%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV497^1 : 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 : n005.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 08:37:22 AM UTC 2026
% Result : Theorem 14.73s 4.96s
% Output : Refutation 15.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 10 unt; 0 typ; 5 def)
% Number of atoms : 261 ( 57 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 1178 ( 61 ~; 42 |; 11 &;1047 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 96 ( 96 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 3 con; 0-6 aty)
% Number of variables : 131 ( 0 ^; 126 !; 0 ?; 131 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf(skt1_type,type,
skt1: $tType ).
thf(skt2_type,type,
skt2: $tType ).
thf(skt3_type,type,
skt3: $tType ).
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/iterate/support_decl',type,
'const/iterate/support':
!>[TA: $tType,TB: $tType] : ( ( TB > TB > TB ) > ( TA > TB ) > ( TA > $o ) > TA > $o ) ).
thf('const/iterate/neutral_decl',type,
'const/iterate/neutral':
!>[TA: $tType] : ( ( TA > TA > TA ) > TA ) ).
thf('const/iterate/monoidal_decl',type,
'const/iterate/monoidal':
!>[TA: $tType] : ( ( TA > TA > TA ) > $o ) ).
thf('const/iterate/iterate_decl',type,
'const/iterate/iterate':
!>[TA: $tType,TB: $tType] : ( ( TA > TA > TA ) > ( TB > $o ) > ( TB > TA ) > TA ) ).
thf('const/class/COND_decl',type,
'const/class/COND':
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(sk1_decl,type,
sk1: skt3 > skt3 > skt3 ).
thf(sk2_decl,type,
sk2: skt1 > skt3 ).
thf(sk3_decl,type,
sk3: skt2 > skt3 ).
thf(sk4_decl,type,
sk4: skt2 ).
thf(sk5_decl,type,
sk5: skt2 > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt3 > skt3 > skt3] :
~ ( ( 'const/iterate/monoidal' @ skt3 @ A )
=> ( ! [B: skt1 > skt3] :
( ( 'const/iterate/iterate' @ skt1 @ skt3 @ A @ ( 'const/sets/EMPTY' @ skt1 ) @ B )
= ( 'const/iterate/neutral' @ skt3 @ A ) )
& ! [B: skt2 > skt3,C: skt2,D: skt2 > $o] :
( ( 'const/sets/FINITE' @ skt2 @ D )
=> ( ( 'const/iterate/iterate' @ skt2 @ skt3 @ A @ ( 'const/sets/INSERT' @ skt2 @ C @ D ) @ B )
= ( 'const/class/COND' @ skt3 @ ( 'const/sets/IN' @ skt2 @ C @ D ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ A @ D @ B ) @ ( A @ ( B @ C ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ A @ D @ B ) ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: skt1 > skt3] :
( ( 'const/iterate/iterate' @ skt1 @ skt3 @ sk1 @ ( 'const/sets/EMPTY' @ skt1 ) @ A )
!= ( 'const/iterate/neutral' @ skt3 @ sk1 ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: skt2 > skt3] :
~ ! [B: skt2,C: skt2 > $o] :
( ( 'const/sets/FINITE' @ skt2 @ C )
=> ( ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ ( 'const/sets/INSERT' @ skt2 @ B @ C ) @ A )
= ( 'const/class/COND' @ skt3 @ ( 'const/sets/IN' @ skt2 @ B @ C ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ C @ A ) @ ( sk1 @ ( A @ B ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ C @ A ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: skt2] :
~ ! [B: skt2 > $o] :
( ( 'const/sets/FINITE' @ skt2 @ B )
=> ( ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ ( 'const/sets/INSERT' @ skt2 @ A @ B ) @ sk3 )
= ( 'const/class/COND' @ skt3 @ ( 'const/sets/IN' @ skt2 @ A @ B ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ B @ sk3 ) @ ( sk1 @ ( sk3 @ A ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ B @ sk3 ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: skt2 > $o] :
~ ( ( 'const/sets/FINITE' @ skt2 @ A )
=> ( ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ ( 'const/sets/INSERT' @ skt2 @ sk4 @ A ) @ sk3 )
= ( 'const/class/COND' @ skt3 @ ( 'const/sets/IN' @ skt2 @ sk4 @ A ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ A @ sk3 ) @ ( sk1 @ ( sk3 @ sk4 ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ A @ sk3 ) ) ) ) ) ) ) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > TA] :
( ( 'const/iterate/monoidal' @ TA @ A )
=> ( ! [B: TB > TA] :
( ( 'const/iterate/iterate' @ TB @ TA @ A @ ( 'const/sets/EMPTY' @ TB ) @ B )
= ( 'const/iterate/neutral' @ TA @ A ) )
& ! [B: TB > TA,C: TB,D: TB > $o] :
( ( ( 'const/iterate/monoidal' @ TA @ A )
& ( 'const/sets/FINITE' @ TB @ ( 'const/iterate/support' @ TA @ TB @ A @ B @ D ) ) )
=> ( ( 'const/iterate/iterate' @ TB @ TA @ A @ ( 'const/sets/INSERT' @ TB @ C @ D ) @ B )
= ( 'const/class/COND' @ TA @ ( 'const/sets/IN' @ TB @ C @ D ) @ ( 'const/iterate/iterate' @ TB @ TA @ A @ D @ B ) @ ( A @ ( B @ C ) @ ( 'const/iterate/iterate' @ TB @ TA @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/ITERATE_CLAUSES_GEN_') ).
thf(12,plain,
! [TA: $tType,TB: $tType,A: TA > TA > TA] :
( ( 'const/iterate/monoidal' @ TA @ A )
=> ( ! [B: TB > TA] :
( ( 'const/iterate/iterate' @ TB @ TA @ A @ ( 'const/sets/EMPTY' @ TB ) @ B )
= ( 'const/iterate/neutral' @ TA @ A ) )
& ! [B: TB > TA,C: TB,D: TB > $o] :
( ( ( 'const/iterate/monoidal' @ TA @ A )
& ( 'const/sets/FINITE' @ TB @ ( 'const/iterate/support' @ TA @ TB @ A @ B @ D ) ) )
=> ( ( 'const/iterate/iterate' @ TB @ TA @ A @ ( 'const/sets/INSERT' @ TB @ C @ D ) @ B )
= ( 'const/class/COND' @ TA @ ( 'const/sets/IN' @ TB @ C @ D ) @ ( 'const/iterate/iterate' @ TB @ TA @ A @ D @ B ) @ ( A @ ( B @ C ) @ ( 'const/iterate/iterate' @ TB @ TA @ A @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,plain,
! [TA: $tType,TB: $tType,E: TA > $o,D: TA,C: TA > TB,B: TA > TB,A: TB > TB > TB] :
( ( ~ ( 'const/iterate/monoidal' @ TB @ A )
| ( ( 'const/iterate/iterate' @ TA @ TB @ A @ ( 'const/sets/EMPTY' @ TA ) @ B )
= ( 'const/iterate/neutral' @ TB @ A ) ) )
& ( ~ ( 'const/iterate/monoidal' @ TB @ A )
| ~ ( 'const/iterate/monoidal' @ TB @ A )
| ~ ( 'const/sets/FINITE' @ TA @ ( 'const/iterate/support' @ TB @ TA @ A @ C @ E ) )
| ( ( 'const/iterate/iterate' @ TA @ TB @ A @ ( 'const/sets/INSERT' @ TA @ D @ E ) @ C )
= ( 'const/class/COND' @ TB @ ( 'const/sets/IN' @ TA @ D @ E ) @ ( 'const/iterate/iterate' @ TA @ TB @ A @ E @ C ) @ ( A @ ( C @ D ) @ ( 'const/iterate/iterate' @ TA @ TB @ A @ E @ C ) ) ) ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(15,plain,
! [TA: $tType,TB: $tType,D: TA > $o,C: TA,B: TA > TB,A: TB > TB > TB] :
( ~ ( 'const/iterate/monoidal' @ TB @ A )
| ~ ( 'const/iterate/monoidal' @ TB @ A )
| ~ ( 'const/sets/FINITE' @ TA @ ( 'const/iterate/support' @ TB @ TA @ A @ B @ D ) )
| ( ( 'const/iterate/iterate' @ TA @ TB @ A @ ( 'const/sets/INSERT' @ TA @ C @ D ) @ B )
= ( 'const/class/COND' @ TB @ ( 'const/sets/IN' @ TA @ C @ D ) @ ( 'const/iterate/iterate' @ TA @ TB @ A @ D @ B ) @ ( A @ ( B @ C ) @ ( 'const/iterate/iterate' @ TA @ TB @ A @ D @ B ) ) ) ) ),
inference(cnfConj,[status(thm)],[13]) ).
thf(17,plain,
! [TA: $tType,TB: $tType,D: TA > $o,C: TA,B: TA > TB,A: TB > TB > TB] :
( ( ( 'const/iterate/iterate' @ TA @ TB @ A @ ( 'const/sets/INSERT' @ TA @ C @ D ) @ B )
= ( 'const/class/COND' @ TB @ ( 'const/sets/IN' @ TA @ C @ D ) @ ( 'const/iterate/iterate' @ TA @ TB @ A @ D @ B ) @ ( A @ ( B @ C ) @ ( 'const/iterate/iterate' @ TA @ TB @ A @ D @ B ) ) ) )
| ~ ( 'const/iterate/monoidal' @ TB @ A )
| ~ ( 'const/iterate/monoidal' @ TB @ A )
| ~ ( 'const/sets/FINITE' @ TA @ ( 'const/iterate/support' @ TB @ TA @ A @ B @ D ) ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(18,plain,
! [TA: $tType,TB: $tType,D: TA > $o,C: TA,B: TA > TB,A: TB > TB > TB] :
( ( ( 'const/iterate/iterate' @ TA @ TB @ A @ ( 'const/sets/INSERT' @ TA @ C @ D ) @ B )
= ( 'const/class/COND' @ TB @ ( 'const/sets/IN' @ TA @ C @ D ) @ ( 'const/iterate/iterate' @ TA @ TB @ A @ D @ B ) @ ( A @ ( B @ C ) @ ( 'const/iterate/iterate' @ TA @ TB @ A @ D @ B ) ) ) )
| ~ ( 'const/iterate/monoidal' @ TB @ A )
| ~ ( 'const/sets/FINITE' @ TA @ ( 'const/iterate/support' @ TB @ TA @ A @ B @ D ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(14,plain,
! [TA: $tType,TB: $tType,B: TA > TB,A: TB > TB > TB] :
( ~ ( 'const/iterate/monoidal' @ TB @ A )
| ( ( 'const/iterate/iterate' @ TA @ TB @ A @ ( 'const/sets/EMPTY' @ TA ) @ B )
= ( 'const/iterate/neutral' @ TB @ A ) ) ),
inference(cnfConj,[status(thm)],[13]) ).
thf(16,plain,
! [TA: $tType,TB: $tType,B: TA > TB,A: TB > TB > TB] :
( ( ( 'const/iterate/iterate' @ TA @ TB @ A @ ( 'const/sets/EMPTY' @ TA ) @ B )
= ( 'const/iterate/neutral' @ TB @ A ) )
| ~ ( 'const/iterate/monoidal' @ TB @ A ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(1,conjecture,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TA > TA] :
( ( 'const/iterate/monoidal' @ TA @ A )
=> ( ! [B: TC > TA] :
( ( 'const/iterate/iterate' @ TC @ TA @ A @ ( 'const/sets/EMPTY' @ TC ) @ B )
= ( 'const/iterate/neutral' @ TA @ A ) )
& ! [B: TB > TA,C: TB,D: TB > $o] :
( ( 'const/sets/FINITE' @ TB @ D )
=> ( ( 'const/iterate/iterate' @ TB @ TA @ A @ ( 'const/sets/INSERT' @ TB @ C @ D ) @ B )
= ( 'const/class/COND' @ TA @ ( 'const/sets/IN' @ TB @ C @ D ) @ ( 'const/iterate/iterate' @ TB @ TA @ A @ D @ B ) @ ( A @ ( B @ C ) @ ( 'const/iterate/iterate' @ TB @ TA @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/ITERATE_CLAUSES_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TA > TA] :
( ( 'const/iterate/monoidal' @ TA @ A )
=> ( ! [B: TC > TA] :
( ( 'const/iterate/iterate' @ TC @ TA @ A @ ( 'const/sets/EMPTY' @ TC ) @ B )
= ( 'const/iterate/neutral' @ TA @ A ) )
& ! [B: TB > TA,C: TB,D: TB > $o] :
( ( 'const/sets/FINITE' @ TB @ D )
=> ( ( 'const/iterate/iterate' @ TB @ TA @ A @ ( 'const/sets/INSERT' @ TB @ C @ D ) @ B )
= ( 'const/class/COND' @ TA @ ( 'const/sets/IN' @ TB @ C @ D ) @ ( 'const/iterate/iterate' @ TB @ TA @ A @ D @ B ) @ ( A @ ( B @ C ) @ ( 'const/iterate/iterate' @ TB @ TA @ A @ D @ B ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TA > TA] :
( ( 'const/iterate/monoidal' @ TA @ A )
=> ( ! [B: TC > TA] :
( ( 'const/iterate/iterate' @ TC @ TA @ A @ ( 'const/sets/EMPTY' @ TC ) @ B )
= ( 'const/iterate/neutral' @ TA @ A ) )
& ! [B: TB > TA,C: TB,D: TB > $o] :
( ( 'const/sets/FINITE' @ TB @ D )
=> ( ( 'const/iterate/iterate' @ TB @ TA @ A @ ( 'const/sets/INSERT' @ TB @ C @ D ) @ B )
= ( 'const/class/COND' @ TA @ ( 'const/sets/IN' @ TB @ C @ D ) @ ( 'const/iterate/iterate' @ TB @ TA @ A @ D @ B ) @ ( A @ ( B @ C ) @ ( 'const/iterate/iterate' @ TB @ TA @ A @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
( ( 'const/iterate/monoidal' @ skt3 @ sk1 )
& ( ( ( 'const/iterate/iterate' @ skt1 @ skt3 @ sk1 @ ( 'const/sets/EMPTY' @ skt1 ) @ sk2 )
!= ( 'const/iterate/neutral' @ skt3 @ sk1 ) )
| ( 'const/sets/FINITE' @ skt2 @ sk5 ) )
& ( ( ( 'const/iterate/iterate' @ skt1 @ skt3 @ sk1 @ ( 'const/sets/EMPTY' @ skt1 ) @ sk2 )
!= ( 'const/iterate/neutral' @ skt3 @ sk1 ) )
| ( ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ ( 'const/sets/INSERT' @ skt2 @ sk4 @ sk5 ) @ sk3 )
!= ( 'const/class/COND' @ skt3 @ ( 'const/sets/IN' @ skt2 @ sk4 @ sk5 ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ sk5 @ sk3 ) @ ( sk1 @ ( sk3 @ sk4 ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ sk5 @ sk3 ) ) ) ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(9,plain,
( ( ( 'const/iterate/iterate' @ skt1 @ skt3 @ sk1 @ ( 'const/sets/EMPTY' @ skt1 ) @ sk2 )
!= ( 'const/iterate/neutral' @ skt3 @ sk1 ) )
| ( ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ ( 'const/sets/INSERT' @ skt2 @ sk4 @ sk5 ) @ sk3 )
!= ( 'const/class/COND' @ skt3 @ ( 'const/sets/IN' @ skt2 @ sk4 @ sk5 ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ sk5 @ sk3 ) @ ( sk1 @ ( sk3 @ sk4 ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ sk5 @ sk3 ) ) ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(11,plain,
( ( ( 'const/iterate/iterate' @ skt1 @ skt3 @ sk1 @ ( 'const/sets/EMPTY' @ skt1 ) @ sk2 )
!= ( 'const/iterate/neutral' @ skt3 @ sk1 ) )
| ( ( 'const/class/COND' @ skt3 @ ( 'const/sets/IN' @ skt2 @ sk4 @ sk5 ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ sk5 @ sk3 ) @ ( sk1 @ ( sk3 @ sk4 ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ sk5 @ sk3 ) ) )
!= ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ ( 'const/sets/INSERT' @ skt2 @ sk4 @ sk5 ) @ sk3 ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(32,plain,
! [TA: $tType,B: TA > skt3,A: skt3 > skt3 > skt3] :
( ~ ( 'const/iterate/monoidal' @ skt3 @ A )
| ( ( 'const/iterate/neutral' @ skt3 @ A )
!= ( 'const/iterate/neutral' @ skt3 @ sk1 ) )
| ( ( 'const/class/COND' @ skt3 @ ( 'const/sets/IN' @ skt2 @ sk4 @ sk5 ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ sk5 @ sk3 ) @ ( sk1 @ ( sk3 @ sk4 ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ sk5 @ sk3 ) ) )
!= ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ ( 'const/sets/INSERT' @ skt2 @ sk4 @ sk5 ) @ sk3 ) )
| ( ( 'const/iterate/iterate' @ TA @ skt3 @ A @ ( 'const/sets/EMPTY' @ TA ) @ B )
!= ( 'const/iterate/iterate' @ skt1 @ skt3 @ sk1 @ ( 'const/sets/EMPTY' @ skt1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[16,11]) ).
thf(33,plain,
( ~ ( 'const/iterate/monoidal' @ skt3 @ sk1 )
| ( ( 'const/iterate/neutral' @ skt3 @ sk1 )
!= ( 'const/iterate/neutral' @ skt3 @ sk1 ) )
| ( ( 'const/class/COND' @ skt3 @ ( 'const/sets/IN' @ skt2 @ sk4 @ sk5 ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ sk5 @ sk3 ) @ ( sk1 @ ( sk3 @ sk4 ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ sk5 @ sk3 ) ) )
!= ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ ( 'const/sets/INSERT' @ skt2 @ sk4 @ sk5 ) @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(36,plain,
( ~ ( 'const/iterate/monoidal' @ skt3 @ sk1 )
| ( ( 'const/class/COND' @ skt3 @ ( 'const/sets/IN' @ skt2 @ sk4 @ sk5 ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ sk5 @ sk3 ) @ ( sk1 @ ( sk3 @ sk4 ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ sk5 @ sk3 ) ) )
!= ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ ( 'const/sets/INSERT' @ skt2 @ sk4 @ sk5 ) @ sk3 ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(7,plain,
'const/iterate/monoidal' @ skt3 @ sk1,
inference(cnfConj,[status(thm)],[6]) ).
thf(37,plain,
( ~ $true
| ( ( 'const/class/COND' @ skt3 @ ( 'const/sets/IN' @ skt2 @ sk4 @ sk5 ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ sk5 @ sk3 ) @ ( sk1 @ ( sk3 @ sk4 ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ sk5 @ sk3 ) ) )
!= ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ ( 'const/sets/INSERT' @ skt2 @ sk4 @ sk5 ) @ sk3 ) ) ),
inference(rewrite,[status(thm)],[36,7]) ).
thf(38,plain,
( ( 'const/class/COND' @ skt3 @ ( 'const/sets/IN' @ skt2 @ sk4 @ sk5 ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ sk5 @ sk3 ) @ ( sk1 @ ( sk3 @ sk4 ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ sk5 @ sk3 ) ) )
!= ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ ( 'const/sets/INSERT' @ skt2 @ sk4 @ sk5 ) @ sk3 ) ),
inference(simp,[status(thm)],[37]) ).
thf(65,plain,
! [TA: $tType,D: TA > $o,C: TA,B: TA > skt3,A: skt3 > skt3 > skt3] :
( ~ ( 'const/iterate/monoidal' @ skt3 @ A )
| ~ ( 'const/sets/FINITE' @ TA @ ( 'const/iterate/support' @ skt3 @ TA @ A @ B @ D ) )
| ( ( 'const/iterate/iterate' @ TA @ skt3 @ A @ ( 'const/sets/INSERT' @ TA @ C @ D ) @ B )
!= ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ ( 'const/sets/INSERT' @ skt2 @ sk4 @ sk5 ) @ sk3 ) )
| ( ( 'const/class/COND' @ skt3 @ ( 'const/sets/IN' @ TA @ C @ D ) @ ( 'const/iterate/iterate' @ TA @ skt3 @ A @ D @ B ) @ ( A @ ( B @ C ) @ ( 'const/iterate/iterate' @ TA @ skt3 @ A @ D @ B ) ) )
!= ( 'const/class/COND' @ skt3 @ ( 'const/sets/IN' @ skt2 @ sk4 @ sk5 ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ sk5 @ sk3 ) @ ( sk1 @ ( sk3 @ sk4 ) @ ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ sk5 @ sk3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,38]) ).
thf(116,plain,
( ~ ( 'const/iterate/monoidal' @ skt3 @ sk1 )
| ~ ( 'const/sets/FINITE' @ skt2 @ ( 'const/iterate/support' @ skt3 @ skt2 @ sk1 @ sk3 @ sk5 ) )
| ( ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ ( 'const/sets/INSERT' @ skt2 @ sk4 @ sk5 ) @ sk3 )
!= ( 'const/iterate/iterate' @ skt2 @ skt3 @ sk1 @ ( 'const/sets/INSERT' @ skt2 @ sk4 @ sk5 ) @ sk3 ) ) ),
inference(pre_uni,[status(thm)],[65:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 )),bind(D,$thf( sk5 )),bind_type(TA,$thf( skt2 ))]]) ).
thf(117,plain,
( ~ ( 'const/sets/FINITE' @ skt2 @ ( 'const/iterate/support' @ skt3 @ skt2 @ sk1 @ sk3 @ sk5 ) )
| ~ ( 'const/iterate/monoidal' @ skt3 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[116:[]]) ).
thf(8,plain,
( ( ( 'const/iterate/iterate' @ skt1 @ skt3 @ sk1 @ ( 'const/sets/EMPTY' @ skt1 ) @ sk2 )
!= ( 'const/iterate/neutral' @ skt3 @ sk1 ) )
| ( 'const/sets/FINITE' @ skt2 @ sk5 ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(10,plain,
( ( ( 'const/iterate/iterate' @ skt1 @ skt3 @ sk1 @ ( 'const/sets/EMPTY' @ skt1 ) @ sk2 )
!= ( 'const/iterate/neutral' @ skt3 @ sk1 ) )
| ( 'const/sets/FINITE' @ skt2 @ sk5 ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(25,plain,
! [TA: $tType,TB: $tType,B: TA > TB,A: TB > TB > TB] :
( ( ( 'const/iterate/iterate' @ TA @ TB @ A @ ( 'const/sets/EMPTY' @ TA ) @ B )
= ( 'const/iterate/neutral' @ TB @ A ) )
| ~ $true
| ( ( 'const/iterate/monoidal' @ skt3 @ sk1 )
!= ( 'const/iterate/monoidal' @ TB @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,16]) ).
thf(26,plain,
! [TA: $tType,TB: $tType,B: TA > TB,A: TB > TB > TB] :
( ( ( 'const/iterate/iterate' @ TA @ TB @ A @ ( 'const/sets/EMPTY' @ TA ) @ B )
= ( 'const/iterate/neutral' @ TB @ A ) )
| ( ( 'const/iterate/monoidal' @ skt3 @ sk1 )
!= ( 'const/iterate/monoidal' @ TB @ A ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(27,plain,
! [TA: $tType,A: TA > skt3] :
( ( 'const/iterate/iterate' @ TA @ skt3 @ sk1 @ ( 'const/sets/EMPTY' @ TA ) @ A )
= ( 'const/iterate/neutral' @ skt3 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[26:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( skt3 ))]]) ).
thf(30,plain,
! [TA: $tType,A: TA > skt3] :
( ( 'const/iterate/iterate' @ TA @ skt3 @ sk1 @ ( 'const/sets/EMPTY' @ TA ) @ A )
= ( 'const/iterate/neutral' @ skt3 @ sk1 ) ),
inference(simp,[status(thm)],[27]) ).
thf(41,plain,
( ( ( 'const/iterate/neutral' @ skt3 @ sk1 )
!= ( 'const/iterate/neutral' @ skt3 @ sk1 ) )
| ( 'const/sets/FINITE' @ skt2 @ sk5 ) ),
inference(rewrite,[status(thm)],[10,30]) ).
thf(42,plain,
'const/sets/FINITE' @ skt2 @ sk5,
inference(simp,[status(thm)],[41]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > TB,B: TA > TB,C: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ C )
=> ( 'const/sets/FINITE' @ TA @ ( 'const/iterate/support' @ TB @ TA @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/FINITE_SUPPORT_') ).
thf(19,plain,
! [TA: $tType,TB: $tType,A: TB > TB > TB,B: TA > TB,C: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ C )
=> ( 'const/sets/FINITE' @ TA @ ( 'const/iterate/support' @ TB @ TA @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(20,plain,
! [TA: $tType,TB: $tType,C: TB > $o,B: TB > TA,A: TA > TA > TA] :
( ~ ( 'const/sets/FINITE' @ TB @ C )
| ( 'const/sets/FINITE' @ TB @ ( 'const/iterate/support' @ TA @ TB @ A @ B @ C ) ) ),
inference(cnf,[status(esa)],[19]) ).
thf(49,plain,
! [TA: $tType,TB: $tType,C: TB > $o,B: TB > TA,A: TA > TA > TA] :
( ~ $true
| ( 'const/sets/FINITE' @ TB @ ( 'const/iterate/support' @ TA @ TB @ A @ B @ C ) )
| ( ( 'const/sets/FINITE' @ skt2 @ sk5 )
!= ( 'const/sets/FINITE' @ TB @ C ) ) ),
inference(paramod_ordered,[status(thm)],[42,20]) ).
thf(50,plain,
! [TA: $tType,TB: $tType,C: TB > $o,B: TB > TA,A: TA > TA > TA] :
( ( 'const/sets/FINITE' @ TB @ ( 'const/iterate/support' @ TA @ TB @ A @ B @ C ) )
| ( ( 'const/sets/FINITE' @ skt2 @ sk5 )
!= ( 'const/sets/FINITE' @ TB @ C ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(51,plain,
! [TA: $tType,B: skt2 > TA,A: TA > TA > TA] : ( 'const/sets/FINITE' @ skt2 @ ( 'const/iterate/support' @ TA @ skt2 @ A @ B @ sk5 ) ),
inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk5 )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( skt2 ))]]) ).
thf(214,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[117,51,7]) ).
thf(215,plain,
$false,
inference(simp,[status(thm)],[214]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV497^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % 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 : n005.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 15:53:31 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
% 0.90/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/1.00 % [INFO] Parsing done (214ms).
% 1.25/1.01 % [INFO] Running in sequential loop mode.
% 2.16/1.43 % [INFO] eprover registered as external prover.
% 2.16/1.44 % [INFO] Scanning for conjecture ...
% 2.37/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.55/1.61 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.55/1.63 % [INFO] Problem is higher-order (TPTP THF).
% 2.55/1.63 % [INFO] Type checking passed.
% 2.55/1.64 % [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 ...
% 14.73/4.95 % [INFO] Killing All external provers ...
% 14.73/4.96 % Time passed: 4606ms (effective reasoning time: 3934ms)
% 14.73/4.96 % 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)>
% 14.73/4.96 % Axioms used in derivation (2): thm/iterate/ITERATE_CLAUSES_GEN_, thm/iterate/FINITE_SUPPORT_
% 14.73/4.96 % No. of inferences in proof: 39
% 14.73/4.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4606 ms resp. 3934 ms w/o parsing
% 15.30/5.05 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.30/5.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------