%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : DAT326^1 : 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 : n026.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 07:48:15 AM UTC 2026
% Result : Theorem 20.99s 6.64s
% Output : Refutation 21.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 34 unt; 0 typ; 3 def)
% Number of atoms : 250 ( 65 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 693 ( 21 ~; 27 |; 0 &; 645 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 154 ( 3 ^; 148 !; 0 ?; 154 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% 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/set_of_list_decl',type,
'const/sets/set_of_list':
!>[TA: $tType] : ( ( 'type/ind_types/list' @ TA ) > TA > $o ) ).
thf('const/sets/IN_decl',type,
'const/sets/IN':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf('const/lists/MEM_decl',type,
'const/lists/MEM':
!>[TA: $tType] : ( TA > ( 'type/ind_types/list' @ TA ) > $o ) ).
thf('const/lists/APPEND_decl',type,
'const/lists/APPEND':
!>[TA: $tType] : ( ( 'type/ind_types/list' @ TA ) > ( 'type/ind_types/list' @ TA ) > ( 'type/ind_types/list' @ TA ) ) ).
thf(sk1_decl,type,
sk1: 'type/ind_types/list' @ skt1 ).
thf(sk2_decl,type,
sk2: 'type/ind_types/list' @ skt1 ).
thf(sk4_decl,type,
sk4:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: 'type/ind_types/list' @ skt1] :
~ ! [B: 'type/ind_types/list' @ skt1] :
( ( 'const/sets/set_of_list' @ skt1 @ ( 'const/lists/APPEND' @ skt1 @ A @ B ) )
= ( 'const/sets/UNION' @ skt1 @ ( 'const/sets/set_of_list' @ skt1 @ A ) @ ( 'const/sets/set_of_list' @ skt1 @ B ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: 'type/ind_types/list' @ skt1] :
( ( 'const/sets/set_of_list' @ skt1 @ ( 'const/lists/APPEND' @ skt1 @ sk1 @ A ) )
!= ( 'const/sets/UNION' @ skt1 @ ( 'const/sets/set_of_list' @ skt1 @ sk1 ) @ ( 'const/sets/set_of_list' @ skt1 @ A ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [TA: $tType,A: TA > $o,B: TA > $o] :
@+[C: TA] :
( ( 'const/sets/IN' @ TA @ C @ B )
!= ( 'const/sets/IN' @ TA @ C @ A ) ) ) ) ).
thf(6,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( 'const/sets/IN' @ TA @ C @ A )
= ( 'const/sets/IN' @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/EXTENSION_') ).
thf(19,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( 'const/sets/IN' @ TA @ C @ A )
= ( 'const/sets/IN' @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( 'const/sets/IN' @ TA @ C @ A )
= ( 'const/sets/IN' @ TA @ C @ B ) ) ) ),
inference(cnf,[status(esa)],[19]) ).
thf(21,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( 'const/sets/IN' @ TA @ C @ A )
= ( 'const/sets/IN' @ TA @ C @ B ) ) ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(28,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( A = B )
| ~ ! [C: TA] :
( ( 'const/sets/IN' @ TA @ C @ A )
= ( 'const/sets/IN' @ TA @ C @ B ) ) ),
inference(bool_ext,[status(thm)],[21]) ).
thf(30,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( A = B )
| ~ ! [C: TA] :
( ( 'const/sets/IN' @ TA @ C @ A )
= ( 'const/sets/IN' @ TA @ C @ B ) ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(34,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( A = B )
| ( ( 'const/sets/IN' @ TA @ ( sk4 @ TA @ B @ A ) @ A )
!= ( 'const/sets/IN' @ TA @ ( sk4 @ TA @ B @ A ) @ B ) ) ),
inference(cnf,[status(esa)],[30]) ).
thf(35,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( ( 'const/sets/IN' @ TA @ ( sk4 @ TA @ B @ A ) @ A )
!= ( 'const/sets/IN' @ TA @ ( sk4 @ TA @ B @ A ) @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(1,conjecture,
! [TA: $tType,A: 'type/ind_types/list' @ TA,B: 'type/ind_types/list' @ TA] :
( ( 'const/sets/set_of_list' @ TA @ ( 'const/lists/APPEND' @ TA @ A @ B ) )
= ( 'const/sets/UNION' @ TA @ ( 'const/sets/set_of_list' @ TA @ A ) @ ( 'const/sets/set_of_list' @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SET_OF_LIST_APPEND_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: 'type/ind_types/list' @ TA,B: 'type/ind_types/list' @ TA] :
( ( 'const/sets/set_of_list' @ TA @ ( 'const/lists/APPEND' @ TA @ A @ B ) )
= ( 'const/sets/UNION' @ TA @ ( 'const/sets/set_of_list' @ TA @ A ) @ ( 'const/sets/set_of_list' @ TA @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [TA: $tType,A: 'type/ind_types/list' @ TA,B: 'type/ind_types/list' @ TA] :
( ( 'const/sets/set_of_list' @ TA @ ( 'const/lists/APPEND' @ TA @ A @ B ) )
= ( 'const/sets/UNION' @ TA @ ( 'const/sets/set_of_list' @ TA @ A ) @ ( 'const/sets/set_of_list' @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
( ( 'const/sets/set_of_list' @ skt1 @ ( 'const/lists/APPEND' @ skt1 @ sk1 @ sk2 ) )
!= ( 'const/sets/UNION' @ skt1 @ ( 'const/sets/set_of_list' @ skt1 @ sk1 ) @ ( 'const/sets/set_of_list' @ skt1 @ sk2 ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
( ( 'const/sets/set_of_list' @ skt1 @ ( 'const/lists/APPEND' @ skt1 @ sk1 @ sk2 ) )
!= ( 'const/sets/UNION' @ skt1 @ ( 'const/sets/set_of_list' @ skt1 @ sk1 ) @ ( 'const/sets/set_of_list' @ skt1 @ sk2 ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(1127,plain,
! [B: skt1 > $o,A: skt1 > $o] :
( ( ( 'const/sets/IN' @ skt1 @ ( sk4 @ skt1 @ B @ A ) @ A )
!= ( 'const/sets/IN' @ skt1 @ ( sk4 @ skt1 @ B @ A ) @ B ) )
| ( B
!= ( 'const/sets/UNION' @ skt1 @ ( 'const/sets/set_of_list' @ skt1 @ sk1 ) @ ( 'const/sets/set_of_list' @ skt1 @ sk2 ) ) )
| ( A
!= ( 'const/sets/set_of_list' @ skt1 @ ( 'const/lists/APPEND' @ skt1 @ sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,9]) ).
thf(1128,plain,
! [A: skt1 > $o] :
( ( ( 'const/sets/IN' @ skt1 @ ( sk4 @ skt1 @ A @ ( 'const/sets/set_of_list' @ skt1 @ ( 'const/lists/APPEND' @ skt1 @ sk1 @ sk2 ) ) ) @ ( 'const/sets/set_of_list' @ skt1 @ ( 'const/lists/APPEND' @ skt1 @ sk1 @ sk2 ) ) )
!= ( 'const/sets/IN' @ skt1 @ ( sk4 @ skt1 @ A @ ( 'const/sets/set_of_list' @ skt1 @ ( 'const/lists/APPEND' @ skt1 @ sk1 @ sk2 ) ) ) @ A ) )
| ( A
!= ( 'const/sets/UNION' @ skt1 @ ( 'const/sets/set_of_list' @ skt1 @ sk1 ) @ ( 'const/sets/set_of_list' @ skt1 @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[1127:[bind(A,$thf( 'const/sets/set_of_list' @ skt1 @ ( 'const/lists/APPEND' @ skt1 @ sk1 @ sk2 ) )),bind(B,$thf( B ))]]) ).
thf(1275,plain,
( ( 'const/sets/IN' @ skt1 @ ( sk4 @ skt1 @ ( 'const/sets/UNION' @ skt1 @ ( 'const/sets/set_of_list' @ skt1 @ sk1 ) @ ( 'const/sets/set_of_list' @ skt1 @ sk2 ) ) @ ( 'const/sets/set_of_list' @ skt1 @ ( 'const/lists/APPEND' @ skt1 @ sk1 @ sk2 ) ) ) @ ( 'const/sets/set_of_list' @ skt1 @ ( 'const/lists/APPEND' @ skt1 @ sk1 @ sk2 ) ) )
!= ( 'const/sets/IN' @ skt1 @ ( sk4 @ skt1 @ ( 'const/sets/UNION' @ skt1 @ ( 'const/sets/set_of_list' @ skt1 @ sk1 ) @ ( 'const/sets/set_of_list' @ skt1 @ sk2 ) ) @ ( 'const/sets/set_of_list' @ skt1 @ ( 'const/lists/APPEND' @ skt1 @ sk1 @ sk2 ) ) ) @ ( 'const/sets/UNION' @ skt1 @ ( 'const/sets/set_of_list' @ skt1 @ sk1 ) @ ( 'const/sets/set_of_list' @ skt1 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[1128]) ).
thf(3,axiom,
! [TA: $tType,A: TA,B: 'type/ind_types/list' @ TA] :
( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/set_of_list' @ TA @ B ) )
= ( 'const/lists/MEM' @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_SET_OF_LIST_') ).
thf(10,plain,
! [TA: $tType,A: TA,B: 'type/ind_types/list' @ TA] :
( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/set_of_list' @ TA @ B ) )
= ( 'const/lists/MEM' @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
! [TA: $tType,B: 'type/ind_types/list' @ TA,A: TA] :
( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/set_of_list' @ TA @ B ) )
= ( 'const/lists/MEM' @ TA @ A @ B ) ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
! [TA: $tType,B: 'type/ind_types/list' @ TA,A: TA] :
( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/set_of_list' @ TA @ B ) )
= ( 'const/lists/MEM' @ TA @ A @ B ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(5,axiom,
! [TA: $tType,A: TA,B: 'type/ind_types/list' @ TA,C: 'type/ind_types/list' @ TA] :
( ( 'const/lists/MEM' @ TA @ A @ ( 'const/lists/APPEND' @ TA @ B @ C ) )
= ( ( 'const/lists/MEM' @ TA @ A @ B )
| ( 'const/lists/MEM' @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/MEM_APPEND_') ).
thf(16,plain,
! [TA: $tType,A: TA,B: 'type/ind_types/list' @ TA,C: 'type/ind_types/list' @ TA] :
( ( 'const/lists/MEM' @ TA @ A @ ( 'const/lists/APPEND' @ TA @ B @ C ) )
= ( ( 'const/lists/MEM' @ TA @ A @ B )
| ( 'const/lists/MEM' @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,plain,
! [TA: $tType,C: 'type/ind_types/list' @ TA,B: 'type/ind_types/list' @ TA,A: TA] :
( ( 'const/lists/MEM' @ TA @ A @ ( 'const/lists/APPEND' @ TA @ B @ C ) )
= ( ( 'const/lists/MEM' @ TA @ A @ B )
| ( 'const/lists/MEM' @ TA @ A @ C ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(18,plain,
! [TA: $tType,C: 'type/ind_types/list' @ TA,B: 'type/ind_types/list' @ TA,A: TA] :
( ( ( 'const/lists/MEM' @ TA @ A @ B )
| ( 'const/lists/MEM' @ TA @ A @ C ) )
= ( 'const/lists/MEM' @ TA @ A @ ( 'const/lists/APPEND' @ TA @ B @ C ) ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(92,plain,
! [TA: $tType,TB: $tType,E: 'type/ind_types/list' @ TB,D: 'type/ind_types/list' @ TB,C: TB,B: 'type/ind_types/list' @ TA,A: TA] :
( ( ( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/set_of_list' @ TA @ B ) )
| ( 'const/lists/MEM' @ TB @ C @ E ) )
= ( 'const/lists/MEM' @ TB @ C @ ( 'const/lists/APPEND' @ TB @ D @ E ) ) )
| ( ( 'const/lists/MEM' @ TA @ A @ B )
!= ( 'const/lists/MEM' @ TB @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[12,18]) ).
thf(93,plain,
! [TB: $tType,C: 'type/ind_types/list' @ TB,B: 'type/ind_types/list' @ TB,A: TB] :
( ( ( 'const/sets/IN' @ TB @ A @ ( 'const/sets/set_of_list' @ TB @ B ) )
| ( 'const/lists/MEM' @ TB @ A @ C ) )
= ( 'const/lists/MEM' @ TB @ A @ ( 'const/lists/APPEND' @ TB @ B @ C ) ) ),
inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B )),bind_type(TA,$thf( TB ))]]) ).
thf(112,plain,
! [TA: $tType,C: 'type/ind_types/list' @ TA,B: 'type/ind_types/list' @ TA,A: TA] :
( ( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/set_of_list' @ TA @ B ) )
| ( 'const/lists/MEM' @ TA @ A @ C ) )
= ( 'const/lists/MEM' @ TA @ A @ ( 'const/lists/APPEND' @ TA @ B @ C ) ) ),
inference(simp,[status(thm)],[93]) ).
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(13,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(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(cnf,[status(esa)],[13]) ).
thf(15,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)],[14]) ).
thf(65,plain,
! [TA: $tType,TB: $tType,E: TB,D: TB > $o,C: TB > $o,B: 'type/ind_types/list' @ TA,A: TA] :
( ( ( ( 'const/sets/IN' @ TB @ E @ C )
| ( 'const/lists/MEM' @ TA @ A @ B ) )
= ( 'const/sets/IN' @ TB @ E @ ( 'const/sets/UNION' @ TB @ C @ D ) ) )
| ( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/set_of_list' @ TA @ B ) )
!= ( 'const/sets/IN' @ TB @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[12,15]) ).
thf(66,plain,
! [TB: $tType,C: TB > $o,B: 'type/ind_types/list' @ TB,A: TB] :
( ( ( 'const/sets/IN' @ TB @ A @ C )
| ( 'const/lists/MEM' @ TB @ A @ B ) )
= ( 'const/sets/IN' @ TB @ A @ ( 'const/sets/UNION' @ TB @ C @ ( 'const/sets/set_of_list' @ TB @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( 'const/sets/set_of_list' @ TB @ B )),bind(E,$thf( A )),bind_type(TA,$thf( TB ))]]) ).
thf(81,plain,
! [TA: $tType,C: TA > $o,B: 'type/ind_types/list' @ TA,A: TA] :
( ( ( 'const/sets/IN' @ TA @ A @ C )
| ( 'const/lists/MEM' @ TA @ A @ B ) )
= ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/UNION' @ TA @ C @ ( 'const/sets/set_of_list' @ TA @ B ) ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(242,plain,
! [TA: $tType,TB: $tType,F: TB > $o,E: 'type/ind_types/list' @ TB,D: TB,C: 'type/ind_types/list' @ TA,B: 'type/ind_types/list' @ TA,A: TA] :
( ( ( 'const/lists/MEM' @ TA @ A @ ( 'const/lists/APPEND' @ TA @ B @ C ) )
= ( 'const/sets/IN' @ TB @ D @ ( 'const/sets/UNION' @ TB @ F @ ( 'const/sets/set_of_list' @ TB @ E ) ) ) )
| ( ( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/set_of_list' @ TA @ B ) )
| ( 'const/lists/MEM' @ TA @ A @ C ) )
!= ( ( 'const/sets/IN' @ TB @ D @ F )
| ( 'const/lists/MEM' @ TB @ D @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[112,81]) ).
thf(243,plain,
! [TB: $tType,C: 'type/ind_types/list' @ TB,B: 'type/ind_types/list' @ TB,A: TB] :
( ( 'const/lists/MEM' @ TB @ A @ ( 'const/lists/APPEND' @ TB @ B @ C ) )
= ( 'const/sets/IN' @ TB @ A @ ( 'const/sets/UNION' @ TB @ ( 'const/sets/set_of_list' @ TB @ B ) @ ( 'const/sets/set_of_list' @ TB @ C ) ) ) ),
inference(pattern_uni,[status(thm)],[242:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C )),bind(F,$thf( 'const/sets/set_of_list' @ TB @ B )),bind_type(TA,$thf( TB ))]]) ).
thf(304,plain,
! [TA: $tType,C: 'type/ind_types/list' @ TA,B: 'type/ind_types/list' @ TA,A: TA] :
( ( 'const/lists/MEM' @ TA @ A @ ( 'const/lists/APPEND' @ TA @ B @ C ) )
= ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/UNION' @ TA @ ( 'const/sets/set_of_list' @ TA @ B ) @ ( 'const/sets/set_of_list' @ TA @ C ) ) ) ),
inference(simp,[status(thm)],[243]) ).
thf(311,plain,
! [TA: $tType,TB: $tType,E: 'type/ind_types/list' @ TB,D: TB,C: 'type/ind_types/list' @ TA,B: 'type/ind_types/list' @ TA,A: TA] :
( ( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/UNION' @ TA @ ( 'const/sets/set_of_list' @ TA @ B ) @ ( 'const/sets/set_of_list' @ TA @ C ) ) )
= ( 'const/sets/IN' @ TB @ D @ ( 'const/sets/set_of_list' @ TB @ E ) ) )
| ( ( 'const/lists/MEM' @ TA @ A @ ( 'const/lists/APPEND' @ TA @ B @ C ) )
!= ( 'const/lists/MEM' @ TB @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[304,12]) ).
thf(312,plain,
! [TB: $tType,C: 'type/ind_types/list' @ TB,B: 'type/ind_types/list' @ TB,A: TB] :
( ( 'const/sets/IN' @ TB @ A @ ( 'const/sets/UNION' @ TB @ ( 'const/sets/set_of_list' @ TB @ B ) @ ( 'const/sets/set_of_list' @ TB @ C ) ) )
= ( 'const/sets/IN' @ TB @ A @ ( 'const/sets/set_of_list' @ TB @ ( 'const/lists/APPEND' @ TB @ B @ C ) ) ) ),
inference(pattern_uni,[status(thm)],[311:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( A )),bind(E,$thf( 'const/lists/APPEND' @ TB @ F @ G )),bind_type(TA,$thf( TB ))]]) ).
thf(380,plain,
! [TA: $tType,C: 'type/ind_types/list' @ TA,B: 'type/ind_types/list' @ TA,A: TA] :
( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/UNION' @ TA @ ( 'const/sets/set_of_list' @ TA @ B ) @ ( 'const/sets/set_of_list' @ TA @ C ) ) )
= ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/set_of_list' @ TA @ ( 'const/lists/APPEND' @ TA @ B @ C ) ) ) ),
inference(simp,[status(thm)],[312]) ).
thf(1719,plain,
$false,
inference(simplifyReflect,[status(thm)],[1275,380]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT326^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21 % Computer : n026.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 18:30:31 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.88/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/1.00 % [INFO] Parsing done (208ms).
% 1.20/1.02 % [INFO] Running in sequential loop mode.
% 2.02/1.41 % [INFO] eprover registered as external prover.
% 2.02/1.42 % [INFO] Scanning for conjecture ...
% 2.19/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.19/1.56 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.19/1.58 % [INFO] Problem is higher-order (TPTP THF).
% 2.19/1.59 % [INFO] Type checking passed.
% 2.19/1.59 % [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 ...
% 20.99/6.63 % [INFO] Killing All external provers ...
% 20.99/6.64 % Time passed: 6280ms (effective reasoning time: 5611ms)
% 20.99/6.64 % 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)>
% 20.99/6.64 % Axioms used in derivation (4): thm/sets/EXTENSION_, thm/sets/IN_SET_OF_LIST_, thm/lists/MEM_APPEND_, thm/sets/IN_UNION_
% 20.99/6.64 % No. of inferences in proof: 41
% 20.99/6.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6280 ms resp. 5611 ms w/o parsing
% 21.22/6.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 21.22/6.71 % [INFO] Killing All external provers ...
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