%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA118^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:45:48 AM UTC 2026
% Result : Theorem 12.12s 4.07s
% Output : Refutation 12.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 18 unt; 0 typ; 2 def)
% Number of atoms : 74 ( 34 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 759 ( 17 ~; 9 |; 1 &; 725 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 55 ( 11 ^; 42 !; 0 ?; 55 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% 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_pow_decl',type,
'const/realax/real_pow': 'type/realax/real' > 'type/nums/num' > '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/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/realax/real' ).
thf(sk2_decl,type,
sk2: 'type/nums/num' ).
thf(sk1_def,definition,
( sk1
= ( @+[A: 'type/realax/real'] :
~ ! [B: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ B )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ B ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ A ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: 'type/nums/num'] :
~ ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ A )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ sk1 @ A ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ sk1 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ sk1 ) ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: 'type/realax/real',B: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ B )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ B ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/REAL_SUB_POW_R1_') ).
thf(2,negated_conjecture,
~ ! [A: 'type/realax/real',B: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ B )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ B ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: 'type/realax/real',B: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ B )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ B ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ sk2 )
& ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ sk1 @ sk2 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ sk1 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sk2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ sk1 ) ) ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(9,plain,
( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ sk1 @ sk2 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ sk1 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sk2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ sk1 ) ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(10,plain,
( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ sk1 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sk2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ sk1 ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ sk1 @ sk2 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(8,plain,
'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ sk2,
inference(cnfConj,[status(thm)],[7]) ).
thf(4,axiom,
! [A: 'type/nums/num'] :
( ( 'const/realax/real_pow' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/real/REAL_POW_ONE_') ).
thf(14,plain,
! [A: 'type/nums/num'] :
( ( 'const/realax/real_pow' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,plain,
! [A: 'type/nums/num'] :
( ( 'const/realax/real_pow' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
! [A: 'type/nums/num'] :
( ( 'const/realax/real_pow' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(5,axiom,
! [A: 'type/realax/real',B: 'type/realax/real',C: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ C )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ C ) @ ( 'const/realax/real_pow' @ B @ C ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ B )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ C @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [D: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ A @ D ) @ ( 'const/realax/real_pow' @ B @ ( 'const/arith/-' @ ( 'const/arith/-' @ C @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/REAL_SUB_POW_') ).
thf(17,plain,
! [A: 'type/realax/real',B: 'type/realax/real',C: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ C )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ C ) @ ( 'const/realax/real_pow' @ B @ C ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ B )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ C @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [D: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ A @ D ) @ ( 'const/realax/real_pow' @ B @ ( 'const/arith/-' @ ( 'const/arith/-' @ C @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,plain,
! [C: 'type/nums/num',B: 'type/realax/real',A: 'type/realax/real'] :
( ~ ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ C )
| ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ C ) @ ( 'const/realax/real_pow' @ B @ C ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ B )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ C @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [D: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ A @ D ) @ ( 'const/realax/real_pow' @ B @ ( 'const/arith/-' @ ( 'const/arith/-' @ C @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ D ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(19,plain,
! [C: 'type/nums/num',B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ C ) @ ( 'const/realax/real_pow' @ B @ C ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ B )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ C @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [D: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ A @ D ) @ ( 'const/realax/real_pow' @ B @ ( 'const/arith/-' @ ( 'const/arith/-' @ C @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ D ) ) ) ) ) )
| ~ ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ C ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(40,plain,
! [D: 'type/nums/num',C: 'type/realax/real',B: 'type/realax/real',A: 'type/nums/num'] :
( ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ B @ D ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ B @ C )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ B @ E ) @ ( 'const/realax/real_pow' @ C @ ( 'const/arith/-' @ ( 'const/arith/-' @ D @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ E ) ) ) ) ) )
| ~ ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ D )
| ( ( 'const/realax/real_pow' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A )
!= ( 'const/realax/real_pow' @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[16,19]) ).
thf(41,plain,
! [B: 'type/realax/real',A: 'type/nums/num'] :
( ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ B @ A ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ B @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [C: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ B @ C ) @ ( 'const/realax/real_pow' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/arith/-' @ ( 'const/arith/-' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ C ) ) ) ) ) )
| ~ ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )),bind(D,$thf( A ))]]) ).
thf(162,plain,
! [B: 'type/realax/real',A: 'type/nums/num'] :
( ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ B @ A ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ B @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [C: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ B @ C ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ~ ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ A ) ),
inference(rewrite,[status(thm)],[41,16]) ).
thf(180,plain,
! [B: 'type/realax/real',A: 'type/nums/num'] :
( ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ B @ A ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ B @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [C: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ B @ C ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ~ $true
| ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ sk2 )
!= ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8,162]) ).
thf(181,plain,
! [B: 'type/realax/real',A: 'type/nums/num'] :
( ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ B @ A ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ B @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [C: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ B @ C ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ sk2 )
!= ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ A ) ) ),
inference(simp,[status(thm)],[180]) ).
thf(182,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sk2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [B: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ A @ B ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ sk2 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ),
inference(pattern_uni,[status(thm)],[181:[bind(A,$thf( sk2 ))]]) ).
thf(227,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sk2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [B: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ A @ B ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ sk2 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ),
inference(simp,[status(thm)],[182]) ).
thf(3,axiom,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realarith/REAL_MUL_RID_') ).
thf(11,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= A ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= A ),
inference(lifteq,[status(thm)],[12]) ).
thf(229,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sk2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ A ) ) )
= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ sk2 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ),
inference(rewrite,[status(thm)],[227,13]) ).
thf(230,plain,
( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ sk1 @ sk2 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ sk1 @ sk2 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ),
inference(rewrite,[status(thm)],[10,229]) ).
thf(231,plain,
$false,
inference(simp,[status(thm)],[230]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA118^1 : 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
% 0.08/0.19 % Computer : n026.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 17:45:12 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 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 ...
% 1.24/1.00 % [INFO] Parsing done (214ms).
% 1.24/1.02 % [INFO] Running in sequential loop mode.
% 2.13/1.43 % [INFO] eprover registered as external prover.
% 2.13/1.44 % [INFO] Scanning for conjecture ...
% 2.33/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.33/1.59 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.52/1.60 % [INFO] Problem is higher-order (TPTP THF).
% 2.52/1.61 % [INFO] Type checking passed.
% 2.52/1.61 % [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 ...
% 12.12/4.06 % [INFO] Killing All external provers ...
% 12.12/4.07 % Time passed: 3729ms (effective reasoning time: 3044ms)
% 12.12/4.07 % 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)>
% 12.12/4.07 % Axioms used in derivation (3): thm/real/REAL_POW_ONE_, thm/iterate/REAL_SUB_POW_, thm/realarith/REAL_MUL_RID_
% 12.12/4.07 % No. of inferences in proof: 29
% 12.12/4.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3729 ms resp. 3044 ms w/o parsing
% 12.57/4.14 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.57/4.14 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------