%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA116^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n019.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 07:45:48 AM UTC 2026
% Result : Theorem 74.77s 57.72s
% Output : Refutation 75.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 18 unt; 0 typ; 4 def)
% Number of atoms : 124 ( 58 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 1657 ( 45 ~; 28 |; 0 &;1584 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 4 con; 0-4 aty)
% Number of variables : 122 ( 58 ^; 60 !; 0 ?; 122 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf('type/realax/real_type',type,
'type/realax/real': $tType ).
thf('type/nums/num_type',type,
'type/nums/num': $tType ).
thf('const/realax/real_sub_decl',type,
'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf('const/realax/real_of_num_decl',type,
'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
thf('const/realax/real_mul_decl',type,
'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf('const/nums/NUMERAL_decl',type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf('const/nums/BIT1_decl',type,
'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
thf('const/nums/_0_decl',type,
'const/nums/_0': 'type/nums/num' ).
thf('const/iterate/sum_decl',type,
'const/iterate/sum':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > 'type/realax/real' ) > 'type/realax/real' ) ).
thf('const/iterate/.._decl',type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf('const/class/COND_decl',type,
'const/class/COND':
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf('const/arith/+_decl',type,
'const/arith/+': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf('const/arith/-_decl',type,
'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf('const/arith/<=_decl',type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf(sk1_decl,type,
sk1: 'type/nums/num' > 'type/realax/real' ).
thf(sk2_decl,type,
sk2: 'type/nums/num' > 'type/realax/real' ).
thf(sk3_decl,type,
sk3: 'type/nums/num' ).
thf(sk4_decl,type,
sk4: 'type/nums/num' ).
thf(sk1_def,definition,
( sk1
= ( @+[A: 'type/nums/num' > 'type/realax/real'] :
~ ! [B: 'type/nums/num' > 'type/realax/real',C: 'type/nums/num',D: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( A @ E ) @ ( 'const/realax/real_sub' @ ( B @ E ) @ ( B @ ( 'const/arith/-' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ C @ D )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( A @ ( 'const/arith/+' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( B @ D ) ) @ ( 'const/realax/real_mul' @ ( A @ C ) @ ( B @ ( 'const/arith/-' @ C @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( B @ E ) @ ( 'const/realax/real_sub' @ ( A @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( A @ E ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: 'type/nums/num' > 'type/realax/real'] :
~ ! [B: 'type/nums/num',C: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ B @ C )
@ ^ [D: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk1 @ D ) @ ( 'const/realax/real_sub' @ ( A @ D ) @ ( A @ ( 'const/arith/-' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ B @ C )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( sk1 @ ( 'const/arith/+' @ C @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( A @ C ) ) @ ( 'const/realax/real_mul' @ ( sk1 @ B ) @ ( A @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ B @ C )
@ ^ [D: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( A @ D ) @ ( 'const/realax/real_sub' @ ( sk1 @ ( 'const/arith/+' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk1 @ D ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: 'type/nums/num'] :
~ ! [B: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ B )
@ ^ [C: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk1 @ C ) @ ( 'const/realax/real_sub' @ ( sk2 @ C ) @ ( sk2 @ ( 'const/arith/-' @ C @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ A @ B )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( sk1 @ ( 'const/arith/+' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk2 @ B ) ) @ ( 'const/realax/real_mul' @ ( sk1 @ A ) @ ( sk2 @ ( 'const/arith/-' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ B )
@ ^ [C: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk2 @ C ) @ ( 'const/realax/real_sub' @ ( sk1 @ ( 'const/arith/+' @ C @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk1 @ C ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ A )
@ ^ [B: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk1 @ B ) @ ( 'const/realax/real_sub' @ ( sk2 @ B ) @ ( sk2 @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
!= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ sk3 @ A )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( sk1 @ ( 'const/arith/+' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk2 @ A ) ) @ ( 'const/realax/real_mul' @ ( sk1 @ sk3 ) @ ( sk2 @ ( 'const/arith/-' @ sk3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ A )
@ ^ [B: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk2 @ B ) @ ( 'const/realax/real_sub' @ ( sk1 @ ( 'const/arith/+' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk1 @ B ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ) ) ) ).
thf(4,axiom,
! [A: 'type/nums/num' > 'type/realax/real',B: 'type/nums/num' > 'type/realax/real',C: 'type/nums/num',D: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( A @ E ) @ ( 'const/realax/real_sub' @ ( B @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( B @ E ) ) ) )
= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ C @ D )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( A @ ( 'const/arith/+' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( B @ ( 'const/arith/+' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) @ ( 'const/realax/real_mul' @ ( A @ C ) @ ( B @ C ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( B @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_sub' @ ( A @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( A @ E ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_PARTIAL_SUC_') ).
thf(11,plain,
! [A: 'type/nums/num' > 'type/realax/real',B: 'type/nums/num' > 'type/realax/real',C: 'type/nums/num',D: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( A @ E ) @ ( 'const/realax/real_sub' @ ( B @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( B @ E ) ) ) )
= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ C @ D )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( A @ ( 'const/arith/+' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( B @ ( 'const/arith/+' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) @ ( 'const/realax/real_mul' @ ( A @ C ) @ ( B @ C ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( B @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_sub' @ ( A @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( A @ E ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,plain,
! [D: 'type/nums/num',C: 'type/nums/num',B: 'type/nums/num' > 'type/realax/real',A: 'type/nums/num' > 'type/realax/real'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( A @ E ) @ ( 'const/realax/real_sub' @ ( B @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( B @ E ) ) ) )
= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ C @ D )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( A @ ( 'const/arith/+' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( B @ ( 'const/arith/+' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) @ ( 'const/realax/real_mul' @ ( A @ C ) @ ( B @ C ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( B @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_sub' @ ( A @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( A @ E ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
! [D: 'type/nums/num',C: 'type/nums/num',B: 'type/nums/num' > 'type/realax/real',A: 'type/nums/num' > 'type/realax/real'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( A @ E ) @ ( 'const/realax/real_sub' @ ( B @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( B @ E ) ) ) )
= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ C @ D )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( A @ ( 'const/arith/+' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( B @ ( 'const/arith/+' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) @ ( 'const/realax/real_mul' @ ( A @ C ) @ ( B @ C ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( B @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_sub' @ ( A @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( A @ E ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(1,conjecture,
! [A: 'type/nums/num' > 'type/realax/real',B: 'type/nums/num' > 'type/realax/real',C: 'type/nums/num',D: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( A @ E ) @ ( 'const/realax/real_sub' @ ( B @ E ) @ ( B @ ( 'const/arith/-' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ C @ D )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( A @ ( 'const/arith/+' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( B @ D ) ) @ ( 'const/realax/real_mul' @ ( A @ C ) @ ( B @ ( 'const/arith/-' @ C @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( B @ E ) @ ( 'const/realax/real_sub' @ ( A @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( A @ E ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_PARTIAL_PRE_') ).
thf(2,negated_conjecture,
~ ! [A: 'type/nums/num' > 'type/realax/real',B: 'type/nums/num' > 'type/realax/real',C: 'type/nums/num',D: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( A @ E ) @ ( 'const/realax/real_sub' @ ( B @ E ) @ ( B @ ( 'const/arith/-' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ C @ D )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( A @ ( 'const/arith/+' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( B @ D ) ) @ ( 'const/realax/real_mul' @ ( A @ C ) @ ( B @ ( 'const/arith/-' @ C @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( B @ E ) @ ( 'const/realax/real_sub' @ ( A @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( A @ E ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: 'type/nums/num' > 'type/realax/real',B: 'type/nums/num' > 'type/realax/real',C: 'type/nums/num',D: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( A @ E ) @ ( 'const/realax/real_sub' @ ( B @ E ) @ ( B @ ( 'const/arith/-' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ C @ D )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( A @ ( 'const/arith/+' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( B @ D ) ) @ ( 'const/realax/real_mul' @ ( A @ C ) @ ( B @ ( 'const/arith/-' @ C @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( B @ E ) @ ( 'const/realax/real_sub' @ ( A @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( A @ E ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 )
@ ^ [A: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk1 @ A ) @ ( 'const/realax/real_sub' @ ( sk2 @ A ) @ ( sk2 @ ( 'const/arith/-' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
!= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ sk3 @ sk4 )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( sk1 @ ( 'const/arith/+' @ sk4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk2 @ sk4 ) ) @ ( 'const/realax/real_mul' @ ( sk1 @ sk3 ) @ ( sk2 @ ( 'const/arith/-' @ sk3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 )
@ ^ [A: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk2 @ A ) @ ( 'const/realax/real_sub' @ ( sk1 @ ( 'const/arith/+' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk1 @ A ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(7,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 )
@ ^ [A: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk1 @ A ) @ ( 'const/realax/real_sub' @ ( sk2 @ A ) @ ( sk2 @ ( 'const/arith/-' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
!= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ sk3 @ sk4 )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( sk1 @ ( 'const/arith/+' @ sk4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk2 @ sk4 ) ) @ ( 'const/realax/real_mul' @ ( sk1 @ sk3 ) @ ( sk2 @ ( 'const/arith/-' @ sk3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 )
@ ^ [A: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk2 @ A ) @ ( 'const/realax/real_sub' @ ( sk1 @ ( 'const/arith/+' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk1 @ A ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(17,plain,
! [D: 'type/nums/num',C: 'type/nums/num',B: 'type/nums/num' > 'type/realax/real',A: 'type/nums/num' > 'type/realax/real'] :
( ( ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ C @ D )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( A @ ( 'const/arith/+' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( B @ ( 'const/arith/+' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) @ ( 'const/realax/real_mul' @ ( A @ C ) @ ( B @ C ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( B @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_sub' @ ( A @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( A @ E ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
!= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ sk3 @ sk4 )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( sk1 @ ( 'const/arith/+' @ sk4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk2 @ sk4 ) ) @ ( 'const/realax/real_mul' @ ( sk1 @ sk3 ) @ ( sk2 @ ( 'const/arith/-' @ sk3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk2 @ E ) @ ( 'const/realax/real_sub' @ ( sk1 @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk1 @ E ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) )
| ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( A @ E ) @ ( 'const/realax/real_sub' @ ( B @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( B @ E ) ) ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk1 @ E ) @ ( 'const/realax/real_sub' @ ( sk2 @ E ) @ ( sk2 @ ( 'const/arith/-' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,7]) ).
thf(33,plain,
! [D: 'type/nums/num',C: 'type/nums/num',B: 'type/nums/num' > 'type/realax/real',A: 'type/nums/num' > 'type/realax/real'] :
( ( ( 'const/arith/<=' @ C @ D )
!= ( 'const/arith/<=' @ sk3 @ sk4 ) )
| ( ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( A @ ( 'const/arith/+' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( B @ ( 'const/arith/+' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) @ ( 'const/realax/real_mul' @ ( A @ C ) @ ( B @ C ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( B @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_sub' @ ( A @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( A @ E ) ) ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( sk1 @ ( 'const/arith/+' @ sk4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk2 @ sk4 ) ) @ ( 'const/realax/real_mul' @ ( sk1 @ sk3 ) @ ( sk2 @ ( 'const/arith/-' @ sk3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk2 @ E ) @ ( 'const/realax/real_sub' @ ( sk1 @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk1 @ E ) ) ) ) ) )
| ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
| ( ( 'const/iterate/..' @ C @ D )
!= ( 'const/iterate/..' @ sk3 @ sk4 ) )
| ( ( ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( A @ E ) @ ( 'const/realax/real_sub' @ ( B @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( B @ E ) ) ) )
!= ( ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk1 @ E ) @ ( 'const/realax/real_sub' @ ( sk2 @ E ) @ ( sk2 @ ( 'const/arith/-' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(46,plain,
! [D: 'type/nums/num',C: 'type/nums/num',B: 'type/nums/num' > 'type/realax/real',A: 'type/nums/num' > 'type/realax/real'] :
( ( ( 'const/arith/<=' @ C @ D )
!= ( 'const/arith/<=' @ sk3 @ sk4 ) )
| ( ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( A @ ( 'const/arith/+' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( B @ ( 'const/arith/+' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) @ ( 'const/realax/real_mul' @ ( A @ C ) @ ( B @ C ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( B @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_sub' @ ( A @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( A @ E ) ) ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( sk1 @ ( 'const/arith/+' @ sk4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk2 @ sk4 ) ) @ ( 'const/realax/real_mul' @ ( sk1 @ sk3 ) @ ( sk2 @ ( 'const/arith/-' @ sk3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk2 @ E ) @ ( 'const/realax/real_sub' @ ( sk1 @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk1 @ E ) ) ) ) ) )
| ( ( 'const/iterate/..' @ C @ D )
!= ( 'const/iterate/..' @ sk3 @ sk4 ) )
| ( ( ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( A @ E ) @ ( 'const/realax/real_sub' @ ( B @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( B @ E ) ) ) )
!= ( ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk1 @ E ) @ ( 'const/realax/real_sub' @ ( sk2 @ E ) @ ( sk2 @ ( 'const/arith/-' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(314,plain,
! [D: 'type/nums/num',C: 'type/nums/num',B: 'type/nums/num' > 'type/realax/real',A: 'type/nums/num' > 'type/realax/real'] :
( ( C != sk3 )
| ( D != sk4 )
| ( ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( A @ ( 'const/arith/+' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( B @ ( 'const/arith/+' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) @ ( 'const/realax/real_mul' @ ( A @ C ) @ ( B @ C ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( sk1 @ ( 'const/arith/+' @ sk4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk2 @ sk4 ) ) @ ( 'const/realax/real_mul' @ ( sk1 @ sk3 ) @ ( sk2 @ ( 'const/arith/-' @ sk3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( B @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_sub' @ ( A @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( A @ E ) ) ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk2 @ E ) @ ( 'const/realax/real_sub' @ ( sk1 @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk1 @ E ) ) ) ) )
| ( ( 'const/iterate/..' @ C @ D )
!= ( 'const/iterate/..' @ sk3 @ sk4 ) )
| ( A != sk1 )
| ( ( ^ [E: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( B @ ( 'const/arith/+' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( B @ E ) ) )
!= ( ^ [E: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( sk2 @ E ) @ ( sk2 @ ( 'const/arith/-' @ E @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[46]) ).
thf(515,plain,
! [A: 'type/nums/num' > 'type/realax/real'] :
( ( ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( sk1 @ ( 'const/arith/+' @ sk4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( A @ ( 'const/arith/+' @ sk4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) @ ( 'const/realax/real_mul' @ ( sk1 @ sk3 ) @ ( A @ sk3 ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( sk1 @ ( 'const/arith/+' @ sk4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk2 @ sk4 ) ) @ ( 'const/realax/real_mul' @ ( sk1 @ sk3 ) @ ( sk2 @ ( 'const/arith/-' @ sk3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 )
@ ^ [B: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( A @ ( 'const/arith/+' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_sub' @ ( sk1 @ ( 'const/arith/+' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk1 @ B ) ) ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 )
@ ^ [B: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk2 @ B ) @ ( 'const/realax/real_sub' @ ( sk1 @ ( 'const/arith/+' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk1 @ B ) ) ) ) )
| ( ( ^ [B: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( A @ ( 'const/arith/+' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( A @ B ) ) )
!= ( ^ [B: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( sk2 @ B ) @ ( sk2 @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[314]) ).
thf(1019,plain,
! [A: 'type/nums/num' > 'type/realax/real'] :
( ( ( 'const/realax/real_mul' @ ( sk1 @ ( 'const/arith/+' @ sk4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( A @ ( 'const/arith/+' @ sk4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( 'const/realax/real_mul' @ ( sk1 @ ( 'const/arith/+' @ sk4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk2 @ sk4 ) ) )
| ( ( 'const/realax/real_mul' @ ( sk1 @ sk3 ) @ ( A @ sk3 ) )
!= ( 'const/realax/real_mul' @ ( sk1 @ sk3 ) @ ( sk2 @ ( 'const/arith/-' @ sk3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( 'const/iterate/..' @ sk3 @ sk4 )
!= ( 'const/iterate/..' @ sk3 @ sk4 ) )
| ( ( ^ [B: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( A @ ( 'const/arith/+' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_sub' @ ( sk1 @ ( 'const/arith/+' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk1 @ B ) ) ) )
!= ( ^ [B: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk2 @ B ) @ ( 'const/realax/real_sub' @ ( sk1 @ ( 'const/arith/+' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk1 @ B ) ) ) ) )
| ( ( ^ [B: 'type/nums/num'] : ( A @ ( 'const/arith/+' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= sk2 )
| ( A
!= ( ^ [B: 'type/nums/num'] : ( sk2 @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ),
inference(simp,[status(thm)],[515]) ).
thf(1130,plain,
( ( ( 'const/realax/real_mul' @ ( sk1 @ ( 'const/arith/+' @ sk4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk2 @ ( 'const/arith/-' @ ( 'const/arith/+' @ sk4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( 'const/realax/real_mul' @ ( sk1 @ ( 'const/arith/+' @ sk4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk2 @ sk4 ) ) )
| ( ( 'const/realax/real_mul' @ ( sk1 @ sk3 ) @ ( sk2 @ ( 'const/arith/-' @ sk3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( 'const/realax/real_mul' @ ( sk1 @ sk3 ) @ ( sk2 @ ( 'const/arith/-' @ sk3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [A: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk2 @ ( 'const/arith/-' @ ( 'const/arith/+' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_sub' @ ( sk1 @ ( 'const/arith/+' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk1 @ A ) ) ) )
!= ( ^ [A: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk2 @ A ) @ ( 'const/realax/real_sub' @ ( sk1 @ ( 'const/arith/+' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk1 @ A ) ) ) ) )
| ( ( ^ [A: 'type/nums/num'] : ( sk2 @ ( 'const/arith/-' @ ( 'const/arith/+' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1019]) ).
thf(1131,plain,
( ( ( 'const/realax/real_mul' @ ( sk1 @ ( 'const/arith/+' @ sk4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk2 @ ( 'const/arith/-' @ ( 'const/arith/+' @ sk4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( 'const/realax/real_mul' @ ( sk1 @ ( 'const/arith/+' @ sk4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk2 @ sk4 ) ) )
| ( ( ^ [A: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk2 @ ( 'const/arith/-' @ ( 'const/arith/+' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_sub' @ ( sk1 @ ( 'const/arith/+' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk1 @ A ) ) ) )
!= ( ^ [A: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk2 @ A ) @ ( 'const/realax/real_sub' @ ( sk1 @ ( 'const/arith/+' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk1 @ A ) ) ) ) )
| ( ( ^ [A: 'type/nums/num'] : ( sk2 @ ( 'const/arith/-' @ ( 'const/arith/+' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1130]) ).
thf(3,axiom,
! [A: 'type/nums/num',B: 'type/nums/num'] :
( ( 'const/arith/-' @ ( 'const/arith/+' @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/arith/ADD_SUB_') ).
thf(8,plain,
! [A: 'type/nums/num',B: 'type/nums/num'] :
( ( 'const/arith/-' @ ( 'const/arith/+' @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ( 'const/arith/-' @ ( 'const/arith/+' @ A @ B ) @ B )
= A ),
inference(cnf,[status(esa)],[8]) ).
thf(10,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ( 'const/arith/-' @ ( 'const/arith/+' @ A @ B ) @ B )
= A ),
inference(lifteq,[status(thm)],[9]) ).
thf(1132,plain,
( ( ( 'const/realax/real_mul' @ ( sk1 @ ( 'const/arith/+' @ sk4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk2 @ sk4 ) )
!= ( 'const/realax/real_mul' @ ( sk1 @ ( 'const/arith/+' @ sk4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk2 @ sk4 ) ) )
| ( ( ^ [A: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk2 @ A ) @ ( 'const/realax/real_sub' @ ( sk1 @ ( 'const/arith/+' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk1 @ A ) ) ) )
!= ( ^ [A: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sk2 @ A ) @ ( 'const/realax/real_sub' @ ( sk1 @ ( 'const/arith/+' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sk1 @ A ) ) ) ) )
| ( sk2 != sk2 ) ),
inference(rewrite,[status(thm)],[1131,10]) ).
thf(1133,plain,
$false,
inference(simp,[status(thm)],[1132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA116^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.20 % Computer : n019.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % 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 17:42:17 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.87/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/1.01 % [INFO] Parsing done (225ms).
% 1.46/1.03 % [INFO] Running in sequential loop mode.
% 2.00/1.44 % [INFO] eprover registered as external prover.
% 2.00/1.44 % [INFO] Scanning for conjecture ...
% 2.18/1.57 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.36/1.62 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.36/1.63 % [INFO] Problem is higher-order (TPTP THF).
% 2.36/1.64 % [INFO] Type checking passed.
% 2.36/1.65 % [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 ...
% 74.77/57.71 % [INFO] Killing All external provers ...
% 74.77/57.71 % Time passed: 57373ms (effective reasoning time: 56677ms)
% 74.77/57.71 % 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)>
% 74.77/57.72 % Axioms used in derivation (2): thm/iterate/SUM_PARTIAL_SUC_, thm/arith/ADD_SUB_
% 74.77/57.72 % No. of inferences in proof: 23
% 74.77/57.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 57373 ms resp. 56677 ms w/o parsing
% 75.07/57.80 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 75.07/57.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------