) ).
thf(280,plain,
! [A: $i] :
( ~ ( in @ ( setunion @ sk4 ) @ A )
| ( in @ sk5 @ ( setunion @ A ) ) ),
inference(pattern_uni,[status(thm)],[279:[bind(A,$thf( A )),bind(B,$thf( sk5 )),bind(C,$thf( setunion @ sk4 ))]]) ).
thf(428,plain,
! [A: $i] :
( ~ $true
| ( in @ sk5 @ ( setunion @ A ) )
| ( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ sk5 )
!= ( in @ ( setunion @ sk4 ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,280]) ).
thf(429,plain,
! [A: $i] :
( ( in @ sk5 @ ( setunion @ A ) )
| ( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ sk5 )
!= ( in @ ( setunion @ sk4 ) @ A ) ) ),
inference(simp,[status(thm)],[428]) ).
thf(445,plain,
! [A: $i] :
( ( in @ sk5 @ ( setunion @ A ) )
| ( ( sk2 @ ( setunion @ sk4 ) @ sk5 )
!= ( setunion @ sk4 ) )
| ( sk5 != A ) ),
inference(simp,[status(thm)],[429]) ).
thf(454,plain,
( ( in @ sk5 @ ( setunion @ sk5 ) )
| ( ( sk2 @ ( setunion @ sk4 ) @ sk5 )
!= ( setunion @ sk4 ) ) ),
inference(simp,[status(thm)],[445]) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ( in @ C @ A ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ( in @ C @ A ) ),
inference(simp,[status(thm)],[14]) ).
thf(52,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ~ ( subset @ ( sk3 @ D ) @ D )
| ~ ( in @ E @ D )
| ~ $true
| ( in @ F @ D )
| ( ( in @ C @ A )
!= ( in @ F @ E ) ) ),
inference(paramod_ordered,[status(thm)],[18,18]) ).
thf(53,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ~ ( subset @ ( sk3 @ D ) @ D )
| ~ ( in @ E @ D )
| ( in @ F @ D )
| ( ( in @ C @ A )
!= ( in @ F @ E ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(54,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ~ ( subset @ ( sk3 @ D ) @ D )
| ~ ( in @ A @ D )
| ( in @ C @ D ) ),
inference(pattern_uni,[status(thm)],[53:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( C ))]]) ).
thf(100,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ~ ( subset @ ( sk3 @ D ) @ D )
| ~ ( in @ A @ D )
| ~ ( subset @ ( sk3 @ E ) @ E )
| ~ ( in @ F @ E )
| ~ $true
| ~ ( subset @ ( sk3 @ H ) @ H )
| ~ ( in @ E @ H )
| ( in @ G @ H )
| ( ( in @ C @ D )
!= ( in @ G @ F ) ) ),
inference(paramod_ordered,[status(thm)],[54,54]) ).
thf(101,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ~ ( subset @ ( sk3 @ D ) @ D )
| ~ ( in @ A @ D )
| ~ ( subset @ ( sk3 @ E ) @ E )
| ~ ( in @ F @ E )
| ~ ( subset @ ( sk3 @ H ) @ H )
| ~ ( in @ E @ H )
| ( in @ G @ H )
| ( ( in @ C @ D )
!= ( in @ G @ F ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(102,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ~ ( subset @ ( sk3 @ D ) @ D )
| ~ ( in @ A @ D )
| ~ ( subset @ ( sk3 @ E ) @ E )
| ~ ( in @ D @ E )
| ~ ( subset @ ( sk3 @ F ) @ F )
| ~ ( in @ E @ F )
| ( in @ C @ F ) ),
inference(pattern_uni,[status(thm)],[101:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( D )),bind(G,$thf( C ))]]) ).
thf(134,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ~ ( subset @ ( sk3 @ D ) @ D )
| ~ ( in @ A @ D )
| ~ ( subset @ ( sk3 @ E ) @ E )
| ~ ( in @ D @ E )
| ~ ( subset @ ( sk3 @ F ) @ F )
| ~ ( in @ E @ F )
| ( in @ C @ F ) ),
inference(simp,[status(thm)],[102]) ).
thf(654,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ~ ( subset @ ( sk3 @ D ) @ D )
| ~ ( in @ A @ D )
| ~ ( subset @ ( sk3 @ E ) @ E )
| ~ ( in @ D @ E )
| ~ ( subset @ ( sk3 @ F ) @ F )
| ~ ( in @ E @ F )
| ~ ( subset @ ( sk3 @ G ) @ G )
| ~ ( in @ H @ G )
| ~ $true
| ~ ( subset @ ( sk3 @ J ) @ J )
| ~ ( in @ G @ J )
| ~ ( subset @ ( sk3 @ K ) @ K )
| ~ ( in @ J @ K )
| ~ ( subset @ ( sk3 @ L ) @ L )
| ~ ( in @ K @ L )
| ( in @ I @ L )
| ( ( in @ C @ F )
!= ( in @ I @ H ) ) ),
inference(paramod_ordered,[status(thm)],[134,134]) ).
thf(655,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ~ ( subset @ ( sk3 @ D ) @ D )
| ~ ( in @ A @ D )
| ~ ( subset @ ( sk3 @ E ) @ E )
| ~ ( in @ D @ E )
| ~ ( subset @ ( sk3 @ F ) @ F )
| ~ ( in @ E @ F )
| ~ ( subset @ ( sk3 @ G ) @ G )
| ~ ( in @ H @ G )
| ~ ( subset @ ( sk3 @ J ) @ J )
| ~ ( in @ G @ J )
| ~ ( subset @ ( sk3 @ K ) @ K )
| ~ ( in @ J @ K )
| ~ ( subset @ ( sk3 @ L ) @ L )
| ~ ( in @ K @ L )
| ( in @ I @ L )
| ( ( in @ C @ F )
!= ( in @ I @ H ) ) ),
inference(simp,[status(thm)],[654]) ).
thf(656,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ~ ( subset @ ( sk3 @ D ) @ D )
| ~ ( in @ A @ D )
| ~ ( subset @ ( sk3 @ E ) @ E )
| ~ ( in @ D @ E )
| ~ ( subset @ ( sk3 @ F ) @ F )
| ~ ( in @ E @ F )
| ~ ( subset @ ( sk3 @ G ) @ G )
| ~ ( in @ F @ G )
| ~ ( subset @ ( sk3 @ H ) @ H )
| ~ ( in @ G @ H )
| ~ ( subset @ ( sk3 @ I ) @ I )
| ~ ( in @ H @ I )
| ~ ( subset @ ( sk3 @ J ) @ J )
| ~ ( in @ I @ J )
| ( in @ C @ J ) ),
inference(pattern_uni,[status(thm)],[655:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( F )),bind(I,$thf( C ))]]) ).
thf(807,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ~ ( subset @ ( sk3 @ D ) @ D )
| ~ ( in @ A @ D )
| ~ ( subset @ ( sk3 @ E ) @ E )
| ~ ( in @ D @ E )
| ~ ( subset @ ( sk3 @ F ) @ F )
| ~ ( in @ E @ F )
| ~ ( subset @ ( sk3 @ G ) @ G )
| ~ ( in @ F @ G )
| ~ ( subset @ ( sk3 @ H ) @ H )
| ~ ( in @ G @ H )
| ~ ( subset @ ( sk3 @ I ) @ I )
| ~ ( in @ H @ I )
| ~ ( subset @ ( sk3 @ J ) @ J )
| ~ ( in @ I @ J )
| ( in @ C @ J ) ),
inference(simp,[status(thm)],[656]) ).
thf(1101,plain,
! [T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ~ ( subset @ ( sk3 @ D ) @ D )
| ~ ( in @ A @ D )
| ~ ( subset @ ( sk3 @ E ) @ E )
| ~ ( in @ D @ E )
| ~ ( subset @ ( sk3 @ F ) @ F )
| ~ ( in @ E @ F )
| ~ ( subset @ ( sk3 @ G ) @ G )
| ~ ( in @ F @ G )
| ~ ( subset @ ( sk3 @ H ) @ H )
| ~ ( in @ G @ H )
| ~ ( subset @ ( sk3 @ I ) @ I )
| ~ ( in @ H @ I )
| ~ ( subset @ ( sk3 @ J ) @ J )
| ~ ( in @ I @ J )
| ~ ( subset @ ( sk3 @ K ) @ K )
| ~ ( in @ L @ K )
| ~ $true
| ~ ( subset @ ( sk3 @ N ) @ N )
| ~ ( in @ K @ N )
| ~ ( subset @ ( sk3 @ O ) @ O )
| ~ ( in @ N @ O )
| ~ ( subset @ ( sk3 @ P ) @ P )
| ~ ( in @ O @ P )
| ~ ( subset @ ( sk3 @ Q ) @ Q )
| ~ ( in @ P @ Q )
| ~ ( subset @ ( sk3 @ R ) @ R )
| ~ ( in @ Q @ R )
| ~ ( subset @ ( sk3 @ S ) @ S )
| ~ ( in @ R @ S )
| ~ ( subset @ ( sk3 @ T ) @ T )
| ~ ( in @ S @ T )
| ( in @ M @ T )
| ( ( in @ C @ J )
!= ( in @ M @ L ) ) ),
inference(paramod_ordered,[status(thm)],[807,807]) ).
thf(1102,plain,
! [T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ~ ( subset @ ( sk3 @ D ) @ D )
| ~ ( in @ A @ D )
| ~ ( subset @ ( sk3 @ E ) @ E )
| ~ ( in @ D @ E )
| ~ ( subset @ ( sk3 @ F ) @ F )
| ~ ( in @ E @ F )
| ~ ( subset @ ( sk3 @ G ) @ G )
| ~ ( in @ F @ G )
| ~ ( subset @ ( sk3 @ H ) @ H )
| ~ ( in @ G @ H )
| ~ ( subset @ ( sk3 @ I ) @ I )
| ~ ( in @ H @ I )
| ~ ( subset @ ( sk3 @ J ) @ J )
| ~ ( in @ I @ J )
| ~ ( subset @ ( sk3 @ K ) @ K )
| ~ ( in @ L @ K )
| ~ ( subset @ ( sk3 @ N ) @ N )
| ~ ( in @ K @ N )
| ~ ( subset @ ( sk3 @ O ) @ O )
| ~ ( in @ N @ O )
| ~ ( subset @ ( sk3 @ P ) @ P )
| ~ ( in @ O @ P )
| ~ ( subset @ ( sk3 @ Q ) @ Q )
| ~ ( in @ P @ Q )
| ~ ( subset @ ( sk3 @ R ) @ R )
| ~ ( in @ Q @ R )
| ~ ( subset @ ( sk3 @ S ) @ S )
| ~ ( in @ R @ S )
| ~ ( subset @ ( sk3 @ T ) @ T )
| ~ ( in @ S @ T )
| ( in @ M @ T )
| ( ( in @ C @ J )
!= ( in @ M @ L ) ) ),
inference(simp,[status(thm)],[1101]) ).
thf(1103,plain,
! [R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ~ ( subset @ ( sk3 @ D ) @ D )
| ~ ( in @ A @ D )
| ~ ( subset @ ( sk3 @ E ) @ E )
| ~ ( in @ D @ E )
| ~ ( subset @ ( sk3 @ F ) @ F )
| ~ ( in @ E @ F )
| ~ ( subset @ ( sk3 @ G ) @ G )
| ~ ( in @ F @ G )
| ~ ( subset @ ( sk3 @ H ) @ H )
| ~ ( in @ G @ H )
| ~ ( subset @ ( sk3 @ I ) @ I )
| ~ ( in @ H @ I )
| ~ ( subset @ ( sk3 @ J ) @ J )
| ~ ( in @ I @ J )
| ~ ( subset @ ( sk3 @ K ) @ K )
| ~ ( in @ J @ K )
| ~ ( subset @ ( sk3 @ L ) @ L )
| ~ ( in @ K @ L )
| ~ ( subset @ ( sk3 @ M ) @ M )
| ~ ( in @ L @ M )
| ~ ( subset @ ( sk3 @ N ) @ N )
| ~ ( in @ M @ N )
| ~ ( subset @ ( sk3 @ O ) @ O )
| ~ ( in @ N @ O )
| ~ ( subset @ ( sk3 @ P ) @ P )
| ~ ( in @ O @ P )
| ~ ( subset @ ( sk3 @ Q ) @ Q )
| ~ ( in @ P @ Q )
| ~ ( subset @ ( sk3 @ R ) @ R )
| ~ ( in @ Q @ R )
| ( in @ C @ R ) ),
inference(pattern_uni,[status(thm)],[1102:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( H )),bind(I,$thf( I )),bind(J,$thf( J )),bind(K,$thf( K )),bind(L,$thf( J )),bind(M,$thf( C ))]]) ).
thf(1469,plain,
! [R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ~ ( subset @ ( sk3 @ D ) @ D )
| ~ ( in @ A @ D )
| ~ ( subset @ ( sk3 @ E ) @ E )
| ~ ( in @ D @ E )
| ~ ( subset @ ( sk3 @ F ) @ F )
| ~ ( in @ E @ F )
| ~ ( subset @ ( sk3 @ G ) @ G )
| ~ ( in @ F @ G )
| ~ ( subset @ ( sk3 @ H ) @ H )
| ~ ( in @ G @ H )
| ~ ( subset @ ( sk3 @ I ) @ I )
| ~ ( in @ H @ I )
| ~ ( subset @ ( sk3 @ J ) @ J )
| ~ ( in @ I @ J )
| ~ ( subset @ ( sk3 @ K ) @ K )
| ~ ( in @ J @ K )
| ~ ( subset @ ( sk3 @ L ) @ L )
| ~ ( in @ K @ L )
| ~ ( subset @ ( sk3 @ M ) @ M )
| ~ ( in @ L @ M )
| ~ ( subset @ ( sk3 @ N ) @ N )
| ~ ( in @ M @ N )
| ~ ( subset @ ( sk3 @ O ) @ O )
| ~ ( in @ N @ O )
| ~ ( subset @ ( sk3 @ P ) @ P )
| ~ ( in @ O @ P )
| ~ ( subset @ ( sk3 @ Q ) @ Q )
| ~ ( in @ P @ Q )
| ~ ( subset @ ( sk3 @ R ) @ R )
| ~ ( in @ Q @ R )
| ( in @ C @ R ) ),
inference(simp,[status(thm)],[1103]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk2 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk2 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[7]) ).
thf(12169,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ sk5 @ A )
| ~ $true
| ( subset @ B @ C )
| ( ( in @ ( sk2 @ A @ sk5 ) @ ( setunion @ ( setunion @ sk4 ) ) )
!= ( in @ ( sk2 @ C @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1915,21]) ).
thf(12170,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ sk5 @ A )
| ( subset @ B @ C )
| ( ( in @ ( sk2 @ A @ sk5 ) @ ( setunion @ ( setunion @ sk4 ) ) )
!= ( in @ ( sk2 @ C @ B ) @ C ) ) ),
inference(simp,[status(thm)],[12169]) ).
thf(12171,plain,
( ( subset @ sk5 @ ( setunion @ ( setunion @ sk4 ) ) )
| ( subset @ sk5 @ ( setunion @ ( setunion @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[12170:[bind(A,$thf( setunion @ ( setunion @ sk4 ) )),bind(B,$thf( sk5 )),bind(C,$thf( setunion @ ( setunion @ sk4 ) ))]]) ).
thf(12260,plain,
subset @ sk5 @ ( setunion @ ( setunion @ sk4 ) ),
inference(simp,[status(thm)],[12171]) ).
thf(12343,plain,
( ~ $true
| ( ( subset @ sk5 @ ( setunion @ ( setunion @ sk4 ) ) )
!= ( subset @ sk5 @ ( setunion @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12260,15]) ).
thf(12344,plain,
( ( subset @ sk5 @ ( setunion @ ( setunion @ sk4 ) ) )
!= ( subset @ sk5 @ ( setunion @ sk4 ) ) ),
inference(simp,[status(thm)],[12343]) ).
thf(12482,plain,
( ( sk5 != sk5 )
| ( ( setunion @ ( setunion @ sk4 ) )
!= ( setunion @ sk4 ) ) ),
inference(simp,[status(thm)],[12344]) ).
thf(12546,plain,
( ( setunion @ ( setunion @ sk4 ) )
!= ( setunion @ sk4 ) ),
inference(simp,[status(thm)],[12482]) ).
thf(12597,plain,
( ( setunion @ sk4 )
!= sk4 ),
inference(simp,[status(thm)],[12546]) ).
thf(13640,plain,
! [A: $o] :
( ( in @ ( sk1 @ ~ A @ sk5 @ sk4 ) @ sk4 )
| ~ A ),
inference(prim_subst,[status(thm)],[13334:[bind(A,$thf( ~ ( B ) ))]]) ).
thf(13699,plain,
! [A: $o] :
( ( in @ ( sk1 @ ~ A @ sk5 @ sk4 ) @ sk4 )
| ~ A ),
inference(cnf,[status(esa)],[13640]) ).
thf(13700,plain,
! [A: $o] :
( ( in @ ( sk1 @ ~ A @ sk5 @ sk4 ) @ sk4 )
| ~ A ),
inference(simp,[status(thm)],[13699]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ $true
| ( in @ C @ A )
| ( ( in @ sk5 @ ( setunion @ sk4 ) )
!= ( in @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9,18]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ( in @ C @ A )
| ( ( in @ sk5 @ ( setunion @ sk4 ) )
!= ( in @ C @ B ) ) ),
inference(simp,[status(thm)],[40]) ).
thf(42,plain,
! [A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ ( setunion @ sk4 ) @ A )
| ( in @ sk5 @ A ) ),
inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( A )),bind(B,$thf( setunion @ sk4 )),bind(C,$thf( sk5 ))]]) ).
thf(12007,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk2 @ B @ A ) @ B )
| ~ $true
| ( ( subset @ A @ B )
!= ( subset @ sk5 @ ( setunion @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,15]) ).
thf(12008,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk2 @ B @ A ) @ B )
| ( ( subset @ A @ B )
!= ( subset @ sk5 @ ( setunion @ sk4 ) ) ) ),
inference(simp,[status(thm)],[12007]) ).
thf(12009,plain,
~ ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) ),
inference(pattern_uni,[status(thm)],[12008:[bind(A,$thf( sk5 )),bind(B,$thf( setunion @ sk4 ))]]) ).
thf(12627,plain,
( ~ $true
| ( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) )
!= ( in @ sk5 @ ( setunion @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,12009]) ).
thf(12628,plain,
( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) )
!= ( in @ sk5 @ ( setunion @ sk4 ) ) ),
inference(simp,[status(thm)],[12627]) ).
thf(12659,plain,
( ( ( sk2 @ ( setunion @ sk4 ) @ sk5 )
!= sk5 )
| ( ( setunion @ sk4 )
!= ( setunion @ sk4 ) ) ),
inference(simp,[status(thm)],[12628]) ).
thf(12682,plain,
( ( sk2 @ ( setunion @ sk4 ) @ sk5 )
!= sk5 ),
inference(simp,[status(thm)],[12659]) ).
thf(1776,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk5 )
| ~ $true
| ( in @ sk5 @ ( setunion @ B ) )
| ( ( in @ A @ ( setunion @ ( setunion @ sk4 ) ) )
!= ( in @ ( setunion @ sk4 ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[355,280]) ).
thf(1777,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk5 )
| ( in @ sk5 @ ( setunion @ B ) )
| ( ( in @ A @ ( setunion @ ( setunion @ sk4 ) ) )
!= ( in @ ( setunion @ sk4 ) @ B ) ) ),
inference(simp,[status(thm)],[1776]) ).
thf(1778,plain,
( ~ ( in @ ( setunion @ sk4 ) @ sk5 )
| ( in @ sk5 @ ( setunion @ ( setunion @ ( setunion @ sk4 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1777:[bind(A,$thf( setunion @ sk4 )),bind(B,$thf( setunion @ ( setunion @ sk4 ) ))]]) ).
thf(3075,plain,
! [ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ~ ( subset @ ( sk3 @ D ) @ D )
| ~ ( in @ A @ D )
| ~ ( subset @ ( sk3 @ E ) @ E )
| ~ ( in @ D @ E )
| ~ ( subset @ ( sk3 @ F ) @ F )
| ~ ( in @ E @ F )
| ~ ( subset @ ( sk3 @ G ) @ G )
| ~ ( in @ F @ G )
| ~ ( subset @ ( sk3 @ H ) @ H )
| ~ ( in @ G @ H )
| ~ ( subset @ ( sk3 @ I ) @ I )
| ~ ( in @ H @ I )
| ~ ( subset @ ( sk3 @ J ) @ J )
| ~ ( in @ I @ J )
| ~ ( subset @ ( sk3 @ K ) @ K )
| ~ ( in @ J @ K )
| ~ ( subset @ ( sk3 @ L ) @ L )
| ~ ( in @ K @ L )
| ~ ( subset @ ( sk3 @ M ) @ M )
| ~ ( in @ L @ M )
| ~ ( subset @ ( sk3 @ N ) @ N )
| ~ ( in @ M @ N )
| ~ ( subset @ ( sk3 @ O ) @ O )
| ~ ( in @ N @ O )
| ~ ( subset @ ( sk3 @ P ) @ P )
| ~ ( in @ O @ P )
| ~ ( subset @ ( sk3 @ Q ) @ Q )
| ~ ( in @ P @ Q )
| ~ ( subset @ ( sk3 @ R ) @ R )
| ~ ( in @ Q @ R )
| ~ ( subset @ ( sk3 @ S ) @ S )
| ~ ( in @ T @ S )
| ~ $true
| ~ ( subset @ ( sk3 @ V ) @ V )
| ~ ( in @ S @ V )
| ~ ( subset @ ( sk3 @ W ) @ W )
| ~ ( in @ V @ W )
| ~ ( subset @ ( sk3 @ X ) @ X )
| ~ ( in @ W @ X )
| ~ ( subset @ ( sk3 @ Y ) @ Y )
| ~ ( in @ X @ Y )
| ~ ( subset @ ( sk3 @ Z ) @ Z )
| ~ ( in @ Y @ Z )
| ~ ( subset @ ( sk3 @ ZA ) @ ZA )
| ~ ( in @ Z @ ZA )
| ~ ( subset @ ( sk3 @ ZB ) @ ZB )
| ~ ( in @ ZA @ ZB )
| ~ ( subset @ ( sk3 @ ZC ) @ ZC )
| ~ ( in @ ZB @ ZC )
| ~ ( subset @ ( sk3 @ ZD ) @ ZD )
| ~ ( in @ ZC @ ZD )
| ~ ( subset @ ( sk3 @ ZE ) @ ZE )
| ~ ( in @ ZD @ ZE )
| ~ ( subset @ ( sk3 @ ZF ) @ ZF )
| ~ ( in @ ZE @ ZF )
| ~ ( subset @ ( sk3 @ ZG ) @ ZG )
| ~ ( in @ ZF @ ZG )
| ~ ( subset @ ( sk3 @ ZH ) @ ZH )
| ~ ( in @ ZG @ ZH )
| ~ ( subset @ ( sk3 @ ZI ) @ ZI )
| ~ ( in @ ZH @ ZI )
| ~ ( subset @ ( sk3 @ ZJ ) @ ZJ )
| ~ ( in @ ZI @ ZJ )
| ( in @ U @ ZJ )
| ( ( in @ C @ R )
!= ( in @ U @ T ) ) ),
inference(paramod_ordered,[status(thm)],[1469,1469]) ).
thf(3076,plain,
! [ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ~ ( subset @ ( sk3 @ D ) @ D )
| ~ ( in @ A @ D )
| ~ ( subset @ ( sk3 @ E ) @ E )
| ~ ( in @ D @ E )
| ~ ( subset @ ( sk3 @ F ) @ F )
| ~ ( in @ E @ F )
| ~ ( subset @ ( sk3 @ G ) @ G )
| ~ ( in @ F @ G )
| ~ ( subset @ ( sk3 @ H ) @ H )
| ~ ( in @ G @ H )
| ~ ( subset @ ( sk3 @ I ) @ I )
| ~ ( in @ H @ I )
| ~ ( subset @ ( sk3 @ J ) @ J )
| ~ ( in @ I @ J )
| ~ ( subset @ ( sk3 @ K ) @ K )
| ~ ( in @ J @ K )
| ~ ( subset @ ( sk3 @ L ) @ L )
| ~ ( in @ K @ L )
| ~ ( subset @ ( sk3 @ M ) @ M )
| ~ ( in @ L @ M )
| ~ ( subset @ ( sk3 @ N ) @ N )
| ~ ( in @ M @ N )
| ~ ( subset @ ( sk3 @ O ) @ O )
| ~ ( in @ N @ O )
| ~ ( subset @ ( sk3 @ P ) @ P )
| ~ ( in @ O @ P )
| ~ ( subset @ ( sk3 @ Q ) @ Q )
| ~ ( in @ P @ Q )
| ~ ( subset @ ( sk3 @ R ) @ R )
| ~ ( in @ Q @ R )
| ~ ( subset @ ( sk3 @ S ) @ S )
| ~ ( in @ T @ S )
| ~ ( subset @ ( sk3 @ V ) @ V )
| ~ ( in @ S @ V )
| ~ ( subset @ ( sk3 @ W ) @ W )
| ~ ( in @ V @ W )
| ~ ( subset @ ( sk3 @ X ) @ X )
| ~ ( in @ W @ X )
| ~ ( subset @ ( sk3 @ Y ) @ Y )
| ~ ( in @ X @ Y )
| ~ ( subset @ ( sk3 @ Z ) @ Z )
| ~ ( in @ Y @ Z )
| ~ ( subset @ ( sk3 @ ZA ) @ ZA )
| ~ ( in @ Z @ ZA )
| ~ ( subset @ ( sk3 @ ZB ) @ ZB )
| ~ ( in @ ZA @ ZB )
| ~ ( subset @ ( sk3 @ ZC ) @ ZC )
| ~ ( in @ ZB @ ZC )
| ~ ( subset @ ( sk3 @ ZD ) @ ZD )
| ~ ( in @ ZC @ ZD )
| ~ ( subset @ ( sk3 @ ZE ) @ ZE )
| ~ ( in @ ZD @ ZE )
| ~ ( subset @ ( sk3 @ ZF ) @ ZF )
| ~ ( in @ ZE @ ZF )
| ~ ( subset @ ( sk3 @ ZG ) @ ZG )
| ~ ( in @ ZF @ ZG )
| ~ ( subset @ ( sk3 @ ZH ) @ ZH )
| ~ ( in @ ZG @ ZH )
| ~ ( subset @ ( sk3 @ ZI ) @ ZI )
| ~ ( in @ ZH @ ZI )
| ~ ( subset @ ( sk3 @ ZJ ) @ ZJ )
| ~ ( in @ ZI @ ZJ )
| ( in @ U @ ZJ )
| ( ( in @ C @ R )
!= ( in @ U @ T ) ) ),
inference(simp,[status(thm)],[3075]) ).
thf(3077,plain,
! [ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ~ ( subset @ ( sk3 @ D ) @ D )
| ~ ( in @ A @ D )
| ~ ( subset @ ( sk3 @ E ) @ E )
| ~ ( in @ D @ E )
| ~ ( subset @ ( sk3 @ F ) @ F )
| ~ ( in @ E @ F )
| ~ ( subset @ ( sk3 @ G ) @ G )
| ~ ( in @ F @ G )
| ~ ( subset @ ( sk3 @ H ) @ H )
| ~ ( in @ G @ H )
| ~ ( subset @ ( sk3 @ I ) @ I )
| ~ ( in @ H @ I )
| ~ ( subset @ ( sk3 @ J ) @ J )
| ~ ( in @ I @ J )
| ~ ( subset @ ( sk3 @ K ) @ K )
| ~ ( in @ J @ K )
| ~ ( subset @ ( sk3 @ L ) @ L )
| ~ ( in @ K @ L )
| ~ ( subset @ ( sk3 @ M ) @ M )
| ~ ( in @ L @ M )
| ~ ( subset @ ( sk3 @ N ) @ N )
| ~ ( in @ M @ N )
| ~ ( subset @ ( sk3 @ O ) @ O )
| ~ ( in @ N @ O )
| ~ ( subset @ ( sk3 @ P ) @ P )
| ~ ( in @ O @ P )
| ~ ( subset @ ( sk3 @ Q ) @ Q )
| ~ ( in @ P @ Q )
| ~ ( subset @ ( sk3 @ R ) @ R )
| ~ ( in @ Q @ R )
| ~ ( subset @ ( sk3 @ S ) @ S )
| ~ ( in @ R @ S )
| ~ ( subset @ ( sk3 @ T ) @ T )
| ~ ( in @ S @ T )
| ~ ( subset @ ( sk3 @ U ) @ U )
| ~ ( in @ T @ U )
| ~ ( subset @ ( sk3 @ V ) @ V )
| ~ ( in @ U @ V )
| ~ ( subset @ ( sk3 @ W ) @ W )
| ~ ( in @ V @ W )
| ~ ( subset @ ( sk3 @ X ) @ X )
| ~ ( in @ W @ X )
| ~ ( subset @ ( sk3 @ Y ) @ Y )
| ~ ( in @ X @ Y )
| ~ ( subset @ ( sk3 @ Z ) @ Z )
| ~ ( in @ Y @ Z )
| ~ ( subset @ ( sk3 @ ZA ) @ ZA )
| ~ ( in @ Z @ ZA )
| ~ ( subset @ ( sk3 @ ZB ) @ ZB )
| ~ ( in @ ZA @ ZB )
| ~ ( subset @ ( sk3 @ ZC ) @ ZC )
| ~ ( in @ ZB @ ZC )
| ~ ( subset @ ( sk3 @ ZD ) @ ZD )
| ~ ( in @ ZC @ ZD )
| ~ ( subset @ ( sk3 @ ZE ) @ ZE )
| ~ ( in @ ZD @ ZE )
| ~ ( subset @ ( sk3 @ ZF ) @ ZF )
| ~ ( in @ ZE @ ZF )
| ~ ( subset @ ( sk3 @ ZG ) @ ZG )
| ~ ( in @ ZF @ ZG )
| ~ ( subset @ ( sk3 @ ZH ) @ ZH )
| ~ ( in @ ZG @ ZH )
| ( in @ C @ ZH ) ),
inference(pattern_uni,[status(thm)],[3076:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( H )),bind(I,$thf( I )),bind(J,$thf( J )),bind(K,$thf( K )),bind(L,$thf( L )),bind(M,$thf( M )),bind(N,$thf( N )),bind(O,$thf( O )),bind(P,$thf( P )),bind(Q,$thf( Q )),bind(R,$thf( R )),bind(S,$thf( S )),bind(T,$thf( R )),bind(U,$thf( C ))]]) ).
thf(4307,plain,
! [ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ~ ( subset @ ( sk3 @ D ) @ D )
| ~ ( in @ A @ D )
| ~ ( subset @ ( sk3 @ E ) @ E )
| ~ ( in @ D @ E )
| ~ ( subset @ ( sk3 @ F ) @ F )
| ~ ( in @ E @ F )
| ~ ( subset @ ( sk3 @ G ) @ G )
| ~ ( in @ F @ G )
| ~ ( subset @ ( sk3 @ H ) @ H )
| ~ ( in @ G @ H )
| ~ ( subset @ ( sk3 @ I ) @ I )
| ~ ( in @ H @ I )
| ~ ( subset @ ( sk3 @ J ) @ J )
| ~ ( in @ I @ J )
| ~ ( subset @ ( sk3 @ K ) @ K )
| ~ ( in @ J @ K )
| ~ ( subset @ ( sk3 @ L ) @ L )
| ~ ( in @ K @ L )
| ~ ( subset @ ( sk3 @ M ) @ M )
| ~ ( in @ L @ M )
| ~ ( subset @ ( sk3 @ N ) @ N )
| ~ ( in @ M @ N )
| ~ ( subset @ ( sk3 @ O ) @ O )
| ~ ( in @ N @ O )
| ~ ( subset @ ( sk3 @ P ) @ P )
| ~ ( in @ O @ P )
| ~ ( subset @ ( sk3 @ Q ) @ Q )
| ~ ( in @ P @ Q )
| ~ ( subset @ ( sk3 @ R ) @ R )
| ~ ( in @ Q @ R )
| ~ ( subset @ ( sk3 @ S ) @ S )
| ~ ( in @ R @ S )
| ~ ( subset @ ( sk3 @ T ) @ T )
| ~ ( in @ S @ T )
| ~ ( subset @ ( sk3 @ U ) @ U )
| ~ ( in @ T @ U )
| ~ ( subset @ ( sk3 @ V ) @ V )
| ~ ( in @ U @ V )
| ~ ( subset @ ( sk3 @ W ) @ W )
| ~ ( in @ V @ W )
| ~ ( subset @ ( sk3 @ X ) @ X )
| ~ ( in @ W @ X )
| ~ ( subset @ ( sk3 @ Y ) @ Y )
| ~ ( in @ X @ Y )
| ~ ( subset @ ( sk3 @ Z ) @ Z )
| ~ ( in @ Y @ Z )
| ~ ( subset @ ( sk3 @ ZA ) @ ZA )
| ~ ( in @ Z @ ZA )
| ~ ( subset @ ( sk3 @ ZB ) @ ZB )
| ~ ( in @ ZA @ ZB )
| ~ ( subset @ ( sk3 @ ZC ) @ ZC )
| ~ ( in @ ZB @ ZC )
| ~ ( subset @ ( sk3 @ ZD ) @ ZD )
| ~ ( in @ ZC @ ZD )
| ~ ( subset @ ( sk3 @ ZE ) @ ZE )
| ~ ( in @ ZD @ ZE )
| ~ ( subset @ ( sk3 @ ZF ) @ ZF )
| ~ ( in @ ZE @ ZF )
| ~ ( subset @ ( sk3 @ ZG ) @ ZG )
| ~ ( in @ ZF @ ZG )
| ~ ( subset @ ( sk3 @ ZH ) @ ZH )
| ~ ( in @ ZG @ ZH )
| ( in @ C @ ZH ) ),
inference(simp,[status(thm)],[3077]) ).
thf(14656,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk4 )
| ~ $true
| ( subset @ B @ A )
| ( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ sk5 )
!= ( in @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,24]) ).
thf(14657,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk4 )
| ( subset @ B @ A )
| ( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ sk5 )
!= ( in @ B @ A ) ) ),
inference(simp,[status(thm)],[14656]) ).
thf(14658,plain,
( ~ ( in @ sk5 @ sk4 )
| ( subset @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ sk5 ) ),
inference(pattern_uni,[status(thm)],[14657:[bind(A,$thf( sk5 )),bind(B,$thf( sk2 @ ( setunion @ sk4 ) @ sk5 ))]]) ).
thf(14849,plain,
! [A: $o] :
( A
| ~ $true
| ( ( in @ ( sk1 @ A @ sk5 @ sk4 ) @ sk4 )
!= ( in @ ( setunion @ sk4 ) @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[13334,14842]) ).
thf(14850,plain,
! [A: $o] :
( A
| ( ( in @ ( sk1 @ A @ sk5 @ sk4 ) @ sk4 )
!= ( in @ ( setunion @ sk4 ) @ sk4 ) ) ),
inference(simp,[status(thm)],[14849]) ).
thf(14903,plain,
! [A: $o] :
( A
| ( ( sk1 @ A @ sk5 @ sk4 )
!= ( setunion @ sk4 ) )
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[14850]) ).
thf(14917,plain,
! [A: $o] :
( A
| ( ( sk1 @ A @ sk5 @ sk4 )
!= ( setunion @ sk4 ) ) ),
inference(simp,[status(thm)],[14903]) ).
thf(13743,plain,
! [A: $i] :
( ~ $true
| ( in @ A @ ( setunion @ ( setunion @ sk4 ) ) )
| ( ( in @ ( sk1 @ $false @ sk5 @ sk4 ) @ sk4 )
!= ( in @ A @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[13702,355]) ).
thf(13744,plain,
! [A: $i] :
( ( in @ A @ ( setunion @ ( setunion @ sk4 ) ) )
| ( ( in @ ( sk1 @ $false @ sk5 @ sk4 ) @ sk4 )
!= ( in @ A @ sk5 ) ) ),
inference(simp,[status(thm)],[13743]) ).
thf(13977,plain,
! [A: $i] :
( ( in @ A @ ( setunion @ ( setunion @ sk4 ) ) )
| ( ( sk1 @ $false @ sk5 @ sk4 )
!= A )
| ( sk5 != sk4 ) ),
inference(simp,[status(thm)],[13744]) ).
thf(13996,plain,
( ( in @ ( sk1 @ $false @ sk5 @ sk4 ) @ ( setunion @ ( setunion @ sk4 ) ) )
| ( sk5 != sk4 ) ),
inference(simp,[status(thm)],[13977]) ).
thf(13013,plain,
! [C: $o,B: $i,A: $i] :
( ~ $true
| ( in @ ( sk1 @ C @ B @ A ) @ A )
| C
| ( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ ( setunion @ sk4 ) ) )
!= ( in @ B @ ( setunion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[1790,22]) ).
thf(13014,plain,
! [C: $o,B: $i,A: $i] :
( ( in @ ( sk1 @ C @ B @ A ) @ A )
| C
| ( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ ( setunion @ sk4 ) ) )
!= ( in @ B @ ( setunion @ A ) ) ) ),
inference(simp,[status(thm)],[13013]) ).
thf(13015,plain,
! [A: $o] :
( ( in @ ( sk1 @ A @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) ) @ ( setunion @ sk4 ) )
| A ),
inference(pattern_uni,[status(thm)],[13014:[bind(A,$thf( setunion @ sk4 )),bind(B,$thf( sk2 @ ( setunion @ sk4 ) @ sk5 )),bind(C,$thf( C ))]]) ).
thf(13368,plain,
! [A: $o] :
( ( in @ ( sk1 @ A @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) ) @ ( setunion @ sk4 ) )
| A ),
inference(simp,[status(thm)],[13015]) ).
thf(1922,plain,
! [C: $o,B: $i,A: $i] :
( ~ $true
| ( in @ B @ ( sk1 @ C @ B @ A ) )
| C
| ( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ ( setunion @ sk4 ) ) )
!= ( in @ B @ ( setunion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[1790,17]) ).
thf(1923,plain,
! [C: $o,B: $i,A: $i] :
( ( in @ B @ ( sk1 @ C @ B @ A ) )
| C
| ( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ ( setunion @ sk4 ) ) )
!= ( in @ B @ ( setunion @ A ) ) ) ),
inference(simp,[status(thm)],[1922]) ).
thf(1924,plain,
! [A: $o] :
( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( sk1 @ A @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) ) )
| A ),
inference(pattern_uni,[status(thm)],[1923:[bind(A,$thf( setunion @ sk4 )),bind(B,$thf( sk2 @ ( setunion @ sk4 ) @ sk5 )),bind(C,$thf( C ))]]) ).
thf(1993,plain,
! [A: $o] :
( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( sk1 @ A @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) ) )
| A ),
inference(simp,[status(thm)],[1924]) ).
thf(14879,plain,
( ~ $true
| ( ( in @ ( sk1 @ $false @ sk5 @ sk4 ) @ sk4 )
!= ( in @ ( setunion @ sk4 ) @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[13702,14842]) ).
thf(14880,plain,
( ( in @ ( sk1 @ $false @ sk5 @ sk4 ) @ sk4 )
!= ( in @ ( setunion @ sk4 ) @ sk4 ) ),
inference(simp,[status(thm)],[14879]) ).
thf(14892,plain,
( ( ( sk1 @ $false @ sk5 @ sk4 )
!= ( setunion @ sk4 ) )
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[14880]) ).
thf(14910,plain,
( ( sk1 @ $false @ sk5 @ sk4 )
!= ( setunion @ sk4 ) ),
inference(simp,[status(thm)],[14892]) ).
thf(231,plain,
( ( in @ sk5 @ ( sk1 @ $false @ sk5 @ sk4 ) )
| $false ),
inference(prim_subst,[status(thm)],[205:[bind(A,$thf( $false ))]]) ).
thf(240,plain,
in @ sk5 @ ( sk1 @ $false @ sk5 @ sk4 ),
inference(simp,[status(thm)],[231]) ).
thf(12602,plain,
( ~ $true
| ( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) )
!= ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[27,12009]) ).
thf(12603,plain,
( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) )
!= ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ sk5 ) ),
inference(simp,[status(thm)],[12602]) ).
thf(12656,plain,
( ( ( sk2 @ ( setunion @ sk4 ) @ sk5 )
!= ( sk2 @ ( setunion @ sk4 ) @ sk5 ) )
| ( ( setunion @ sk4 )
!= sk5 ) ),
inference(simp,[status(thm)],[12603]) ).
thf(12680,plain,
( ( setunion @ sk4 )
!= sk5 ),
inference(simp,[status(thm)],[12656]) ).
thf(15167,plain,
( ( in @ ( sk1 @ $false @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) ) @ ( setunion @ sk4 ) )
| $false ),
inference(prim_subst,[status(thm)],[13368:[bind(A,$thf( $false ))]]) ).
thf(15220,plain,
in @ ( sk1 @ $false @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) ) @ ( setunion @ sk4 ),
inference(simp,[status(thm)],[15167]) ).
thf(15569,plain,
! [C: $o,B: $i,A: $i] :
( ~ $true
| ( in @ ( sk1 @ C @ B @ A ) @ A )
| C
| ( ( in @ ( sk1 @ $false @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) ) @ ( setunion @ sk4 ) )
!= ( in @ B @ ( setunion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[15220,22]) ).
thf(15570,plain,
! [C: $o,B: $i,A: $i] :
( ( in @ ( sk1 @ C @ B @ A ) @ A )
| C
| ( ( in @ ( sk1 @ $false @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) ) @ ( setunion @ sk4 ) )
!= ( in @ B @ ( setunion @ A ) ) ) ),
inference(simp,[status(thm)],[15569]) ).
thf(15571,plain,
! [A: $o] :
( ( in @ ( sk1 @ A @ ( sk1 @ $false @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) ) @ sk4 ) @ sk4 )
| A ),
inference(pattern_uni,[status(thm)],[15570:[bind(A,$thf( sk4 )),bind(B,$thf( sk1 @ $false @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) )),bind(C,$thf( C ))]]) ).
thf(15689,plain,
! [A: $o] :
( ( in @ ( sk1 @ A @ ( sk1 @ $false @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) ) @ sk4 ) @ sk4 )
| A ),
inference(simp,[status(thm)],[15571]) ).
thf(16047,plain,
( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( sk1 @ $false @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) ) )
| $false ),
inference(prim_subst,[status(thm)],[1993:[bind(A,$thf( $false ))]]) ).
thf(16094,plain,
in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( sk1 @ $false @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) ),
inference(simp,[status(thm)],[16047]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ $true
| ( in @ C @ A )
| ( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ sk5 )
!= ( in @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[27,18]) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ( in @ C @ A )
| ( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ sk5 )
!= ( in @ C @ B ) ) ),
inference(simp,[status(thm)],[46]) ).
thf(48,plain,
! [A: $i] :
( ~ ( subset @ ( sk3 @ A ) @ A )
| ~ ( in @ sk5 @ A )
| ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ A ) ),
inference(pattern_uni,[status(thm)],[47:[bind(A,$thf( A )),bind(B,$thf( sk5 )),bind(C,$thf( sk2 @ ( setunion @ sk4 ) @ sk5 ))]]) ).
thf(14853,plain,
! [A: $i] :
( ~ ( in @ A @ sk5 )
| ~ $true
| ( ( in @ A @ ( setunion @ ( setunion @ sk4 ) ) )
!= ( in @ ( setunion @ sk4 ) @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[355,14842]) ).
thf(14854,plain,
! [A: $i] :
( ~ ( in @ A @ sk5 )
| ( ( in @ A @ ( setunion @ ( setunion @ sk4 ) ) )
!= ( in @ ( setunion @ sk4 ) @ sk4 ) ) ),
inference(simp,[status(thm)],[14853]) ).
thf(14902,plain,
! [A: $i] :
( ~ ( in @ A @ sk5 )
| ( A
!= ( setunion @ sk4 ) )
| ( ( setunion @ ( setunion @ sk4 ) )
!= sk4 ) ),
inference(simp,[status(thm)],[14854]) ).
thf(14916,plain,
( ~ ( in @ ( setunion @ sk4 ) @ sk5 )
| ( ( setunion @ ( setunion @ sk4 ) )
!= sk4 ) ),
inference(simp,[status(thm)],[14902]) ).
thf(14873,plain,
( ~ $true
| ( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ sk5 )
!= ( in @ ( setunion @ sk4 ) @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[27,14842]) ).
thf(14874,plain,
( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ sk5 )
!= ( in @ ( setunion @ sk4 ) @ sk4 ) ),
inference(simp,[status(thm)],[14873]) ).
thf(14896,plain,
( ( ( sk2 @ ( setunion @ sk4 ) @ sk5 )
!= ( setunion @ sk4 ) )
| ( sk5 != sk4 ) ),
inference(simp,[status(thm)],[14874]) ).
thf(227,plain,
! [A: $o] :
( A
| ( ( in @ sk5 @ ( sk1 @ A @ sk5 @ sk4 ) )
!= A )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[205]) ).
thf(235,plain,
! [A: $o] :
( A
| ( ( in @ sk5 @ ( sk1 @ A @ sk5 @ sk4 ) )
!= A ) ),
inference(simp,[status(thm)],[227]) ).
thf(12063,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ~ $true
| ( subset @ C @ D )
| ( ( in @ ( sk2 @ B @ A ) @ A )
!= ( in @ ( sk2 @ D @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[20,21]) ).
thf(12064,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ( subset @ C @ D )
| ( ( in @ ( sk2 @ B @ A ) @ A )
!= ( in @ ( sk2 @ D @ C ) @ D ) ) ),
inference(simp,[status(thm)],[12063]) ).
thf(12065,plain,
! [A: $i] :
( ( subset @ A @ A )
| ( subset @ A @ A ) ),
inference(pattern_uni,[status(thm)],[12064:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(12273,plain,
! [A: $i] : ( subset @ A @ A ),
inference(simp,[status(thm)],[12065]) ).
thf(15447,plain,
( ~ $true
| ( ( in @ ( sk1 @ $false @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) ) @ ( setunion @ sk4 ) )
!= ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[15220,12009]) ).
thf(15448,plain,
( ( in @ ( sk1 @ $false @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) ) @ ( setunion @ sk4 ) )
!= ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) ) ),
inference(simp,[status(thm)],[15447]) ).
thf(15636,plain,
( ( ( sk1 @ $false @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) )
!= ( sk2 @ ( setunion @ sk4 ) @ sk5 ) )
| ( ( setunion @ sk4 )
!= ( setunion @ sk4 ) ) ),
inference(simp,[status(thm)],[15448]) ).
thf(15653,plain,
( ( sk1 @ $false @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) )
!= ( sk2 @ ( setunion @ sk4 ) @ sk5 ) ),
inference(simp,[status(thm)],[15636]) ).
thf(1774,plain,
! [B: $i,A: $o] :
( ~ A
| ~ $true
| ( in @ B @ ( setunion @ ( setunion @ sk4 ) ) )
| ( ( in @ sk5 @ ( sk1 @ ~ A @ sk5 @ sk4 ) )
!= ( in @ B @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[238,355]) ).
thf(1775,plain,
! [B: $i,A: $o] :
( ~ A
| ( in @ B @ ( setunion @ ( setunion @ sk4 ) ) )
| ( ( in @ sk5 @ ( sk1 @ ~ A @ sk5 @ sk4 ) )
!= ( in @ B @ sk5 ) ) ),
inference(simp,[status(thm)],[1774]) ).
thf(1885,plain,
! [A: $i] :
( ( in @ A @ ( setunion @ ( setunion @ sk4 ) ) )
| ( sk5 != A )
| ( ( sk1 @ ~ $true @ sk5 @ sk4 )
!= sk5 ) ),
inference(simp,[status(thm)],[1775]) ).
thf(1908,plain,
( ( in @ sk5 @ ( setunion @ ( setunion @ sk4 ) ) )
| ( ( sk1 @ $false @ sk5 @ sk4 )
!= sk5 ) ),
inference(simp,[status(thm)],[1885]) ).
thf(17022,plain,
( ~ $true
| ( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( sk1 @ $false @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) ) )
!= ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[16094,12009]) ).
thf(17023,plain,
( ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( sk1 @ $false @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) ) )
!= ( in @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) ) ),
inference(simp,[status(thm)],[17022]) ).
thf(17219,plain,
( ( ( sk2 @ ( setunion @ sk4 ) @ sk5 )
!= ( sk2 @ ( setunion @ sk4 ) @ sk5 ) )
| ( ( sk1 @ $false @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) )
!= ( setunion @ sk4 ) ) ),
inference(simp,[status(thm)],[17023]) ).
thf(17265,plain,
( ( sk1 @ $false @ ( sk2 @ ( setunion @ sk4 ) @ sk5 ) @ ( setunion @ sk4 ) )
!= ( setunion @ sk4 ) ),
inference(simp,[status(thm)],[17219]) ).
thf(6,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ( in @ C @ A ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ ( sk3 @ A ) @ A )
| ~ ( in @ B @ A )
| ~ ( in @ C @ B )
| ( in @ C @ A ) ),
inference(simp,[status(thm)],[6]) ).
thf(232,plain,
! [B: $o,A: $o] :
( ( in @ sk5
@ ( sk1
@ ( A
| B )
@ sk5
@ sk4 ) )
| A
| B ),
inference(prim_subst,[status(thm)],[205:[bind(A,$thf( B | C ))]]) ).
thf(241,plain,
! [B: $o,A: $o] :
( ( in @ sk5
@ ( sk1
@ ( A
| B )
@ sk5
@ sk4 ) )
| A
| B ),
inference(cnf,[status(esa)],[232]) ).
thf(242,plain,
! [B: $o,A: $o] :
( ( in @ sk5
@ ( sk1
@ ( A
| B )
@ sk5
@ sk4 ) )
| A
| B ),
inference(simp,[status(thm)],[241]) ).
thf(19150,plain,
$false,
inference(e,[status(thm)],[238,1915,14681,14893,17,13334,1790,15,454,1469,12597,13700,42,24,12009,12682,20,1778,280,4307,14658,14917,12260,21,12546,13996,9,134,205,13368,22,27,12,54,1993,14910,240,12680,15689,13702,3,16094,355,48,18,14842,15220,14916,14896,235,12273,15653,1908,17265,19,242,807]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU815^2 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.09/0.20 % Computer : n004.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:33:52 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 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
% 0.66/0.50 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.93/0.61 % [INFO] Parsing done (108ms).
% 0.93/0.62 % [INFO] Running in sequential loop mode.
% 1.43/0.85 % [INFO] eprover registered as external prover.
% 1.43/0.86 % [INFO] Scanning for conjecture ...
% 1.68/0.93 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.68/0.95 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.68/0.95 % [INFO] Problem is higher-order (TPTP THF).
% 1.68/0.95 % [INFO] Type checking passed.
% 1.68/0.96 % [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 ...
% 76.52/23.04 % External prover 'e' found a proof!
% 76.52/23.04 % [INFO] Killing All external provers ...
% 76.52/23.04 % Time passed: 22763ms (effective reasoning time: 22421ms)
% 76.52/23.04 % 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)>
% 76.52/23.04 % Axioms used in derivation (0):
% 76.52/23.04 % No. of inferences in proof: 180
% 76.52/23.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 22763 ms resp. 22421 ms w/o parsing
% 69.89/23.19 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 69.89/23.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------