%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV478^1 : 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 : 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 08:37:21 AM UTC 2026
% Result : Theorem 22.51s 8.45s
% Output : Refutation 22.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 15 unt; 0 typ; 5 def)
% Number of atoms : 172 ( 57 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 942 ( 43 ~; 19 |; 6 &; 860 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 4 con; 0-5 aty)
% Number of variables : 101 ( 30 ^; 66 !; 0 ?; 101 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf('type/nums/num_type',type,
'type/nums/num': $tType ).
thf(skt1_type,type,
skt1: $tType ).
thf('const/sets/ITSET_decl',type,
'const/sets/ITSET':
!>[TA: $tType,TB: $tType] : ( ( TB > TA > TA ) > ( TB > $o ) > TA > TA ) ).
thf('const/sets/INSERT_decl',type,
'const/sets/INSERT':
!>[TA: $tType] : ( TA > ( TA > $o ) > TA > $o ) ).
thf('const/sets/IN_decl',type,
'const/sets/IN':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf('const/sets/FINITE_decl',type,
'const/sets/FINITE':
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf('const/sets/EMPTY_decl',type,
'const/sets/EMPTY':
!>[TA: $tType] : ( TA > $o ) ).
thf('const/sets/CARD_decl',type,
'const/sets/CARD':
!>[TA: $tType] : ( ( TA > $o ) > 'type/nums/num' ) ).
thf('const/nums/SUC_decl',type,
'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
thf('const/nums/NUMERAL_decl',type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf('const/nums/_0_decl',type,
'const/nums/_0': 'type/nums/num' ).
thf('const/class/COND_decl',type,
'const/class/COND':
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(sk1_decl,type,
sk1: skt1 ).
thf(sk2_decl,type,
sk2: skt1 > $o ).
thf(sk3_decl,type,
sk3:
!>[TA: $tType,TB: $tType] : ( TB > ( TA > TB > TB ) > TA ) ).
thf(sk4_decl,type,
sk4:
!>[TA: $tType,TB: $tType] : ( TB > ( TA > TB > TB ) > TA ) ).
thf(sk5_decl,type,
sk5:
!>[TA: $tType,TB: $tType] : ( TB > ( TA > TB > TB ) > TB ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1] :
~ ! [B: skt1 > $o] :
( ( 'const/sets/FINITE' @ skt1 @ B )
=> ( ( 'const/sets/CARD' @ skt1 @ ( 'const/sets/INSERT' @ skt1 @ A @ B ) )
= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ skt1 @ A @ B ) @ ( 'const/sets/CARD' @ skt1 @ B ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ skt1 @ B ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: skt1 > $o] :
~ ( ( 'const/sets/FINITE' @ skt1 @ A )
=> ( ( 'const/sets/CARD' @ skt1 @ ( 'const/sets/INSERT' @ skt1 @ sk1 @ A ) )
= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ skt1 @ sk1 @ A ) @ ( 'const/sets/CARD' @ skt1 @ A ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ skt1 @ A ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [TA: $tType,TB: $tType,A: TB,B: TA > TB > TB] :
@+[C: TA] :
~ ! [D: TA,E: TB] :
( ( C != D )
=> ( ( B @ C @ ( B @ D @ E ) )
= ( B @ D @ ( B @ C @ E ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [TA: $tType,TB: $tType,A: TB,B: TA > TB > TB] :
@+[C: TA] :
~ ! [D: TB] :
( ( ( sk3 @ TB @ TA @ A @ B )
!= C )
=> ( ( B @ ( sk3 @ TB @ TA @ A @ B ) @ ( B @ C @ D ) )
= ( B @ C @ ( B @ ( sk3 @ TB @ TA @ A @ B ) @ D ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [TA: $tType,TB: $tType,A: TB,B: TA > TB > TB] :
@+[C: TB] :
~ ( ( ( sk3 @ TB @ TA @ A @ B )
!= ( sk4 @ TB @ TA @ A @ B ) )
=> ( ( B @ ( sk3 @ TB @ TA @ A @ B ) @ ( B @ ( sk4 @ TB @ TA @ A @ B ) @ C ) )
= ( B @ ( sk4 @ TB @ TA @ A @ B ) @ ( B @ ( sk3 @ TB @ TA @ A @ B ) @ C ) ) ) ) ) ) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > TA,B: TA] :
( ! [C: TB,D: TB,E: TA] :
( ( C != D )
=> ( ( A @ C @ ( A @ D @ E ) )
= ( A @ D @ ( A @ C @ E ) ) ) )
=> ( ( ( 'const/sets/ITSET' @ TB @ TA @ A @ ( 'const/sets/EMPTY' @ TB ) @ B )
= B )
& ! [C: TB,D: TB > $o] :
( ( 'const/sets/FINITE' @ TB @ D )
=> ( ( 'const/sets/ITSET' @ TB @ TA @ A @ ( 'const/sets/INSERT' @ TB @ C @ D ) @ B )
= ( 'const/class/COND' @ TA @ ( 'const/sets/IN' @ TB @ C @ D ) @ ( 'const/sets/ITSET' @ TB @ TA @ A @ D @ B ) @ ( A @ C @ ( 'const/sets/ITSET' @ TB @ TA @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_RECURSION_') ).
thf(13,plain,
! [TA: $tType,TB: $tType,A: TB > TA > TA,B: TA] :
( ! [C: TB,D: TB,E: TA] :
( ( C != D )
=> ( ( A @ C @ ( A @ D @ E ) )
= ( A @ D @ ( A @ C @ E ) ) ) )
=> ( ( ( 'const/sets/ITSET' @ TB @ TA @ A @ ( 'const/sets/EMPTY' @ TB ) @ B )
= B )
& ! [C: TB,D: TB > $o] :
( ( 'const/sets/FINITE' @ TB @ D )
=> ( ( 'const/sets/ITSET' @ TB @ TA @ A @ ( 'const/sets/INSERT' @ TB @ C @ D ) @ B )
= ( 'const/class/COND' @ TA @ ( 'const/sets/IN' @ TB @ C @ D ) @ ( 'const/sets/ITSET' @ TB @ TA @ A @ D @ B ) @ ( A @ C @ ( 'const/sets/ITSET' @ TB @ TA @ A @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,plain,
! [TA: $tType,TB: $tType,D: TA > $o,C: TA,B: TB,A: TA > TB > TB] :
( ( ( ( sk3 @ TB @ TA @ B @ A )
!= ( sk4 @ TB @ TA @ B @ A ) )
| ( ( 'const/sets/ITSET' @ TA @ TB @ A @ ( 'const/sets/EMPTY' @ TA ) @ B )
= B ) )
& ( ( ( sk3 @ TB @ TA @ B @ A )
!= ( sk4 @ TB @ TA @ B @ A ) )
| ~ ( 'const/sets/FINITE' @ TA @ D )
| ( ( 'const/sets/ITSET' @ TA @ TB @ A @ ( 'const/sets/INSERT' @ TA @ C @ D ) @ B )
= ( 'const/class/COND' @ TB @ ( 'const/sets/IN' @ TA @ C @ D ) @ ( 'const/sets/ITSET' @ TA @ TB @ A @ D @ B ) @ ( A @ C @ ( 'const/sets/ITSET' @ TA @ TB @ A @ D @ B ) ) ) ) )
& ( ( ( A @ ( sk3 @ TB @ TA @ B @ A ) @ ( A @ ( sk4 @ TB @ TA @ B @ A ) @ ( sk5 @ TB @ TA @ B @ A ) ) )
!= ( A @ ( sk4 @ TB @ TA @ B @ A ) @ ( A @ ( sk3 @ TB @ TA @ B @ A ) @ ( sk5 @ TB @ TA @ B @ A ) ) ) )
| ( ( 'const/sets/ITSET' @ TA @ TB @ A @ ( 'const/sets/EMPTY' @ TA ) @ B )
= B ) )
& ( ( ( A @ ( sk3 @ TB @ TA @ B @ A ) @ ( A @ ( sk4 @ TB @ TA @ B @ A ) @ ( sk5 @ TB @ TA @ B @ A ) ) )
!= ( A @ ( sk4 @ TB @ TA @ B @ A ) @ ( A @ ( sk3 @ TB @ TA @ B @ A ) @ ( sk5 @ TB @ TA @ B @ A ) ) ) )
| ~ ( 'const/sets/FINITE' @ TA @ D )
| ( ( 'const/sets/ITSET' @ TA @ TB @ A @ ( 'const/sets/INSERT' @ TA @ C @ D ) @ B )
= ( 'const/class/COND' @ TB @ ( 'const/sets/IN' @ TA @ C @ D ) @ ( 'const/sets/ITSET' @ TA @ TB @ A @ D @ B ) @ ( A @ C @ ( 'const/sets/ITSET' @ TA @ TB @ A @ D @ B ) ) ) ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(18,plain,
! [TA: $tType,TB: $tType,D: TA > $o,C: TA,B: TB,A: TA > TB > TB] :
( ( ( A @ ( sk3 @ TB @ TA @ B @ A ) @ ( A @ ( sk4 @ TB @ TA @ B @ A ) @ ( sk5 @ TB @ TA @ B @ A ) ) )
!= ( A @ ( sk4 @ TB @ TA @ B @ A ) @ ( A @ ( sk3 @ TB @ TA @ B @ A ) @ ( sk5 @ TB @ TA @ B @ A ) ) ) )
| ~ ( 'const/sets/FINITE' @ TA @ D )
| ( ( 'const/sets/ITSET' @ TA @ TB @ A @ ( 'const/sets/INSERT' @ TA @ C @ D ) @ B )
= ( 'const/class/COND' @ TB @ ( 'const/sets/IN' @ TA @ C @ D ) @ ( 'const/sets/ITSET' @ TA @ TB @ A @ D @ B ) @ ( A @ C @ ( 'const/sets/ITSET' @ TA @ TB @ A @ D @ B ) ) ) ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(22,plain,
! [TA: $tType,TB: $tType,D: TA > $o,C: TA,B: TB,A: TA > TB > TB] :
( ( ( A @ ( sk4 @ TB @ TA @ B @ A ) @ ( A @ ( sk3 @ TB @ TA @ B @ A ) @ ( sk5 @ TB @ TA @ B @ A ) ) )
!= ( A @ ( sk3 @ TB @ TA @ B @ A ) @ ( A @ ( sk4 @ TB @ TA @ B @ A ) @ ( sk5 @ TB @ TA @ B @ A ) ) ) )
| ( ( 'const/sets/ITSET' @ TA @ TB @ A @ ( 'const/sets/INSERT' @ TA @ C @ D ) @ B )
= ( 'const/class/COND' @ TB @ ( 'const/sets/IN' @ TA @ C @ D ) @ ( 'const/sets/ITSET' @ TA @ TB @ A @ D @ B ) @ ( A @ C @ ( 'const/sets/ITSET' @ TA @ TB @ A @ D @ B ) ) ) )
| ~ ( 'const/sets/FINITE' @ TA @ D ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(3,axiom,
! [TA: $tType,A: TA > $o] :
( ( 'const/sets/CARD' @ TA @ A )
= ( 'const/sets/ITSET' @ TA @ 'type/nums/num'
@ ^ [B: TA] : 'const/nums/SUC'
@ A
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/CARD_') ).
thf(10,plain,
! [TA: $tType,A: TA > $o] :
( ( 'const/sets/CARD' @ TA @ A )
= ( 'const/sets/ITSET' @ TA @ 'type/nums/num'
@ ^ [B: TA] : 'const/nums/SUC'
@ A
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
! [TA: $tType,A: TA > $o] :
( ( 'const/sets/CARD' @ TA @ A )
= ( 'const/sets/ITSET' @ TA @ 'type/nums/num'
@ ^ [B: TA] : 'const/nums/SUC'
@ A
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
! [TA: $tType,A: TA > $o] :
( ( 'const/sets/CARD' @ TA @ A )
= ( 'const/sets/ITSET' @ TA @ 'type/nums/num'
@ ^ [B: TA] : 'const/nums/SUC'
@ A
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(1,conjecture,
! [TA: $tType,A: TA,B: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ B )
=> ( ( 'const/sets/CARD' @ TA @ ( 'const/sets/INSERT' @ TA @ A @ B ) )
= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ TA @ A @ B ) @ ( 'const/sets/CARD' @ TA @ B ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/CARD_CLAUSES_1') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA,B: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ B )
=> ( ( 'const/sets/CARD' @ TA @ ( 'const/sets/INSERT' @ TA @ A @ B ) )
= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ TA @ A @ B ) @ ( 'const/sets/CARD' @ TA @ B ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ TA @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [TA: $tType,A: TA,B: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ B )
=> ( ( 'const/sets/CARD' @ TA @ ( 'const/sets/INSERT' @ TA @ A @ B ) )
= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ TA @ A @ B ) @ ( 'const/sets/CARD' @ TA @ B ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
( ( 'const/sets/FINITE' @ skt1 @ sk2 )
& ( ( 'const/sets/CARD' @ skt1 @ ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 ) )
!= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ skt1 @ sk1 @ sk2 ) @ ( 'const/sets/CARD' @ skt1 @ sk2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ skt1 @ sk2 ) ) ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(8,plain,
( ( 'const/sets/CARD' @ skt1 @ ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 ) )
!= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ skt1 @ sk1 @ sk2 ) @ ( 'const/sets/CARD' @ skt1 @ sk2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ skt1 @ sk2 ) ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(9,plain,
( ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ skt1 @ sk1 @ sk2 ) @ ( 'const/sets/CARD' @ skt1 @ sk2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ skt1 @ sk2 ) ) )
!= ( 'const/sets/CARD' @ skt1 @ ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(23,plain,
! [TA: $tType,A: TA > $o] :
( ( ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ skt1 @ sk1 @ sk2 )
@ ( 'const/sets/ITSET' @ TA @ 'type/nums/num'
@ ^ [B: TA] : 'const/nums/SUC'
@ A
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ skt1 @ sk2 ) ) )
!= ( 'const/sets/CARD' @ skt1 @ ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 ) ) )
| ( ( 'const/sets/CARD' @ TA @ A )
!= ( 'const/sets/CARD' @ skt1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[12,9]) ).
thf(24,plain,
( ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ skt1 @ sk1 @ sk2 )
@ ( 'const/sets/ITSET' @ skt1 @ 'type/nums/num'
@ ^ [A: skt1] : 'const/nums/SUC'
@ sk2
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ skt1 @ sk2 ) ) )
!= ( 'const/sets/CARD' @ skt1 @ ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[23:[bind(A,$thf( sk2 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(27,plain,
! [TA: $tType,A: TA > $o] :
( ( ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ skt1 @ sk1 @ sk2 )
@ ( 'const/sets/ITSET' @ skt1 @ 'type/nums/num'
@ ^ [B: skt1] : 'const/nums/SUC'
@ sk2
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/SUC'
@ ( 'const/sets/ITSET' @ TA @ 'type/nums/num'
@ ^ [B: TA] : 'const/nums/SUC'
@ A
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) )
!= ( 'const/sets/CARD' @ skt1 @ ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 ) ) )
| ( ( 'const/sets/CARD' @ TA @ A )
!= ( 'const/sets/CARD' @ skt1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[12,24]) ).
thf(28,plain,
( ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ skt1 @ sk1 @ sk2 )
@ ( 'const/sets/ITSET' @ skt1 @ 'type/nums/num'
@ ^ [A: skt1] : 'const/nums/SUC'
@ sk2
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/SUC'
@ ( 'const/sets/ITSET' @ skt1 @ 'type/nums/num'
@ ^ [A: skt1] : 'const/nums/SUC'
@ sk2
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) )
!= ( 'const/sets/CARD' @ skt1 @ ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( sk2 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(522,plain,
! [TA: $tType,D: TA > $o,C: TA,B: 'type/nums/num',A: TA > 'type/nums/num' > 'type/nums/num'] :
( ( ( A @ ( sk4 @ 'type/nums/num' @ TA @ B @ A ) @ ( A @ ( sk3 @ 'type/nums/num' @ TA @ B @ A ) @ ( sk5 @ 'type/nums/num' @ TA @ B @ A ) ) )
!= ( A @ ( sk3 @ 'type/nums/num' @ TA @ B @ A ) @ ( A @ ( sk4 @ 'type/nums/num' @ TA @ B @ A ) @ ( sk5 @ 'type/nums/num' @ TA @ B @ A ) ) ) )
| ~ ( 'const/sets/FINITE' @ TA @ D )
| ( ( 'const/sets/ITSET' @ TA @ 'type/nums/num' @ A @ ( 'const/sets/INSERT' @ TA @ C @ D ) @ B )
!= ( 'const/sets/CARD' @ skt1 @ ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 ) ) )
| ( ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ TA @ C @ D ) @ ( 'const/sets/ITSET' @ TA @ 'type/nums/num' @ A @ D @ B ) @ ( A @ C @ ( 'const/sets/ITSET' @ TA @ 'type/nums/num' @ A @ D @ B ) ) )
!= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ skt1 @ sk1 @ sk2 )
@ ( 'const/sets/ITSET' @ skt1 @ 'type/nums/num'
@ ^ [E: skt1] : 'const/nums/SUC'
@ sk2
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/SUC'
@ ( 'const/sets/ITSET' @ skt1 @ 'type/nums/num'
@ ^ [E: skt1] : 'const/nums/SUC'
@ sk2
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[22,28]) ).
thf(566,plain,
( ( ( 'const/nums/SUC'
@ ( 'const/nums/SUC'
@ ( sk5 @ 'type/nums/num' @ skt1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
@ ^ [A: skt1] : 'const/nums/SUC' ) ) )
!= ( 'const/nums/SUC'
@ ( 'const/nums/SUC'
@ ( sk5 @ 'type/nums/num' @ skt1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
@ ^ [A: skt1] : 'const/nums/SUC' ) ) ) )
| ~ ( 'const/sets/FINITE' @ skt1 @ sk2 )
| ( ( 'const/sets/ITSET' @ skt1 @ 'type/nums/num'
@ ^ [A: skt1] : 'const/nums/SUC'
@ ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/sets/CARD' @ skt1 @ ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 ) ) ) ),
inference(pre_uni,[status(thm)],[522:[bind(A,$thf( ^ [E: skt1] : 'const/nums/SUC' )),bind(B,$thf( 'const/nums/NUMERAL' @ 'const/nums/_0' )),bind(C,$thf( sk1 )),bind(D,$thf( sk2 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(611,plain,
( ~ ( 'const/sets/FINITE' @ skt1 @ sk2 )
| ( ( 'const/sets/ITSET' @ skt1 @ 'type/nums/num'
@ ^ [A: skt1] : 'const/nums/SUC'
@ ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/sets/CARD' @ skt1 @ ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[566]) ).
thf(7,plain,
'const/sets/FINITE' @ skt1 @ sk2,
inference(cnfConj,[status(thm)],[6]) ).
thf(647,plain,
( ~ $true
| ( ( 'const/sets/ITSET' @ skt1 @ 'type/nums/num'
@ ^ [A: skt1] : 'const/nums/SUC'
@ ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/sets/CARD' @ skt1 @ ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 ) ) ) ),
inference(rewrite,[status(thm)],[611,7]) ).
thf(648,plain,
( ( 'const/sets/ITSET' @ skt1 @ 'type/nums/num'
@ ^ [A: skt1] : 'const/nums/SUC'
@ ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/sets/CARD' @ skt1 @ ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[647]) ).
thf(649,plain,
$false,
inference(simplifyReflect,[status(thm)],[648,12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV478^1 : 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 : n004.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 15:52:40 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 ...
% 1.22/1.00 % [INFO] Parsing done (209ms).
% 1.22/1.02 % [INFO] Running in sequential loop mode.
% 2.17/1.41 % [INFO] eprover registered as external prover.
% 2.17/1.42 % [INFO] Scanning for conjecture ...
% 2.35/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.35/1.57 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.53/1.60 % [INFO] Problem is higher-order (TPTP THF).
% 2.53/1.60 % [INFO] Type checking passed.
% 2.53/1.61 % [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 ...
% 22.51/8.44 % [INFO] Killing All external provers ...
% 22.51/8.45 % Time passed: 8093ms (effective reasoning time: 7419ms)
% 22.51/8.45 % 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)>
% 22.51/8.45 % Axioms used in derivation (2): thm/sets/FINITE_RECURSION_, thm/sets/CARD_
% 22.51/8.45 % No. of inferences in proof: 26
% 22.51/8.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 8093 ms resp. 7419 ms w/o parsing
% 22.83/8.53 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.83/8.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------