%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV452^1 : TPTP v9.3.1. Released v7.0.0.
% 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 : n006.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 08:37:19 AM UTC 2026
% Result : Theorem 184.93s 94.69s
% Output : Refutation 185.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 4
% Syntax : Number of formulae : 66 ( 26 unt; 0 typ; 1 def)
% Number of atoms : 338 ( 71 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 888 ( 88 ~; 68 |; 22 &; 710 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 156 ( 156 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 4 usr; 5 con; 0-4 aty)
% Number of variables : 280 ( 55 ^; 224 !; 0 ?; 280 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(skt1_type,type,
skt1: $tType ).
thf('const/sets/INTER_decl',type,
'const/sets/INTER':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA > $o ) ).
thf('const/sets/IN_decl',type,
'const/sets/IN':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf(sk1_decl,type,
sk1: skt1 > $o ).
thf(sk2_decl,type,
sk2: skt1 ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1 > $o] :
( ( 'const/sets/INTER' @ skt1 @ A @ A )
!= A ) ) ) ).
thf(3,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( 'const/sets/IN' @ TA @ B @ A )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(9,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( 'const/sets/IN' @ TA @ B @ A )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( 'const/sets/IN' @ TA @ B @ A )
= ( A @ B ) ),
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( 'const/sets/IN' @ TA @ B @ A )
= ( A @ B ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/INTER' @ TA @ A @ B ) )
= ( ( 'const/sets/IN' @ TA @ C @ A )
& ( 'const/sets/IN' @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_INTER_') ).
thf(12,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/INTER' @ TA @ A @ B ) )
= ( ( 'const/sets/IN' @ TA @ C @ A )
& ( 'const/sets/IN' @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
( ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/INTER' @ TA @ A @ B ) )
= ( ( 'const/sets/IN' @ TA @ C @ A )
& ( 'const/sets/IN' @ TA @ C @ B ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(14,plain,
! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
( ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/INTER' @ TA @ A @ B ) )
= ( ( 'const/sets/IN' @ TA @ C @ A )
& ( 'const/sets/IN' @ TA @ C @ B ) ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(136,plain,
! [TA: $tType,TB: $tType,E: TB,D: TB > $o,C: TB > $o,B: TA,A: TA > $o] :
( ( ( 'const/sets/IN' @ TA @ B @ A )
= ( ( 'const/sets/IN' @ TB @ E @ C )
& ( 'const/sets/IN' @ TB @ E @ D ) ) )
| ( ( A @ B )
!= ( 'const/sets/IN' @ TB @ E @ ( 'const/sets/INTER' @ TB @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,14]) ).
thf(149,plain,
! [TA: $tType,TB: $tType,F: TA > TB > TB > $o,E: TA > TB > TB > $o,D: TA > TB,C: TB > $o,B: TB > $o,A: TA] :
( ( ( 'const/sets/IN' @ TA @ A
@ ^ [G: TA] :
( 'const/sets/IN' @ TB @ ( D @ G )
@ ^ [H: TB] : ( 'const/sets/INTER' @ TB @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
= ( ( 'const/sets/IN' @ TB @ ( D @ A ) @ B )
& ( 'const/sets/IN' @ TB @ ( D @ A ) @ C ) ) )
| ( ( E @ A )
!= ( ^ [G: TB] : B ) )
| ( ( F @ A )
!= ( ^ [G: TB] : C ) ) ),
inference(pre_uni,[status(thm)],[136:[bind(A,$thf( ^ [I: TA] : ( 'const/sets/IN' @ TB @ ( F @ I ) @ ^ [J: TB] : ( 'const/sets/INTER' @ TB @ ( H @ I @ J ) @ ( I @ I @ J ) @ J ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( F @ B ))]]) ).
thf(150,plain,
! [TA: $tType,TB: $tType,F: TA > TB > TB > $o,E: TA > TB > TB > $o,D: TA > TB,C: TB > $o,B: TB > $o,A: TA] :
( ( ( 'const/sets/IN' @ TA @ A
@ ^ [G: TA] :
( 'const/sets/IN' @ TB @ ( D @ G )
@ ^ [H: TB] : ( 'const/sets/INTER' @ TB @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
= ( ( 'const/sets/IN' @ TB @ ( D @ A ) @ B )
& ( 'const/sets/IN' @ TB @ ( D @ A ) @ C ) ) )
| ( ( E @ A )
!= ( ^ [G: TB] : B ) )
| ( ( F @ A )
!= ( ^ [G: TB] : C ) ) ),
inference(pre_uni,[status(thm)],[149:[]]) ).
thf(163,plain,
! [TA: $tType,TB: $tType,F: TA > TB > TB > $o,E: TA > TB > TB > $o,D: TA > TB,C: TB > $o,B: TB > $o,A: TA] :
( ( ( 'const/sets/IN' @ TA @ A
@ ^ [G: TA] :
( 'const/sets/IN' @ TB @ ( D @ G )
@ ^ [H: TB] : ( 'const/sets/INTER' @ TB @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
= ( ( 'const/sets/IN' @ TB @ ( D @ A ) @ B )
& ( 'const/sets/IN' @ TB @ ( D @ A ) @ C ) ) )
| ( ( E @ A )
!= ( ^ [G: TB] : B ) )
| ( ( F @ A )
!= ( ^ [G: TB] : C ) ) ),
inference(simp,[status(thm)],[150]) ).
thf(130,plain,
! [TA: $tType,TB: $tType,E: TB,D: TB > $o,C: TB > $o,B: TA,A: TA > $o] :
( ( ( A @ B )
= ( ( 'const/sets/IN' @ TB @ E @ C )
& ( 'const/sets/IN' @ TB @ E @ D ) ) )
| ( ( 'const/sets/IN' @ TA @ B @ A )
!= ( 'const/sets/IN' @ TB @ E @ ( 'const/sets/INTER' @ TB @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,14]) ).
thf(131,plain,
! [TB: $tType,C: TB > $o,B: TB > $o,A: TB] :
( ( ( 'const/sets/IN' @ TB @ A @ B )
& ( 'const/sets/IN' @ TB @ A @ C ) )
= ( 'const/sets/INTER' @ TB @ B @ C @ A ) ),
inference(pattern_uni,[status(thm)],[130:[bind(A,$thf( 'const/sets/INTER' @ TB @ C @ D )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind_type(TA,$thf( TB ))]]) ).
thf(151,plain,
! [TA: $tType,C: TA > $o,B: TA > $o,A: TA] :
( ( ( 'const/sets/IN' @ TA @ A @ B )
& ( 'const/sets/IN' @ TA @ A @ C ) )
= ( 'const/sets/INTER' @ TA @ B @ C @ A ) ),
inference(simp,[status(thm)],[131]) ).
thf(17518,plain,
! [TA: $tType,TB: $tType,F: TA > TB > TB > $o,E: TA > TB > TB > $o,D: TA > TB,C: TB > $o,B: TB > $o,A: TA] :
( ( ( 'const/sets/IN' @ TA @ A
@ ^ [G: TA] :
( 'const/sets/IN' @ TB @ ( D @ G )
@ ^ [H: TB] : ( 'const/sets/INTER' @ TB @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
= ( 'const/sets/INTER' @ TB @ B @ C @ ( D @ A ) ) )
| ( ( E @ A )
!= ( ^ [G: TB] : B ) )
| ( ( F @ A )
!= ( ^ [G: TB] : C ) ) ),
inference(rewrite,[status(thm)],[163,151]) ).
thf(1,conjecture,
! [TA: $tType,A: TA > $o] :
( ( 'const/sets/INTER' @ TA @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INTER_IDEMPOT_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > $o] :
( ( 'const/sets/INTER' @ TA @ A @ A )
= A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [TA: $tType,A: TA > $o] :
( ( 'const/sets/INTER' @ TA @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
( ( 'const/sets/INTER' @ skt1 @ sk1 @ sk1 )
!= sk1 ),
inference(cnf,[status(esa)],[6]) ).
thf(8,plain,
( ( 'const/sets/INTER' @ skt1 @ sk1 @ sk1 )
!= sk1 ),
inference(lifteq,[status(thm)],[7]) ).
thf(18,plain,
( ( 'const/sets/INTER' @ skt1 @ sk1 @ sk1 @ sk2 )
!= ( sk1 @ sk2 ) ),
inference(func_ext,[status(esa)],[8]) ).
thf(20,plain,
( ( 'const/sets/INTER' @ skt1 @ sk1 @ sk1 @ sk2 )
| ( sk1 @ sk2 ) ),
inference(bool_ext,[status(thm)],[18]) ).
thf(22,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( 'const/sets/IN' @ TA @ B @ A )
| ~ ( A @ B ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(118,plain,
! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
( ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/INTER' @ TA @ A @ B ) )
| ~ ( ( 'const/sets/IN' @ TA @ C @ A )
& ( 'const/sets/IN' @ TA @ C @ B ) ) ),
inference(bool_ext,[status(thm)],[14]) ).
thf(162,plain,
! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
( ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/INTER' @ TA @ A @ B ) )
| ~ ( 'const/sets/IN' @ TA @ C @ A )
| ~ ( 'const/sets/IN' @ TA @ C @ B ) ),
inference(cnf,[status(esa)],[118]) ).
thf(128,plain,
! [TA: $tType,TB: $tType,E: TB,D: TB > $o,C: TA,B: TA > $o,A: TA > $o] :
( ( ( ( 'const/sets/IN' @ TA @ C @ A )
& ( 'const/sets/IN' @ TA @ C @ B ) )
= ( 'const/sets/IN' @ TB @ E @ D ) )
| ( ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/INTER' @ TA @ A @ B ) )
!= ( D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[14,11]) ).
thf(146,plain,
! [TA: $tType,TB: $tType,F: TB > TA > TA > $o,E: TB > TA > TA > $o,D: TB > TA,C: TB,B: TA > $o,A: TA > $o] :
( ( ( ( 'const/sets/IN' @ TA @ ( D @ C ) @ A )
& ( 'const/sets/IN' @ TA @ ( D @ C ) @ B ) )
= ( 'const/sets/IN' @ TB @ C
@ ^ [G: TB] :
( 'const/sets/IN' @ TA @ ( D @ G )
@ ^ [H: TA] : ( 'const/sets/INTER' @ TA @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) ) )
| ( ( ^ [G: TA] : A )
!= ( E @ C ) )
| ( ( ^ [G: TA] : B )
!= ( F @ C ) ) ),
inference(pre_uni,[status(thm)],[128:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( F @ E )),bind(D,$thf( ^ [I: TB] : ( 'const/sets/IN' @ TA @ ( F @ I ) @ ^ [J: TA] : ( 'const/sets/INTER' @ TA @ ( H @ I @ J ) @ ( I @ I @ J ) @ J ) ) )),bind(E,$thf( E ))]]) ).
thf(147,plain,
! [TA: $tType,TB: $tType,F: TB > TA > TA > $o,E: TB > TA > TA > $o,D: TB > TA,C: TB,B: TA > $o,A: TA > $o] :
( ( ( ( 'const/sets/IN' @ TA @ ( D @ C ) @ A )
& ( 'const/sets/IN' @ TA @ ( D @ C ) @ B ) )
= ( 'const/sets/IN' @ TB @ C
@ ^ [G: TB] :
( 'const/sets/IN' @ TA @ ( D @ G )
@ ^ [H: TA] : ( 'const/sets/INTER' @ TA @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) ) )
| ( ( ^ [G: TA] : A )
!= ( E @ C ) )
| ( ( ^ [G: TA] : B )
!= ( F @ C ) ) ),
inference(pre_uni,[status(thm)],[146:[]]) ).
thf(157,plain,
! [TA: $tType,TB: $tType,F: TB > TA > TA > $o,E: TB > TA > TA > $o,D: TB > TA,C: TB,B: TA > $o,A: TA > $o] :
( ( ( ( 'const/sets/IN' @ TA @ ( D @ C ) @ A )
& ( 'const/sets/IN' @ TA @ ( D @ C ) @ B ) )
= ( 'const/sets/IN' @ TB @ C
@ ^ [G: TB] :
( 'const/sets/IN' @ TA @ ( D @ G )
@ ^ [H: TA] : ( 'const/sets/INTER' @ TA @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) ) )
| ( ( ^ [G: TA] : A )
!= ( E @ C ) )
| ( ( ^ [G: TA] : B )
!= ( F @ C ) ) ),
inference(simp,[status(thm)],[147]) ).
thf(11468,plain,
! [TA: $tType,TB: $tType,F: TB > TA > TA > $o,E: TB > TA > TA > $o,D: TB > TA,C: TB,B: TA > $o,A: TA > $o] :
( ( ( 'const/sets/INTER' @ TA @ A @ B @ ( D @ C ) )
= ( 'const/sets/IN' @ TB @ C
@ ^ [G: TB] :
( 'const/sets/IN' @ TA @ ( D @ G )
@ ^ [H: TA] : ( 'const/sets/INTER' @ TA @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) ) )
| ( ( ^ [G: TA] : A )
!= ( E @ C ) )
| ( ( ^ [G: TA] : B )
!= ( F @ C ) ) ),
inference(rewrite,[status(thm)],[157,151]) ).
thf(19,plain,
( ~ ( 'const/sets/INTER' @ skt1 @ sk1 @ sk1 @ sk2 )
| ~ ( sk1 @ sk2 ) ),
inference(bool_ext,[status(thm)],[18]) ).
thf(11632,plain,
! [TA: $tType,TB: $tType,F: TB > TA > TA > $o,E: TB > TA > TA > $o,D: TB > TA,C: TB,B: TA > $o,A: TA > $o] :
( ( ( ^ [G: TA] : A )
!= ( E @ C ) )
| ( ( ^ [G: TA] : B )
!= ( F @ C ) )
| ~ ( 'const/sets/IN' @ TB @ C
@ ^ [G: TB] :
( 'const/sets/IN' @ TA @ ( D @ G )
@ ^ [H: TA] : ( 'const/sets/INTER' @ TA @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
| ~ ( sk1 @ sk2 )
| ( ( 'const/sets/INTER' @ TA @ A @ B @ ( D @ C ) )
!= ( 'const/sets/INTER' @ skt1 @ sk1 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[11468,19]) ).
thf(11690,plain,
! [TB: $tType,C: TB > skt1 > skt1 > $o,B: TB > skt1 > skt1 > $o,A: TB] :
( ( ( ^ [D: skt1] : sk1 )
!= ( B @ A ) )
| ( ( ^ [D: skt1] : sk1 )
!= ( C @ A ) )
| ~ ( 'const/sets/IN' @ TB @ A
@ ^ [D: TB] :
( 'const/sets/IN' @ skt1 @ sk2
@ ^ [E: skt1] : ( 'const/sets/INTER' @ skt1 @ ( B @ D @ E ) @ ( C @ D @ E ) @ E ) ) )
| ~ ( sk1 @ sk2 ) ),
inference(pre_uni,[status(thm)],[11632:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 )),bind(C,$thf( C )),bind(D,$thf( ^ [G: TB] : sk2 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(11691,plain,
! [TB: $tType,A: TB] :
( ~ ( sk1 @ sk2 )
| ~ ( 'const/sets/IN' @ TB @ A
@ ^ [B: TB] : ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/INTER' @ skt1 @ sk1 @ sk1 ) ) ) ),
inference(pre_uni,[status(thm)],[11690:[bind(A,$thf( (@) )),bind(B,$thf( ^ [D: TB] : ^ [E: skt1] : sk1 )),bind(C,$thf( ^ [D: TB] : ^ [E: skt1] : sk1 ))]]) ).
thf(11886,plain,
! [TA: $tType,A: TA] :
( ~ ( sk1 @ sk2 )
| ~ ( 'const/sets/IN' @ TA @ A
@ ^ [B: TA] : ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/INTER' @ skt1 @ sk1 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[11691]) ).
thf(26954,plain,
! [TA: $tType,TB: $tType,C: TB,B: TA,A: TA > $o] :
( ~ ( A @ B )
| ~ ( sk1 @ sk2 )
| ~ $true
| ( ( 'const/sets/IN' @ TA @ B @ A )
!= ( 'const/sets/IN' @ TB @ C
@ ^ [D: TB] : ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/INTER' @ skt1 @ sk1 @ sk1 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[22,11886]) ).
thf(26955,plain,
! [TA: $tType,TB: $tType,C: TB,B: TA,A: TA > $o] :
( ~ ( A @ B )
| ~ ( sk1 @ sk2 )
| ( ( 'const/sets/IN' @ TA @ B @ A )
!= ( 'const/sets/IN' @ TB @ C
@ ^ [D: TB] : ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/INTER' @ skt1 @ sk1 @ sk1 ) ) ) ) ),
inference(simp,[status(thm)],[26954]) ).
thf(26956,plain,
( ~ ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/INTER' @ skt1 @ sk1 @ sk1 ) )
| ~ ( sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[26955:[bind(A,$thf( ^ [D: TB] : ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/INTER' @ skt1 @ sk1 @ sk1 ) ) )),bind(B,$thf( B )),bind(C,$thf( B )),bind_type(TA,$thf( TB ))]]) ).
thf(27080,plain,
! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
( ~ ( 'const/sets/IN' @ TA @ C @ A )
| ~ ( 'const/sets/IN' @ TA @ C @ B )
| ~ $true
| ~ ( sk1 @ sk2 )
| ( ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/INTER' @ TA @ A @ B ) )
!= ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/INTER' @ skt1 @ sk1 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[162,26956]) ).
thf(27081,plain,
! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
( ~ ( 'const/sets/IN' @ TA @ C @ A )
| ~ ( 'const/sets/IN' @ TA @ C @ B )
| ~ ( sk1 @ sk2 )
| ( ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/INTER' @ TA @ A @ B ) )
!= ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/INTER' @ skt1 @ sk1 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[27080]) ).
thf(27082,plain,
( ~ ( 'const/sets/IN' @ skt1 @ sk2 @ sk1 )
| ~ ( 'const/sets/IN' @ skt1 @ sk2 @ sk1 )
| ~ ( sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[27081:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(27120,plain,
( ~ ( 'const/sets/IN' @ skt1 @ sk2 @ sk1 )
| ~ ( sk1 @ sk2 ) ),
inference(simp,[status(thm)],[27082]) ).
thf(27348,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ~ ( A @ B )
| ~ $true
| ~ ( sk1 @ sk2 )
| ( ( 'const/sets/IN' @ TA @ B @ A )
!= ( 'const/sets/IN' @ skt1 @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[22,27120]) ).
thf(27349,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ~ ( A @ B )
| ~ ( sk1 @ sk2 )
| ( ( 'const/sets/IN' @ TA @ B @ A )
!= ( 'const/sets/IN' @ skt1 @ sk2 @ sk1 ) ) ),
inference(simp,[status(thm)],[27348]) ).
thf(27350,plain,
( ~ ( sk1 @ sk2 )
| ~ ( sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[27349:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(27400,plain,
~ ( sk1 @ sk2 ),
inference(simp,[status(thm)],[27350]) ).
thf(27406,plain,
( ( 'const/sets/INTER' @ skt1 @ sk1 @ sk1 @ sk2 )
| $false ),
inference(rewrite,[status(thm)],[20,27400]) ).
thf(27407,plain,
'const/sets/INTER' @ skt1 @ sk1 @ sk1 @ sk2,
inference(simp,[status(thm)],[27406]) ).
thf(27614,plain,
! [TA: $tType,TB: $tType,F: TA > TB > TB > $o,E: TA > TB > TB > $o,D: TA > TB,C: TB > $o,B: TB > $o,A: TA] :
( ( ( E @ A )
!= ( ^ [G: TB] : B ) )
| ( ( F @ A )
!= ( ^ [G: TB] : C ) )
| ( 'const/sets/IN' @ TA @ A
@ ^ [G: TA] :
( 'const/sets/IN' @ TB @ ( D @ G )
@ ^ [H: TB] : ( 'const/sets/INTER' @ TB @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
| ( ( 'const/sets/INTER' @ TB @ B @ C @ ( D @ A ) )
!= ( 'const/sets/INTER' @ skt1 @ sk1 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[17518,27407]) ).
thf(27644,plain,
! [TA: $tType,C: TA > skt1 > skt1 > $o,B: TA > skt1 > skt1 > $o,A: TA] :
( ( ( B @ A )
!= ( ^ [D: skt1] : sk1 ) )
| ( ( C @ A )
!= ( ^ [D: skt1] : sk1 ) )
| ( 'const/sets/IN' @ TA @ A
@ ^ [D: TA] :
( 'const/sets/IN' @ skt1 @ sk2
@ ^ [E: skt1] : ( 'const/sets/INTER' @ skt1 @ ( B @ D @ E ) @ ( C @ D @ E ) @ E ) ) ) ),
inference(pre_uni,[status(thm)],[27614:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk1 )),bind(D,$thf( ^ [G: TA] : sk2 )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( skt1 ))]]) ).
thf(27645,plain,
! [TA: $tType,A: TA] :
( 'const/sets/IN' @ TA @ A
@ ^ [B: TA] : ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/INTER' @ skt1 @ sk1 @ sk1 ) ) ),
inference(pre_uni,[status(thm)],[27644:[bind(A,$thf( (>) )),bind(B,$thf( ^ [D: TA] : ^ [E: skt1] : sk1 )),bind(C,$thf( ^ [D: TA] : ^ [E: skt1] : sk1 ))]]) ).
thf(21,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ~ ( 'const/sets/IN' @ TA @ B @ A )
| ( A @ B ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(29023,plain,
! [TA: $tType,TB: $tType,C: TB,B: TB > $o,A: TA] :
( ~ $true
| ( B @ C )
| ( ( 'const/sets/IN' @ TA @ A
@ ^ [D: TA] : ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/INTER' @ skt1 @ sk1 @ sk1 ) ) )
!= ( 'const/sets/IN' @ TB @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[27645,21]) ).
thf(29024,plain,
! [TA: $tType,TB: $tType,C: TB,B: TB > $o,A: TA] :
( ( B @ C )
| ( ( 'const/sets/IN' @ TA @ A
@ ^ [D: TA] : ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/INTER' @ skt1 @ sk1 @ sk1 ) ) )
!= ( 'const/sets/IN' @ TB @ C @ B ) ) ),
inference(simp,[status(thm)],[29023]) ).
thf(29025,plain,
'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/INTER' @ skt1 @ sk1 @ sk1 ),
inference(pattern_uni,[status(thm)],[29024:[bind(A,$thf( A )),bind(B,$thf( ^ [D: TB] : ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/INTER' @ skt1 @ sk1 @ sk1 ) ) )),bind(C,$thf( A )),bind_type(TA,$thf( TB ))]]) ).
thf(134,plain,
! [TA: $tType,TB: $tType,E: TB,D: TB > $o,C: TB > $o,B: TA,A: TA > $o] :
( ( ( ( A @ B )
& ( 'const/sets/IN' @ TB @ E @ D ) )
= ( 'const/sets/IN' @ TB @ E @ ( 'const/sets/INTER' @ TB @ C @ D ) ) )
| ( ( 'const/sets/IN' @ TA @ B @ A )
!= ( 'const/sets/IN' @ TB @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[11,14]) ).
thf(135,plain,
! [TB: $tType,C: TB > $o,B: TB,A: TB > $o] :
( ( ( A @ B )
& ( 'const/sets/IN' @ TB @ B @ C ) )
= ( 'const/sets/IN' @ TB @ B @ ( 'const/sets/INTER' @ TB @ A @ C ) ) ),
inference(pattern_uni,[status(thm)],[134:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( B )),bind_type(TA,$thf( TB ))]]) ).
thf(153,plain,
! [TA: $tType,C: TA > $o,B: TA,A: TA > $o] :
( ( ( A @ B )
& ( 'const/sets/IN' @ TA @ B @ C ) )
= ( 'const/sets/IN' @ TA @ B @ ( 'const/sets/INTER' @ TA @ A @ C ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(29157,plain,
! [TA: $tType,C: TA > $o,B: TA,A: TA > $o] :
( ( ( A @ B )
& ( 'const/sets/IN' @ TA @ B @ C ) )
| ( ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/INTER' @ skt1 @ sk1 @ sk1 ) )
!= ( 'const/sets/IN' @ TA @ B @ ( 'const/sets/INTER' @ TA @ A @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[29025,153]) ).
thf(29158,plain,
( ( sk1 @ sk2 )
& ( 'const/sets/IN' @ skt1 @ sk2 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[29157:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk1 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(29230,plain,
( ( sk1 @ sk2 )
& ( 'const/sets/IN' @ skt1 @ sk2 @ sk1 ) ),
inference(cnf,[status(esa)],[29158]) ).
thf(29231,plain,
sk1 @ sk2,
inference(cnfConj,[status(thm)],[29230]) ).
thf(29236,plain,
$false,
inference(rewrite,[status(thm)],[29231,27400]) ).
thf(29237,plain,
$false,
inference(simp,[status(thm)],[29236]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV452^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.09 % 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
% 0.11/0.23 % Computer : n006.cluster.edu
% 0.11/0.23 % Model : x86_64 x86_64
% 0.11/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.23 % Memory : 8046.5625MB
% 0.11/0.23 % OS : Linux 6.8.0-71-generic
% 0.11/0.23 % CPULimit : 300
% 0.11/0.23 % WCLimit : 300
% 0.11/0.23 % DateTime : Tue Sep 29 15:48:08 UTC 2026
% 0.11/0.23 % CPUTime :
% 0.11/0.23 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
% 1.04/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/1.00 % [INFO] Parsing done (195ms).
% 1.22/1.02 % [INFO] Running in sequential loop mode.
% 2.00/1.43 % [INFO] eprover registered as external prover.
% 2.00/1.44 % [INFO] Scanning for conjecture ...
% 2.20/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.20/1.56 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.20/1.58 % [INFO] Problem is higher-order (TPTP THF).
% 2.20/1.59 % [INFO] Type checking passed.
% 2.20/1.59 % [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 ...
% 184.93/94.68 % [INFO] Killing All external provers ...
% 184.93/94.69 % Time passed: 94313ms (effective reasoning time: 93657ms)
% 184.93/94.69 % 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)>
% 184.93/94.69 % Axioms used in derivation (2): thm/sets/IN_, thm/sets/IN_INTER_
% 184.93/94.69 % No. of inferences in proof: 65
% 184.93/94.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 94313 ms resp. 93657 ms w/o parsing
% 185.04/94.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 185.04/94.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------