%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA098^1 : 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 : n003.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 07:45:46 AM UTC 2026
% Result : Theorem 54.85s 39.47s
% Output : Refutation 55.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 30 unt; 0 typ; 2 def)
% Number of atoms : 135 ( 46 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 790 ( 16 ~; 10 |; 0 &; 764 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 95 ( 95 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 1 con; 0-6 aty)
% Number of variables : 158 ( 33 ^; 123 !; 0 ?; 158 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf('type/realax/real_type',type,
'type/realax/real': $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/FINITE_decl',type,
'const/sets/FINITE':
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf('const/realax/real_add_decl',type,
'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
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/sum_decl',type,
'const/iterate/sum':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > 'type/realax/real' ) > 'type/realax/real' ) ).
thf('const/iterate/neutral_decl',type,
'const/iterate/neutral':
!>[TA: $tType] : ( ( TA > TA > TA ) > TA ) ).
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: skt1 > 'type/realax/real' ).
thf(sk2_decl,type,
sk2: skt1 > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1 > 'type/realax/real'] :
~ ! [B: skt1 > $o] :
( ( 'const/iterate/sum' @ skt1 @ ( 'const/iterate/support' @ 'type/realax/real' @ skt1 @ 'const/realax/real_add' @ A @ B ) @ A )
= ( 'const/iterate/sum' @ skt1 @ B @ A ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: skt1 > $o] :
( ( 'const/iterate/sum' @ skt1 @ ( 'const/iterate/support' @ 'type/realax/real' @ skt1 @ 'const/realax/real_add' @ sk1 @ A ) @ sk1 )
!= ( 'const/iterate/sum' @ skt1 @ A @ sk1 ) ) ) ) ).
thf(1,conjecture,
! [TA: $tType,A: TA > 'type/realax/real',B: TA > $o] :
( ( 'const/iterate/sum' @ TA @ ( 'const/iterate/support' @ 'type/realax/real' @ TA @ 'const/realax/real_add' @ A @ B ) @ A )
= ( 'const/iterate/sum' @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_SUPPORT_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > 'type/realax/real',B: TA > $o] :
( ( 'const/iterate/sum' @ TA @ ( 'const/iterate/support' @ 'type/realax/real' @ TA @ 'const/realax/real_add' @ A @ B ) @ A )
= ( 'const/iterate/sum' @ TA @ B @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [TA: $tType,A: TA > 'type/realax/real',B: TA > $o] :
( ( 'const/iterate/sum' @ TA @ ( 'const/iterate/support' @ 'type/realax/real' @ TA @ 'const/realax/real_add' @ A @ B ) @ A )
= ( 'const/iterate/sum' @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
( ( 'const/iterate/sum' @ skt1 @ ( 'const/iterate/support' @ 'type/realax/real' @ skt1 @ 'const/realax/real_add' @ sk1 @ sk2 ) @ sk1 )
!= ( 'const/iterate/sum' @ skt1 @ sk2 @ sk1 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(8,plain,
( ( 'const/iterate/sum' @ skt1 @ ( 'const/iterate/support' @ 'type/realax/real' @ skt1 @ 'const/realax/real_add' @ sk1 @ sk2 ) @ sk1 )
!= ( 'const/iterate/sum' @ skt1 @ sk2 @ sk1 ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > TB,B: TA > TB,C: TA > $o] :
( ( 'const/iterate/support' @ TB @ TA @ A @ B @ ( 'const/iterate/support' @ TB @ TA @ A @ B @ C ) )
= ( 'const/iterate/support' @ TB @ TA @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUPPORT_SUPPORT_') ).
thf(15,plain,
! [TA: $tType,TB: $tType,A: TB > TB > TB,B: TA > TB,C: TA > $o] :
( ( 'const/iterate/support' @ TB @ TA @ A @ B @ ( 'const/iterate/support' @ TB @ TA @ A @ B @ C ) )
= ( 'const/iterate/support' @ TB @ TA @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,plain,
! [TA: $tType,TB: $tType,C: TB > $o,B: TB > TA,A: TA > TA > TA] :
( ( 'const/iterate/support' @ TA @ TB @ A @ B @ ( 'const/iterate/support' @ TA @ TB @ A @ B @ C ) )
= ( 'const/iterate/support' @ TA @ TB @ A @ B @ C ) ),
inference(cnf,[status(esa)],[15]) ).
thf(17,plain,
! [TA: $tType,TB: $tType,C: TB > $o,B: TB > TA,A: TA > TA > TA] :
( ( 'const/iterate/support' @ TA @ TB @ A @ B @ ( 'const/iterate/support' @ TA @ TB @ A @ B @ C ) )
= ( 'const/iterate/support' @ TA @ TB @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o,C: TA > TA > TA] :
( ( 'const/iterate/iterate' @ TB @ TA @ C @ B @ A )
= ( 'const/class/COND' @ TA @ ( 'const/sets/FINITE' @ TB @ ( 'const/iterate/support' @ TA @ TB @ C @ A @ B ) )
@ ( 'const/sets/ITSET' @ TB @ TA
@ ^ [D: TB] : ( C @ ( A @ D ) )
@ ( 'const/iterate/support' @ TA @ TB @ C @ A @ B )
@ ( 'const/iterate/neutral' @ TA @ C ) )
@ ( 'const/iterate/neutral' @ TA @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/iterate_') ).
thf(12,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o,C: TA > TA > TA] :
( ( 'const/iterate/iterate' @ TB @ TA @ C @ B @ A )
= ( 'const/class/COND' @ TA @ ( 'const/sets/FINITE' @ TB @ ( 'const/iterate/support' @ TA @ TB @ C @ A @ B ) )
@ ( 'const/sets/ITSET' @ TB @ TA
@ ^ [D: TB] : ( C @ ( A @ D ) )
@ ( 'const/iterate/support' @ TA @ TB @ C @ A @ B )
@ ( 'const/iterate/neutral' @ TA @ C ) )
@ ( 'const/iterate/neutral' @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
! [TA: $tType,TB: $tType,C: TB > TB > TB,B: TA > $o,A: TA > TB] :
( ( 'const/iterate/iterate' @ TA @ TB @ C @ B @ A )
= ( 'const/class/COND' @ TB @ ( 'const/sets/FINITE' @ TA @ ( 'const/iterate/support' @ TB @ TA @ C @ A @ B ) )
@ ( 'const/sets/ITSET' @ TA @ TB
@ ^ [D: TA] : ( C @ ( A @ D ) )
@ ( 'const/iterate/support' @ TB @ TA @ C @ A @ B )
@ ( 'const/iterate/neutral' @ TB @ C ) )
@ ( 'const/iterate/neutral' @ TB @ C ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(14,plain,
! [TA: $tType,TB: $tType,C: TB > TB > TB,B: TA > $o,A: TA > TB] :
( ( 'const/iterate/iterate' @ TA @ TB @ C @ B @ A )
= ( 'const/class/COND' @ TB @ ( 'const/sets/FINITE' @ TA @ ( 'const/iterate/support' @ TB @ TA @ C @ A @ B ) )
@ ( 'const/sets/ITSET' @ TA @ TB
@ ^ [D: TA] : ( C @ ( A @ D ) )
@ ( 'const/iterate/support' @ TB @ TA @ C @ A @ B )
@ ( 'const/iterate/neutral' @ TB @ C ) )
@ ( 'const/iterate/neutral' @ TB @ C ) ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(51,plain,
! [TA: $tType,TC: $tType,TD: $tType,F: TD > TD > TD,E: TC > $o,D: TC > TD,C: TC > $o,B: TC > TA,A: TA > TA > TA] :
( ( ( 'const/class/COND' @ TD @ ( 'const/sets/FINITE' @ TC @ ( 'const/iterate/support' @ TA @ TC @ A @ B @ C ) )
@ ( 'const/sets/ITSET' @ TC @ TD
@ ^ [G: TC] : ( F @ ( D @ G ) )
@ ( 'const/iterate/support' @ TD @ TC @ F @ D @ E )
@ ( 'const/iterate/neutral' @ TD @ F ) )
@ ( 'const/iterate/neutral' @ TD @ F ) )
= ( 'const/iterate/iterate' @ TC @ TD @ F @ E @ D ) )
| ( ( 'const/iterate/support' @ TA @ TC @ A @ B @ ( 'const/iterate/support' @ TA @ TC @ A @ B @ C ) )
!= ( 'const/iterate/support' @ TD @ TC @ F @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[17,14]) ).
thf(52,plain,
! [TC: $tType,TD: $tType,C: TC > $o,B: TC > TD,A: TD > TD > TD] :
( ( 'const/class/COND' @ TD @ ( 'const/sets/FINITE' @ TC @ ( 'const/iterate/support' @ TD @ TC @ A @ B @ C ) )
@ ( 'const/sets/ITSET' @ TC @ TD
@ ^ [D: TC] : ( A @ ( B @ D ) )
@ ( 'const/iterate/support' @ TD @ TC @ A @ B @ ( 'const/iterate/support' @ TD @ TC @ A @ B @ C ) )
@ ( 'const/iterate/neutral' @ TD @ A ) )
@ ( 'const/iterate/neutral' @ TD @ A ) )
= ( 'const/iterate/iterate' @ TC @ TD @ A @ ( 'const/iterate/support' @ TD @ TC @ A @ B @ C ) @ B ) ),
inference(pattern_uni,[status(thm)],[51:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( 'const/iterate/support' @ TD @ TC @ A @ B @ C )),bind(F,$thf( A )),bind_type(TA,$thf( TD ))]]) ).
thf(63,plain,
! [TA: $tType,TB: $tType,C: TA > $o,B: TA > TB,A: TB > TB > TB] :
( ( 'const/class/COND' @ TB @ ( 'const/sets/FINITE' @ TA @ ( 'const/iterate/support' @ TB @ TA @ A @ B @ C ) )
@ ( 'const/sets/ITSET' @ TA @ TB
@ ^ [D: TA] : ( A @ ( B @ D ) )
@ ( 'const/iterate/support' @ TB @ TA @ A @ B @ ( 'const/iterate/support' @ TB @ TA @ A @ B @ C ) )
@ ( 'const/iterate/neutral' @ TB @ A ) )
@ ( 'const/iterate/neutral' @ TB @ A ) )
= ( 'const/iterate/iterate' @ TA @ TB @ A @ ( 'const/iterate/support' @ TB @ TA @ A @ B @ C ) @ B ) ),
inference(simp,[status(thm)],[52]) ).
thf(3,axiom,
! [TA: $tType] :
( ( 'const/iterate/sum' @ TA )
= ( 'const/iterate/iterate' @ TA @ 'type/realax/real' @ 'const/realax/real_add' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/sum_') ).
thf(9,plain,
! [TA: $tType] :
( ( 'const/iterate/sum' @ TA )
= ( 'const/iterate/iterate' @ TA @ 'type/realax/real' @ 'const/realax/real_add' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,plain,
! [TA: $tType] :
( ( 'const/iterate/sum' @ TA )
= ( 'const/iterate/iterate' @ TA @ 'type/realax/real' @ 'const/realax/real_add' ) ),
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
! [TA: $tType] :
( ( 'const/iterate/iterate' @ TA @ 'type/realax/real' @ 'const/realax/real_add' )
= ( 'const/iterate/sum' @ TA ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(19,plain,
! [TA: $tType,B: TA > 'type/realax/real',A: TA > $o] :
( ( 'const/iterate/iterate' @ TA @ 'type/realax/real' @ 'const/realax/real_add' @ A @ B )
= ( 'const/iterate/sum' @ TA @ A @ B ) ),
inference(func_ext,[status(esa)],[11]) ).
thf(59,plain,
! [TA: $tType,TC: $tType,E: TC > 'type/realax/real',D: TC > $o,C: 'type/realax/real' > 'type/realax/real' > 'type/realax/real',B: TA > $o,A: TA > 'type/realax/real'] :
( ( ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/sets/FINITE' @ TA @ ( 'const/iterate/support' @ 'type/realax/real' @ TA @ C @ A @ B ) )
@ ( 'const/sets/ITSET' @ TA @ 'type/realax/real'
@ ^ [F: TA] : ( C @ ( A @ F ) )
@ ( 'const/iterate/support' @ 'type/realax/real' @ TA @ C @ A @ B )
@ ( 'const/iterate/neutral' @ 'type/realax/real' @ C ) )
@ ( 'const/iterate/neutral' @ 'type/realax/real' @ C ) )
= ( 'const/iterate/sum' @ TC @ D @ E ) )
| ( ( 'const/iterate/iterate' @ TA @ 'type/realax/real' @ C @ B @ A )
!= ( 'const/iterate/iterate' @ TC @ 'type/realax/real' @ 'const/realax/real_add' @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[14,19]) ).
thf(60,plain,
! [TC: $tType,B: TC > $o,A: TC > 'type/realax/real'] :
( ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/sets/FINITE' @ TC @ ( 'const/iterate/support' @ 'type/realax/real' @ TC @ 'const/realax/real_add' @ A @ B ) )
@ ( 'const/sets/ITSET' @ TC @ 'type/realax/real'
@ ^ [C: TC] : ( 'const/realax/real_add' @ ( A @ C ) )
@ ( 'const/iterate/support' @ 'type/realax/real' @ TC @ 'const/realax/real_add' @ A @ B )
@ ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' ) )
@ ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' ) )
= ( 'const/iterate/sum' @ TC @ B @ A ) ),
inference(pattern_uni,[status(thm)],[59:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( 'const/realax/real_add' )),bind(D,$thf( B )),bind(E,$thf( A )),bind_type(TA,$thf( TC ))]]) ).
thf(67,plain,
! [TA: $tType,B: TA > $o,A: TA > 'type/realax/real'] :
( ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/sets/FINITE' @ TA @ ( 'const/iterate/support' @ 'type/realax/real' @ TA @ 'const/realax/real_add' @ A @ B ) )
@ ( 'const/sets/ITSET' @ TA @ 'type/realax/real'
@ ^ [C: TA] : ( 'const/realax/real_add' @ ( A @ C ) )
@ ( 'const/iterate/support' @ 'type/realax/real' @ TA @ 'const/realax/real_add' @ A @ B )
@ ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' ) )
@ ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' ) )
= ( 'const/iterate/sum' @ TA @ B @ A ) ),
inference(simp,[status(thm)],[60]) ).
thf(93,plain,
! [TA: $tType,TC: $tType,E: TC > $o,D: TC > 'type/realax/real',C: TC > $o,B: TC > TA,A: TA > TA > TA] :
( ( ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/sets/FINITE' @ TC @ ( 'const/iterate/support' @ 'type/realax/real' @ TC @ 'const/realax/real_add' @ D @ E ) )
@ ( 'const/sets/ITSET' @ TC @ 'type/realax/real'
@ ^ [F: TC] : ( 'const/realax/real_add' @ ( D @ F ) )
@ ( 'const/iterate/support' @ TA @ TC @ A @ B @ ( 'const/iterate/support' @ TA @ TC @ A @ B @ C ) )
@ ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' ) )
@ ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' ) )
= ( 'const/iterate/sum' @ TC @ E @ D ) )
| ( ( 'const/iterate/support' @ TA @ TC @ A @ B @ C )
!= ( 'const/iterate/support' @ 'type/realax/real' @ TC @ 'const/realax/real_add' @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[17,67]) ).
thf(94,plain,
! [TC: $tType,B: TC > $o,A: TC > 'type/realax/real'] :
( ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/sets/FINITE' @ TC @ ( 'const/iterate/support' @ 'type/realax/real' @ TC @ 'const/realax/real_add' @ A @ B ) )
@ ( 'const/sets/ITSET' @ TC @ 'type/realax/real'
@ ^ [C: TC] : ( 'const/realax/real_add' @ ( A @ C ) )
@ ( 'const/iterate/support' @ 'type/realax/real' @ TC @ 'const/realax/real_add' @ A @ ( 'const/iterate/support' @ 'type/realax/real' @ TC @ 'const/realax/real_add' @ A @ B ) )
@ ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' ) )
@ ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' ) )
= ( 'const/iterate/sum' @ TC @ B @ A ) ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( 'const/realax/real_add' )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C )),bind_type(TA,$thf( 'type/realax/real' ))]]) ).
thf(105,plain,
! [TA: $tType,B: TA > $o,A: TA > 'type/realax/real'] :
( ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/sets/FINITE' @ TA @ ( 'const/iterate/support' @ 'type/realax/real' @ TA @ 'const/realax/real_add' @ A @ B ) )
@ ( 'const/sets/ITSET' @ TA @ 'type/realax/real'
@ ^ [C: TA] : ( 'const/realax/real_add' @ ( A @ C ) )
@ ( 'const/iterate/support' @ 'type/realax/real' @ TA @ 'const/realax/real_add' @ A @ ( 'const/iterate/support' @ 'type/realax/real' @ TA @ 'const/realax/real_add' @ A @ B ) )
@ ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' ) )
@ ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' ) )
= ( 'const/iterate/sum' @ TA @ B @ A ) ),
inference(simp,[status(thm)],[94]) ).
thf(581,plain,
! [TA: $tType,TC: $tType,E: TC > $o,D: TC > 'type/realax/real',C: TA > $o,B: TA > 'type/realax/real',A: 'type/realax/real' > 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/iterate/iterate' @ TA @ 'type/realax/real' @ A @ ( 'const/iterate/support' @ 'type/realax/real' @ TA @ A @ B @ C ) @ B )
= ( 'const/iterate/sum' @ TC @ E @ D ) )
| ( ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/sets/FINITE' @ TA @ ( 'const/iterate/support' @ 'type/realax/real' @ TA @ A @ B @ C ) )
@ ( 'const/sets/ITSET' @ TA @ 'type/realax/real'
@ ^ [F: TA] : ( A @ ( B @ F ) )
@ ( 'const/iterate/support' @ 'type/realax/real' @ TA @ A @ B @ ( 'const/iterate/support' @ 'type/realax/real' @ TA @ A @ B @ C ) )
@ ( 'const/iterate/neutral' @ 'type/realax/real' @ A ) )
@ ( 'const/iterate/neutral' @ 'type/realax/real' @ A ) )
!= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/sets/FINITE' @ TC @ ( 'const/iterate/support' @ 'type/realax/real' @ TC @ 'const/realax/real_add' @ D @ E ) )
@ ( 'const/sets/ITSET' @ TC @ 'type/realax/real'
@ ^ [F: TC] : ( 'const/realax/real_add' @ ( D @ F ) )
@ ( 'const/iterate/support' @ 'type/realax/real' @ TC @ 'const/realax/real_add' @ D @ ( 'const/iterate/support' @ 'type/realax/real' @ TC @ 'const/realax/real_add' @ D @ E ) )
@ ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' ) )
@ ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' ) ) ) ),
inference(paramod_ordered,[status(thm)],[63,105]) ).
thf(630,plain,
! [TC: $tType,D: TC > $o,C: TC > 'type/realax/real',B: TC > $o,A: TC > 'type/realax/real'] :
( ( ( 'const/iterate/iterate' @ TC @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/iterate/support' @ 'type/realax/real' @ TC @ 'const/realax/real_add' @ A @ B ) @ A )
= ( 'const/iterate/sum' @ TC @ D @ C ) )
| ( ( ^ [E: TC] : A )
!= ( ^ [E: TC] : C ) )
| ( ( ^ [E: TC] : B )
!= ( ^ [E: TC] : D ) )
| ( ( ^ [E: TC] : A )
!= ( ^ [E: TC] : C ) )
| ( ( ^ [E: TC,F: TC] : A )
!= ( ^ [E: TC,F: TC] : C ) )
| ( ( ^ [E: TC,F: TC] : B )
!= ( ^ [E: TC,F: TC] : D ) )
| ( ( ^ [E: TC,F: 'type/realax/real'] : ( A @ E ) )
!= ( ^ [E: TC,F: 'type/realax/real'] : ( C @ E ) ) ) ),
inference(pre_uni,[status(thm)],[581:[bind(A,$thf( 'const/realax/real_add' )),bind_type(TA,$thf( TC ))]]) ).
thf(631,plain,
! [TC: $tType,B: TC > $o,A: TC > 'type/realax/real'] :
( ( 'const/iterate/iterate' @ TC @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/iterate/support' @ 'type/realax/real' @ TC @ 'const/realax/real_add' @ A @ B ) @ A )
= ( 'const/iterate/sum' @ TC @ B @ A ) ),
inference(pattern_uni,[status(thm)],[630:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(661,plain,
! [TA: $tType,B: TA > $o,A: TA > 'type/realax/real'] :
( ( 'const/iterate/iterate' @ TA @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/iterate/support' @ 'type/realax/real' @ TA @ 'const/realax/real_add' @ A @ B ) @ A )
= ( 'const/iterate/sum' @ TA @ B @ A ) ),
inference(simp,[status(thm)],[631]) ).
thf(664,plain,
! [TA: $tType,B: TA > $o,A: TA > 'type/realax/real'] :
( ( 'const/iterate/sum' @ TA @ ( 'const/iterate/support' @ 'type/realax/real' @ TA @ 'const/realax/real_add' @ A @ B ) @ A )
= ( 'const/iterate/sum' @ TA @ B @ A ) ),
inference(rewrite,[status(thm)],[661,19]) ).
thf(665,plain,
$false,
inference(simplifyReflect,[status(thm)],[8,664]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA098^1 : 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
% 0.10/0.19 % Computer : n003.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 17:42:59 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 0.88/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/0.98 % [INFO] Parsing done (199ms).
% 1.22/0.99 % [INFO] Running in sequential loop mode.
% 2.16/1.41 % [INFO] eprover registered as external prover.
% 2.16/1.42 % [INFO] Scanning for conjecture ...
% 2.16/1.49 % [INFO] No direction of definition thm/iterate/sum_ detected. Treating as axiom ...
% 2.34/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.34/1.57 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.34/1.57 % [INFO] No direction of definition thm/iterate/sum_ detected. Treating as axiom ...
% 2.34/1.59 % [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 ...
% 54.85/39.46 % [INFO] Killing All external provers ...
% 54.85/39.47 % Time passed: 39124ms (effective reasoning time: 38462ms)
% 54.85/39.47 % 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)>
% 54.85/39.47 % Axioms used in derivation (3): thm/iterate/SUPPORT_SUPPORT_, thm/iterate/iterate_, thm/iterate/sum_
% 54.85/39.47 % No. of inferences in proof: 33
% 54.85/39.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 39124 ms resp. 38462 ms w/o parsing
% 55.06/39.55 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 55.06/39.55 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------