%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV450^1 : 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 : n012.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 08:37:18 AM UTC 2026
% Result : Theorem 84.09s 42.31s
% Output : Refutation 84.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 4
% Syntax : Number of formulae : 68 ( 25 unt; 0 typ; 1 def)
% Number of atoms : 349 ( 70 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 918 ( 90 ~; 92 |; 1 &; 735 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 159 ( 159 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 4 usr; 5 con; 0-4 aty)
% Number of variables : 287 ( 55 ^; 231 !; 0 ?; 287 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(skt1_type,type,
skt1: $tType ).
thf('const/sets/UNION_decl',type,
'const/sets/UNION':
!>[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/UNION' @ 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/UNION' @ 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_UNION_') ).
thf(12,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/UNION' @ 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/UNION' @ 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/UNION' @ 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/UNION' @ 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 > $o,A: TA] :
( ( ( 'const/sets/IN' @ TA @ A
@ ^ [G: TA] :
( 'const/sets/IN' @ TB @ ( D @ G )
@ ^ [H: TB] : ( 'const/sets/UNION' @ TB @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
= ( ( 'const/sets/IN' @ TB @ ( D @ A ) @ B )
| ( 'const/sets/IN' @ TB @ ( D @ A ) @ C ) ) )
| ( ( E @ A )
!= ( ^ [G: TB] : B ) )
| ( ( F @ A )
!= ( ^ [G: TB] : C ) ) ),
inference(pre_uni,[status(thm)],[136:[bind(A,$thf( ^ [I: TA] : ( 'const/sets/IN' @ TB @ ( F @ I ) @ ^ [J: TB] : ( 'const/sets/UNION' @ 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/UNION' @ 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/UNION' @ 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/UNION' @ TB @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,14]) ).
thf(131,plain,
! [TB: $tType,C: TB > $o,B: TB > $o,A: TB] :
( ( ( 'const/sets/IN' @ TB @ A @ B )
| ( 'const/sets/IN' @ TB @ A @ C ) )
= ( 'const/sets/UNION' @ TB @ B @ C @ A ) ),
inference(pattern_uni,[status(thm)],[130:[bind(A,$thf( 'const/sets/UNION' @ 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/UNION' @ TA @ B @ C @ A ) ),
inference(simp,[status(thm)],[131]) ).
thf(16396,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/UNION' @ TB @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
= ( 'const/sets/UNION' @ 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/UNION' @ TA @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/UNION_IDEMPOT_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > $o] :
( ( 'const/sets/UNION' @ TA @ A @ A )
= A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [TA: $tType,A: TA > $o] :
( ( 'const/sets/UNION' @ TA @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
( ( 'const/sets/UNION' @ skt1 @ sk1 @ sk1 )
!= sk1 ),
inference(cnf,[status(esa)],[6]) ).
thf(8,plain,
( ( 'const/sets/UNION' @ skt1 @ sk1 @ sk1 )
!= sk1 ),
inference(lifteq,[status(thm)],[7]) ).
thf(18,plain,
( ( 'const/sets/UNION' @ skt1 @ sk1 @ sk1 @ sk2 )
!= ( sk1 @ sk2 ) ),
inference(func_ext,[status(esa)],[8]) ).
thf(20,plain,
( ( 'const/sets/UNION' @ 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/UNION' @ TA @ A @ B ) )
| ~ ( ( 'const/sets/IN' @ TA @ C @ A )
| ( 'const/sets/IN' @ TA @ C @ B ) ) ),
inference(bool_ext,[status(thm)],[14]) ).
thf(160,plain,
! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
( ( ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/UNION' @ TA @ A @ B ) )
| ~ ( 'const/sets/IN' @ TA @ C @ A ) )
& ( ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/UNION' @ TA @ A @ B ) )
| ~ ( 'const/sets/IN' @ TA @ C @ B ) ) ),
inference(cnf,[status(esa)],[118]) ).
thf(161,plain,
! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
( ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/UNION' @ TA @ A @ B ) )
| ~ ( 'const/sets/IN' @ TA @ C @ A ) ),
inference(cnfConj,[status(thm)],[160]) ).
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/UNION' @ 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 > $o] :
( ( ( ( 'const/sets/IN' @ TA @ ( D @ C ) @ A )
| ( 'const/sets/IN' @ TA @ ( D @ C ) @ B ) )
= ( 'const/sets/IN' @ TB @ C
@ ^ [G: TB] :
( 'const/sets/IN' @ TA @ ( D @ G )
@ ^ [H: TA] : ( 'const/sets/UNION' @ TA @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) ) )
| ( ( ^ [G: TA] : A )
!= ( E @ C ) )
| ( ( ^ [G: TA] : B )
!= ( F @ C ) ) ),
inference(pre_uni,[status(thm)],[128:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( F @ E )),bind(D,$thf( ^ [I: TB] : ( 'const/sets/IN' @ TA @ ( F @ I ) @ ^ [J: TA] : ( 'const/sets/UNION' @ TA @ ( H @ I @ J ) @ ( I @ I @ J ) @ J ) ) )),bind(E,$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/UNION' @ 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/UNION' @ TA @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) ) )
| ( ( ^ [G: TA] : A )
!= ( E @ C ) )
| ( ( ^ [G: TA] : B )
!= ( F @ C ) ) ),
inference(simp,[status(thm)],[147]) ).
thf(10658,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/UNION' @ TA @ A @ B @ ( D @ C ) )
= ( 'const/sets/IN' @ TB @ C
@ ^ [G: TB] :
( 'const/sets/IN' @ TA @ ( D @ G )
@ ^ [H: TA] : ( 'const/sets/UNION' @ 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/UNION' @ skt1 @ sk1 @ sk1 @ sk2 )
| ~ ( sk1 @ sk2 ) ),
inference(bool_ext,[status(thm)],[18]) ).
thf(10835,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/UNION' @ TA @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
| ~ ( sk1 @ sk2 )
| ( ( 'const/sets/UNION' @ TA @ A @ B @ ( D @ C ) )
!= ( 'const/sets/UNION' @ skt1 @ sk1 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[10658,19]) ).
thf(10980,plain,
! [TB: $tType,C: TB > skt1 > skt1 > $o,B: TB > skt1 > skt1 > $o,A: TB] :
( ( ( ^ [D: skt1] : sk1 )
!= ( B @ A ) )
| ( ( ^ [D: skt1] : sk1 )
!= ( C @ A ) )
| ~ ( 'const/sets/IN' @ TB @ A
@ ^ [D: TB] :
( 'const/sets/IN' @ skt1 @ sk2
@ ^ [E: skt1] : ( 'const/sets/UNION' @ skt1 @ ( B @ D @ E ) @ ( C @ D @ E ) @ E ) ) )
| ~ ( sk1 @ sk2 ) ),
inference(pre_uni,[status(thm)],[10835:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 )),bind(C,$thf( C )),bind(D,$thf( ^ [G: TB] : sk2 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(10981,plain,
! [TB: $tType,A: TB] :
( ~ ( sk1 @ sk2 )
| ~ ( 'const/sets/IN' @ TB @ A
@ ^ [B: TB] : ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/UNION' @ skt1 @ sk1 @ sk1 ) ) ) ),
inference(pre_uni,[status(thm)],[10980:[bind(A,$thf( (@) )),bind(B,$thf( ^ [D: TB] : ^ [E: skt1] : sk1 )),bind(C,$thf( ^ [D: TB] : ^ [E: skt1] : sk1 ))]]) ).
thf(11148,plain,
! [TA: $tType,A: TA] :
( ~ ( sk1 @ sk2 )
| ~ ( 'const/sets/IN' @ TA @ A
@ ^ [B: TA] : ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/UNION' @ skt1 @ sk1 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[10981]) ).
thf(24638,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/UNION' @ skt1 @ sk1 @ sk1 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[22,11148]) ).
thf(24639,plain,
! [TA: $tType,TB: $tType,C: TB,B: TA,A: TA > $o] :
( ~ ( A @ B )
| ~ ( sk1 @ sk2 )
| ( ( 'const/sets/IN' @ TA @ B @ A )
!= ( 'const/sets/IN' @ TB @ C
@ ^ [D: TB] : ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/UNION' @ skt1 @ sk1 @ sk1 ) ) ) ) ),
inference(simp,[status(thm)],[24638]) ).
thf(24640,plain,
( ~ ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/UNION' @ skt1 @ sk1 @ sk1 ) )
| ~ ( sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[24639:[bind(A,$thf( ^ [D: TB] : ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/UNION' @ skt1 @ sk1 @ sk1 ) ) )),bind(B,$thf( B )),bind(C,$thf( B )),bind_type(TA,$thf( TB ))]]) ).
thf(24758,plain,
! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
( ~ ( 'const/sets/IN' @ TA @ C @ A )
| ~ $true
| ~ ( sk1 @ sk2 )
| ( ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/UNION' @ TA @ A @ B ) )
!= ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/UNION' @ skt1 @ sk1 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[161,24640]) ).
thf(24759,plain,
! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
( ~ ( 'const/sets/IN' @ TA @ C @ A )
| ~ ( sk1 @ sk2 )
| ( ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/UNION' @ TA @ A @ B ) )
!= ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/UNION' @ skt1 @ sk1 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[24758]) ).
thf(24760,plain,
( ~ ( 'const/sets/IN' @ skt1 @ sk2 @ sk1 )
| ~ ( sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[24759:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(24854,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)],[22,24760]) ).
thf(24855,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ~ ( A @ B )
| ~ ( sk1 @ sk2 )
| ( ( 'const/sets/IN' @ TA @ B @ A )
!= ( 'const/sets/IN' @ skt1 @ sk2 @ sk1 ) ) ),
inference(simp,[status(thm)],[24854]) ).
thf(24856,plain,
( ~ ( sk1 @ sk2 )
| ~ ( sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[24855:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(24910,plain,
~ ( sk1 @ sk2 ),
inference(simp,[status(thm)],[24856]) ).
thf(24927,plain,
( ( 'const/sets/UNION' @ skt1 @ sk1 @ sk1 @ sk2 )
| $false ),
inference(rewrite,[status(thm)],[20,24910]) ).
thf(24928,plain,
'const/sets/UNION' @ skt1 @ sk1 @ sk1 @ sk2,
inference(simp,[status(thm)],[24927]) ).
thf(25036,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/UNION' @ TB @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
| ( ( 'const/sets/UNION' @ TB @ B @ C @ ( D @ A ) )
!= ( 'const/sets/UNION' @ skt1 @ sk1 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[16396,24928]) ).
thf(25056,plain,
! [TA: $tType,C: TA > skt1 > skt1 > $o,B: TA > skt1 > skt1 > $o,A: TA] :
( ( ( B @ A )
!= ( ^ [D: skt1] : sk1 ) )
| ( ( C @ A )
!= ( ^ [D: skt1] : sk1 ) )
| ( 'const/sets/IN' @ TA @ A
@ ^ [D: TA] :
( 'const/sets/IN' @ skt1 @ sk2
@ ^ [E: skt1] : ( 'const/sets/UNION' @ skt1 @ ( B @ D @ E ) @ ( C @ D @ E ) @ E ) ) ) ),
inference(pre_uni,[status(thm)],[25036:[bind(A,$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(25057,plain,
! [TA: $tType,A: TA] :
( 'const/sets/IN' @ TA @ A
@ ^ [B: TA] : ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/UNION' @ skt1 @ sk1 @ sk1 ) ) ),
inference(pre_uni,[status(thm)],[25056:[bind(A,$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(26848,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/UNION' @ skt1 @ sk1 @ sk1 ) ) )
!= ( 'const/sets/IN' @ TB @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[25057,21]) ).
thf(26849,plain,
! [TA: $tType,TB: $tType,C: TB,B: TB > $o,A: TA] :
( ( B @ C )
| ( ( 'const/sets/IN' @ TA @ A
@ ^ [D: TA] : ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/UNION' @ skt1 @ sk1 @ sk1 ) ) )
!= ( 'const/sets/IN' @ TB @ C @ B ) ) ),
inference(simp,[status(thm)],[26848]) ).
thf(26850,plain,
'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/UNION' @ skt1 @ sk1 @ sk1 ),
inference(pattern_uni,[status(thm)],[26849:[bind(A,$thf( A )),bind(B,$thf( ^ [D: TB] : ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/UNION' @ skt1 @ sk1 @ sk1 ) ) )),bind(C,$thf( A )),bind_type(TA,$thf( TB ))]]) ).
thf(117,plain,
! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
( ~ ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/UNION' @ TA @ A @ B ) )
| ( 'const/sets/IN' @ TA @ C @ A )
| ( 'const/sets/IN' @ TA @ C @ B ) ),
inference(bool_ext,[status(thm)],[14]) ).
thf(159,plain,
! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
( ~ ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/UNION' @ TA @ A @ B ) )
| ( 'const/sets/IN' @ TA @ C @ A )
| ( 'const/sets/IN' @ TA @ C @ B ) ),
inference(cnf,[status(esa)],[117]) ).
thf(27030,plain,
! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
( ~ $true
| ( 'const/sets/IN' @ TA @ C @ A )
| ( 'const/sets/IN' @ TA @ C @ B )
| ( ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/UNION' @ skt1 @ sk1 @ sk1 ) )
!= ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/UNION' @ TA @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[26850,159]) ).
thf(27031,plain,
! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
( ( 'const/sets/IN' @ TA @ C @ A )
| ( 'const/sets/IN' @ TA @ C @ B )
| ( ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/UNION' @ skt1 @ sk1 @ sk1 ) )
!= ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/UNION' @ TA @ A @ B ) ) ) ),
inference(simp,[status(thm)],[27030]) ).
thf(27032,plain,
( ( 'const/sets/IN' @ skt1 @ sk2 @ sk1 )
| ( 'const/sets/IN' @ skt1 @ sk2 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[27031:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(27077,plain,
'const/sets/IN' @ skt1 @ sk2 @ sk1,
inference(simp,[status(thm)],[27032]) ).
thf(27111,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ~ $true
| ( A @ B )
| ( ( 'const/sets/IN' @ skt1 @ sk2 @ sk1 )
!= ( 'const/sets/IN' @ TA @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27077,21]) ).
thf(27112,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( A @ B )
| ( ( 'const/sets/IN' @ skt1 @ sk2 @ sk1 )
!= ( 'const/sets/IN' @ TA @ B @ A ) ) ),
inference(simp,[status(thm)],[27111]) ).
thf(27113,plain,
sk1 @ sk2,
inference(pattern_uni,[status(thm)],[27112:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(27214,plain,
$false,
inference(rewrite,[status(thm)],[27113,24910]) ).
thf(27215,plain,
$false,
inference(simp,[status(thm)],[27214]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEV450^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % 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
% 0.08/0.12 % Computer : n012.cluster.edu
% 0.08/0.12 % Model : x86_64 x86_64
% 0.08/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.12 % Memory : 8046.5625MB
% 0.08/0.12 % OS : Linux 6.8.0-71-generic
% 0.08/0.12 % CPULimit : 300
% 0.08/0.12 % WCLimit : 300
% 0.08/0.12 % DateTime : Tue Sep 29 15:48:02 UTC 2026
% 0.08/0.12 % CPUTime :
% 0.08/0.12 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
% 0.40/0.39 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.56/0.48 % [INFO] Parsing done (88ms).
% 0.56/0.49 % [INFO] Running in sequential loop mode.
% 0.86/0.68 % [INFO] eprover registered as external prover.
% 0.86/0.68 % [INFO] Scanning for conjecture ...
% 1.02/0.72 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 1.02/0.74 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.02/0.75 % [INFO] Problem is higher-order (TPTP THF).
% 1.02/0.75 % [INFO] Type checking passed.
% 1.02/0.76 % [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 ...
% 84.09/42.31 % [INFO] Killing All external provers ...
% 84.09/42.31 % Time passed: 42118ms (effective reasoning time: 41821ms)
% 84.09/42.31 % 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)>
% 84.09/42.31 % Axioms used in derivation (2): thm/sets/IN_, thm/sets/IN_UNION_
% 84.09/42.31 % No. of inferences in proof: 67
% 84.09/42.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 42118 ms resp. 41821 ms w/o parsing
% 84.09/42.35 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 84.09/42.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------