TSTP Solution File: ANA118^1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ANA118^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:27:55 EDT 2024
% Result : Theorem 8.86s 2.60s
% Output : Refutation 8.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 42 ( 16 unt; 15 typ; 0 def)
% Number of atoms : 57 ( 27 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 623 ( 12 ~; 7 |; 0 &; 599 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 50 ( 10 ^ 39 !; 0 ?; 50 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% 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\'_type',type,
'\'const/realax/real_sub\'': '\'type/realax/real\'' > '\'type/realax/real\'' > '\'type/realax/real\'' ).
thf('\'const/realax/real_pow\'_type',type,
'\'const/realax/real_pow\'': '\'type/realax/real\'' > '\'type/nums/num\'' > '\'type/realax/real\'' ).
thf('\'const/realax/real_of_num\'_type',type,
'\'const/realax/real_of_num\'': '\'type/nums/num\'' > '\'type/realax/real\'' ).
thf('\'const/realax/real_mul\'_type',type,
'\'const/realax/real_mul\'': '\'type/realax/real\'' > '\'type/realax/real\'' > '\'type/realax/real\'' ).
thf('\'const/nums/NUMERAL\'_type',type,
'\'const/nums/NUMERAL\'': '\'type/nums/num\'' > '\'type/nums/num\'' ).
thf('\'const/nums/BIT1\'_type',type,
'\'const/nums/BIT1\'': '\'type/nums/num\'' > '\'type/nums/num\'' ).
thf('\'const/nums/_0\'_type',type,
'\'const/nums/_0\'': '\'type/nums/num\'' ).
thf('\'const/iterate/sum\'_type',type,
'\'const/iterate/sum\'':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > '\'type/realax/real\'' ) > '\'type/realax/real\'' ) ).
thf('\'const/iterate/..\'_type',type,
'\'const/iterate/..\'': '\'type/nums/num\'' > '\'type/nums/num\'' > '\'type/nums/num\'' > $o ).
thf('\'const/arith/-\'_type',type,
'\'const/arith/-\'': '\'type/nums/num\'' > '\'type/nums/num\'' > '\'type/nums/num\'' ).
thf('\'const/arith/<=\'_type',type,
'\'const/arith/<=\'': '\'type/nums/num\'' > '\'type/nums/num\'' > $o ).
thf(sk1_type,type,
sk1: '\'type/realax/real\'' ).
thf(sk2_type,type,
sk2: '\'type/nums/num\'' ).
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/sandbox2/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/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_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)],[7]) ).
thf(8,plain,
'\'const/arith/<=\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) @ sk2,
inference(cnf,[status(esa)],[6]) ).
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/sandbox2/benchmark/theBenchmark.p','thm/real/REAL_POW_ONE_') ).
thf(13,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(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(cnf,[status(esa)],[13]) ).
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(lifteq,[status(thm)],[14]) ).
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/sandbox2/benchmark/theBenchmark.p','thm/iterate/REAL_SUB_POW_') ).
thf(16,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(17,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)],[16]) ).
thf(18,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)],[17]) ).
thf(43,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)],[15,18]) ).
thf(44,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)],[43:[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(160,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)],[44,15]) ).
thf(187,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(paramod_ordered,[status(thm)],[8,160]) ).
thf(188,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)],[187:[bind(A,$thf( sk2 ))]]) ).
thf(225,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)],[188]) ).
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/sandbox2/benchmark/theBenchmark.p','thm/realarith/REAL_MUL_RID_') ).
thf(10,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(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(cnf,[status(esa)],[10]) ).
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(lifteq,[status(thm)],[11]) ).
thf(226,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)],[225,12]) ).
thf(227,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)],[9,226]) ).
thf(228,plain,
$false,
inference(simp,[status(thm)],[227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : ANA118^1 : TPTP v8.1.2. Released v7.0.0.
% 0.14/0.17 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n024.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Mon May 6 12:44:24 EDT 2024
% 0.17/0.38 % CPUTime :
% 0.97/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/0.99 % [INFO] Parsing done (113ms).
% 1.31/1.00 % [INFO] Running in sequential loop mode.
% 1.73/1.20 % [INFO] eprover registered as external prover.
% 1.73/1.20 % [INFO] cvc4 registered as external prover.
% 1.73/1.21 % [INFO] Scanning for conjecture ...
% 1.98/1.26 % [INFO] Found a conjecture and 3 axioms. Running axiom selection ...
% 1.98/1.29 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.98/1.30 % [INFO] Problem is higher-order (TPTP THF).
% 1.98/1.30 % [INFO] Type checking passed.
% 1.98/1.30 % [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 ...
% 8.86/2.60 % [INFO] Killing All external provers ...
% 8.86/2.60 % Time passed: 2055ms (effective reasoning time: 1598ms)
% 8.86/2.60 % 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)>
% 8.86/2.60 % Axioms used in derivation (3): thm/real/REAL_POW_ONE_, thm/iterate/REAL_SUB_POW_, thm/realarith/REAL_MUL_RID_
% 8.86/2.60 % No. of inferences in proof: 27
% 8.86/2.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2055 ms resp. 1598 ms w/o parsing
% 8.86/2.64 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.86/2.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------