%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA119^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 : Wed Feb 25 08:38:55 AM UTC 2026
% Result : Theorem 1.56s 1.27s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 85 ( 37 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 650 ( 14 ~; 4 |; 4 &; 620 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 53 ( 14 ^; 35 !; 4 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(type_def_7,type,
'type/nums/num': $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'type/nums/num': $tType ).
thf(func_def_2,type,
'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_3,type,
'const/realax/real_pow': 'type/realax/real' > 'type/nums/num' > 'type/realax/real' ).
thf(func_def_4,type,
'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
thf(func_def_5,type,
'const/realax/real_neg': 'type/realax/real' > 'type/realax/real' ).
thf(func_def_6,type,
'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_7,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_8,type,
'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_9,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_10,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_11,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_12,type,
'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_13,type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_15,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_20,type,
sK0: 'type/realax/real' ).
thf(func_def_21,type,
sK1: 'type/nums/num' ).
thf(func_def_23,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f44,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
( ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ sK0 @ sK1 ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ sK0 @ sK1 ) ) ),
inference(superposition,[status(thm)],[f21,f30]) ).
thf(f30,plain,
! [X0: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ X0 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sK1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ X0 ) ) )
= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ X0 @ sK1 ) ) ),
inference(forward_demodulation,[status(thm)],[f28,f18]) ).
thf(f18,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_sub' @ X0 @ X1 ) )
= ( 'const/realax/real_sub' @ X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_sub' @ X0 @ X1 ) )
= ( 'const/realax/real_sub' @ X1 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.QrpXl7JjAY/DTF2THF_18358.p','thm/realarith/REAL_NEG_SUB_') ).
thf(f28,plain,
! [X0: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ X0 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sK1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ X0 ) ) )
= ( 'const/realax/real_neg' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ sK1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ),
inference(superposition,[status(thm)],[f22,f26]) ).
thf(f26,plain,
! [X0: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ ( '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/-' @ sK1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ X0 ) ) )
= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ sK1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ ( '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/-' @ sK1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ X0 ) ) )
= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ sK1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f20,f15]) ).
thf(f15,plain,
( $true
= ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ sK0 )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sK1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_pow' @ sK0 @ Y0 ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ sK0 @ sK1 ) ) )
& ( $true
= ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f11,f13]) ).
thf(f13,plain,
( ? [X0: 'type/realax/real',X1: 'type/nums/num'] :
( ( ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ X0 @ X1 ) )
!= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ X0 )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_pow' @ X0 @ Y0 ) ) ) )
& ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X1 )
= $true ) )
=> ( ( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ sK0 )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sK1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_pow' @ sK0 @ Y0 ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ sK0 @ sK1 ) ) )
& ( $true
= ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
? [X0: 'type/realax/real',X1: 'type/nums/num'] :
( ( ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ X0 @ X1 ) )
!= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ X0 )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_pow' @ X0 @ Y0 ) ) ) )
& ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: 'type/realax/real',X1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X1 )
= $true )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ X0 @ X1 ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ X0 )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_pow' @ X0 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: 'type/realax/real',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X1 )
=> ( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ X0 )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [X2: 'type/nums/num'] : ( 'const/realax/real_pow' @ X0 @ X2 ) ) )
= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X0: 'type/realax/real',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X1 )
=> ( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ X0 )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [X2: 'type/nums/num'] : ( 'const/realax/real_pow' @ X0 @ X2 ) ) )
= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [X0: 'type/realax/real',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X1 )
=> ( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ X0 )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [X2: 'type/nums/num'] : ( 'const/realax/real_pow' @ X0 @ X2 ) ) )
= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QrpXl7JjAY/DTF2THF_18358.p','thm/iterate/REAL_SUB_POW_L1_') ).
thf(f20,plain,
! [X0: 'type/realax/real',X1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X1 )
!= $true )
| ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ X1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ ( '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/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ X0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: 'type/realax/real',X1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X1 )
!= $true )
| ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ X1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ ( '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/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_pow' @ X0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: 'type/realax/real',X1: 'type/nums/num'] :
( ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ X1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ ( '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/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_pow' @ X0 @ Y0 ) ) ) )
| ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: 'type/realax/real',X1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X1 )
= $true )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ X1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ ( '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/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_pow' @ X0 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: 'type/realax/real',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X1 )
=> ( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ ( '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/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [X2: 'type/nums/num'] : ( 'const/realax/real_pow' @ X0 @ X2 ) ) )
= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ X1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: 'type/realax/real',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X1 )
=> ( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ ( '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/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [X2: 'type/nums/num'] : ( 'const/realax/real_pow' @ X0 @ X2 ) ) )
= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ X1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QrpXl7JjAY/DTF2THF_18358.p','thm/iterate/REAL_SUB_POW_R1_') ).
thf(f22,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X1 @ X0 ) @ X2 )
= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ X1 ) @ X2 ) ) ),
inference(superposition,[status(thm)],[f19,f18]) ).
thf(f19,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ X0 ) @ X1 )
= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ X0 ) @ X1 )
= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QrpXl7JjAY/DTF2THF_18358.p','thm/calc_int/REAL_MUL_LNEG_') ).
thf(f21,plain,
( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ sK0 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sK1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ sK0 ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ sK0 @ sK1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ sK0 )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sK1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_pow' @ sK0 @ Y0 ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA119^1 : TPTP v9.2.1. Released v7.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n005.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 03:51:14 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : ANA119^1 : TPTP v9.2.1. Released v7.0.0.
% 0.30/0.46 % Domain : Analysis
% 0.30/0.46 % Problem : REAL_SUB_POW_L1
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Kal16]
% 0.30/0.46 % Names : REAL_SUB_POW_L1_.p [Kal16]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v7.1.0
% 0.30/0.46 % Syntax : Number of formulae : 18 ( 2 unt; 14 typ; 0 def)
% 0.30/0.46 % Number of atoms : 8 ( 4 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.30/0.46 % Number of connectives : 73 ( 0 ~; 0 |; 0 &; 71 @)
% 0.30/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 8 ( 6 avg)
% 0.30/0.46 % Number of types : 3 ( 2 usr)
% 0.30/0.46 % Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 13 ( 12 usr; 1 con; 0-3 aty)
% 0.30/0.46 % Number of variables : 11 ( 2 ^; 8 !; 0 ?; 11 :)
% 0.30/0.46 % ( 1 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.46 % SPC : TH1_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : Exported from core HOL Light.
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf('thf_type_type/realax/real',type,
% 0.30/0.46 'type/realax/real': $tType ).
% 0.30/0.46
% 0.30/0.46 thf('thf_type_type/nums/num',type,
% 0.30/0.46 'type/nums/num': $tType ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/realax/real_sub',type,
% 0.30/0.46 'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/realax/real_pow',type,
% 0.30/0.46 'const/realax/real_pow': 'type/realax/real' > 'type/nums/num' > 'type/realax/real' ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/realax/real_of_num',type,
% 0.30/0.46 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/realax/real_neg',type,
% 0.30/0.46 'const/realax/real_neg': 'type/realax/real' > 'type/realax/real' ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/realax/real_mul',type,
% 0.30/0.46 'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/nums/NUMERAL',type,
% 0.30/0.46 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/nums/BIT1',type,
% 0.30/0.46 'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/nums/_0',type,
% 0.30/0.46 'const/nums/_0': 'type/nums/num' ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/iterate/sum',type,
% 0.30/0.46 'const/iterate/sum':
% 0.30/0.46 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/iterate/..',type,
% 0.30/0.46 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/arith/-',type,
% 0.30/0.46 'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/arith/<=',type,
% 0.30/0.46 'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
% 0.30/0.46
% 0.30/0.46 thf('thm/calc_int/REAL_MUL_LNEG_',axiom,
% 0.30/0.46 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 0.30/0.46 ( ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ A ) @ A0 )
% 0.30/0.46 = ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ A @ A0 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf('thm/iterate/REAL_SUB_POW_R1_',axiom,
% 0.30/0.46 ! [A: 'type/realax/real',A0: 'type/nums/num'] :
% 0.30/0.46 ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ A0 )
% 0.30/0.46 => ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ A0 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
% 0.30/0.46 = ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
% 0.30/0.46 @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ A0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
% 0.30/0.46 @ ^ [A1: 'type/nums/num'] : ( 'const/realax/real_pow' @ A @ A1 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf('thm/realarith/REAL_NEG_SUB_',axiom,
% 0.30/0.46 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 0.30/0.46 ( ( 'const/realax/real_neg' @ ( 'const/realax/real_sub' @ A @ A0 ) )
% 0.30/0.46 = ( 'const/realax/real_sub' @ A0 @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf('thm/iterate/REAL_SUB_POW_L1_',conjecture,
% 0.30/0.46 ! [A: 'type/realax/real',A0: 'type/nums/num'] :
% 0.30/0.46 ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ A0 )
% 0.30/0.46 => ( ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ A @ A0 ) )
% 0.30/0.46 = ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A )
% 0.30/0.46 @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ A0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
% 0.30/0.46 @ ^ [A1: 'type/nums/num'] : ( 'const/realax/real_pow' @ A @ A1 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.56/1.23 ---- Embedded in THF ---
% 1.56/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.56/1.23 %%% Generated on Tue Feb 24 03:51:15 EST 2026
% 1.56/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.56/1.23 %%% Logic specification used:
% 1.56/1.23 %%% thf(spec, logic, $$dhol).
% 1.56/1.23
% 1.56/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.QrpXl7JjAY/DTF2DTF18358.p
% See solution above
% 1.56/1.23 ------------------------
% 1.56/1.24 ---- Cleaned THF ---
% 1.56/1.24 thf('thf_type_type/realax/real',type,
% 1.56/1.24 'type/realax/real': $tType ).
% 1.56/1.24
% 1.56/1.24 thf('thf_type_type/nums/num',type,
% 1.56/1.24 'type/nums/num': $tType ).
% 1.56/1.24
% 1.56/1.24 thf('thf_const_const/realax/real_sub',type,
% 1.56/1.24 'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 1.56/1.24
% 1.56/1.24 thf('thf_const_const/realax/real_pow',type,
% 1.56/1.24 'const/realax/real_pow': 'type/realax/real' > 'type/nums/num' > 'type/realax/real' ).
% 1.56/1.24
% 1.56/1.24 thf('thf_const_const/realax/real_of_num',type,
% 1.56/1.24 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
% 1.56/1.24
% 1.56/1.24 thf('thf_const_const/realax/real_neg',type,
% 1.56/1.24 'const/realax/real_neg': 'type/realax/real' > 'type/realax/real' ).
% 1.56/1.24
% 1.56/1.24 thf('thf_const_const/realax/real_mul',type,
% 1.56/1.24 'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 1.56/1.24
% 1.56/1.24 thf('thf_const_const/nums/NUMERAL',type,
% 1.56/1.24 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 1.56/1.24
% 1.56/1.24 thf('thf_const_const/nums/BIT1',type,
% 1.56/1.24 'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
% 1.56/1.24
% 1.56/1.24 thf('thf_const_const/nums/_0',type,
% 1.56/1.24 'const/nums/_0': 'type/nums/num' ).
% 1.56/1.24
% 1.56/1.24 thf('thf_const_const/iterate/sum',type,
% 1.56/1.24 'const/iterate/sum':
% 1.56/1.24 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 1.56/1.24
% 1.56/1.24 thf('thf_const_const/iterate/..',type,
% 1.56/1.24 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
% 1.56/1.24
% 1.56/1.24 thf('thf_const_const/arith/-',type,
% 1.56/1.24 'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
% 1.56/1.24
% 1.56/1.24 thf('thf_const_const/arith/<=',type,
% 1.56/1.24 'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
% 1.56/1.24
% 1.56/1.24 thf('thm/calc_int/REAL_MUL_LNEG_',axiom,
% 1.56/1.24 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 1.56/1.24 ( ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ A ) @ A0 )
% 1.56/1.24 = ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ A @ A0 ) ) ) ).
% 1.56/1.24
% 1.56/1.24 thf('thm/iterate/REAL_SUB_POW_R1_',axiom,
% 1.56/1.24 ! [A: 'type/realax/real',A0: 'type/nums/num'] :
% 1.56/1.24 ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ A0 )
% 1.56/1.24 => ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ A0 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
% 1.56/1.24 = ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
% 1.56/1.24 @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ A0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
% 1.56/1.24 @ ^ [A1: 'type/nums/num'] : ( 'const/realax/real_pow' @ A @ A1 ) ) ) ) ) ).
% 1.56/1.24
% 1.56/1.24 thf('thm/realarith/REAL_NEG_SUB_',axiom,
% 1.56/1.24 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 1.56/1.24 ( ( 'const/realax/real_neg' @ ( 'const/realax/real_sub' @ A @ A0 ) )
% 1.56/1.24 = ( 'const/realax/real_sub' @ A0 @ A ) ) ).
% 1.56/1.24
% 1.56/1.24 thf('thm/iterate/REAL_SUB_POW_L1_',conjecture,
% 1.56/1.24 ! [A: 'type/realax/real',A0: 'type/nums/num'] :
% 1.56/1.24 ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ A0 )
% 1.56/1.24 => ( ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ A @ A0 ) )
% 1.56/1.24 = ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A )
% 1.56/1.24 @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ A0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
% 1.56/1.24 @ ^ [A1: 'type/nums/num'] : ( 'const/realax/real_pow' @ A @ A1 ) ) ) ) ) ).
% 1.56/1.24 ------------------------
% 1.56/1.26 % (18458)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18358 for (2999ds/2Mi)
% 1.56/1.26 % (18458)Instruction limit reached!
% 1.56/1.26 % (18458)------------------------------
% 1.56/1.26 % (18458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.26 % (18458)Termination reason: Unknown
% 1.56/1.26 % (18458)Termination phase: Preprocessing 3
% 1.56/1.26
% 1.56/1.26 % (18458)Memory used [KB]: 895
% 1.56/1.26 % (18458)Time elapsed: 0.002 s
% 1.56/1.26 % (18458)Instructions burned: 2 (million)
% 1.56/1.26 % (18458)------------------------------
% 1.56/1.26 % (18458)------------------------------
% 1.56/1.26 % (18457)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_18358 for (2999ds/27Mi)
% 1.56/1.26 % (18457)First to succeed.
% 1.56/1.26 % (18455)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18358 for (2999ds/183Mi)
% 1.56/1.26 % (18456)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_18358 for (2999ds/4Mi)
% 1.56/1.26 % (18459)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_18358 for (2999ds/2Mi)
% 1.56/1.26 % (18460)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_18358 for (2999ds/275Mi)
% 1.56/1.26 % (18461)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18358 for (2999ds/18Mi)
% 1.56/1.27 % (18459)Instruction limit reached!
% 1.56/1.27 % (18459)------------------------------
% 1.56/1.27 % (18459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.27 % (18459)Termination reason: Unknown
% 1.56/1.27 % (18459)Termination phase: Property scanning
% 1.56/1.27
% 1.56/1.27 % (18459)Memory used [KB]: 895
% 1.56/1.27 % (18459)Time elapsed: 0.003 s
% 1.56/1.27 % (18459)Instructions burned: 2 (million)
% 1.56/1.27 % (18459)------------------------------
% 1.56/1.27 % (18459)------------------------------
% 1.56/1.27 % (18457)Refutation found. Thanks to Tanya!
% 1.56/1.27 % SZS status Theorem for DTF2THF_18358
% 1.56/1.27 % SZS output start Proof for DTF2THF_18358
% 1.56/1.27 thf(type_def_5, type, 'type/realax/real': $tType).
% 1.56/1.27 thf(type_def_7, type, 'type/nums/num': $tType).
% 1.56/1.27 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.56/1.27 thf(func_def_1, type, 'type/nums/num': $tType).
% 1.56/1.27 thf(func_def_2, type, 'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > 'type/realax/real').
% 1.56/1.27 thf(func_def_3, type, 'const/realax/real_pow': 'type/realax/real' > 'type/nums/num' > 'type/realax/real').
% 1.56/1.27 thf(func_def_4, type, 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real').
% 1.56/1.27 thf(func_def_5, type, 'const/realax/real_neg': 'type/realax/real' > 'type/realax/real').
% 1.56/1.27 thf(func_def_6, type, 'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real').
% 1.56/1.27 thf(func_def_7, type, 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num').
% 1.56/1.27 thf(func_def_8, type, 'const/nums/BIT1': 'type/nums/num' > 'type/nums/num').
% 1.56/1.27 thf(func_def_9, type, 'const/nums/_0': 'type/nums/num').
% 1.56/1.27 thf(func_def_10, type, 'const/iterate/sum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real')).
% 1.56/1.27 thf(func_def_11, type, 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o).
% 1.56/1.27 thf(func_def_12, type, 'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num').
% 1.56/1.27 thf(func_def_13, type, 'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o).
% 1.56/1.27 thf(func_def_15, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.56/1.27 thf(func_def_20, type, sK0: 'type/realax/real').
% 1.56/1.27 thf(func_def_21, type, sK1: 'type/nums/num').
% 1.56/1.27 thf(func_def_23, type, ph3: !>[X0: $tType]:(X0)).
% 1.56/1.27 thf(f44,plain,(
% 1.56/1.27 $false),
% 1.56/1.27 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.56/1.27 thf(f38,plain,(
% 1.56/1.27 (('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ ('const/realax/real_pow' @ sK0 @ sK1)) != ('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ ('const/realax/real_pow' @ sK0 @ sK1)))),
% 1.56/1.27 inference(superposition,[status(thm)],[f21,f30])).
% 1.56/1.27 thf(f30,plain,(
% 1.56/1.27 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_mul' @ ('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ X0) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ sK1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ ('const/realax/real_pow' @ X0))) = ('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ ('const/realax/real_pow' @ X0 @ sK1)))) )),
% 1.56/1.27 inference(forward_demodulation,[status(thm)],[f28,f18])).
% 1.56/1.27 thf(f18,plain,(
% 1.56/1.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_neg' @ ('const/realax/real_sub' @ X0 @ X1)) = ('const/realax/real_sub' @ X1 @ X0))) )),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f3])).
% 1.56/1.27 thf(f3,axiom,(
% 1.56/1.27 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_neg' @ ('const/realax/real_sub' @ X0 @ X1)) = ('const/realax/real_sub' @ X1 @ X0))),
% 1.56/1.27 file('/export/starexec/sandbox/tmp/tmp.QrpXl7JjAY/DTF2THF_18358.p','thm/realarith/REAL_NEG_SUB_')).
% 1.56/1.27 thf(f28,plain,(
% 1.56/1.27 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_mul' @ ('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ X0) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ sK1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ ('const/realax/real_pow' @ X0))) = ('const/realax/real_neg' @ ('const/realax/real_sub' @ ('const/realax/real_pow' @ X0 @ sK1) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))))) )),
% 1.56/1.27 inference(superposition,[status(thm)],[f22,f26])).
% 1.56/1.27 thf(f26,plain,(
% 1.56/1.27 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_mul' @ ('const/realax/real_sub' @ X0 @ ('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/-' @ sK1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ ('const/realax/real_pow' @ X0))) = ('const/realax/real_sub' @ ('const/realax/real_pow' @ X0 @ sK1) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))) )),
% 1.56/1.27 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.56/1.27 thf(f25,plain,(
% 1.56/1.27 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_mul' @ ('const/realax/real_sub' @ X0 @ ('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/-' @ sK1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ ('const/realax/real_pow' @ X0))) = ('const/realax/real_sub' @ ('const/realax/real_pow' @ X0 @ sK1) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) | ($true != $true)) )),
% 1.56/1.27 inference(superposition,[status(thm)],[f20,f15])).
% 1.56/1.27 thf(f15,plain,(
% 1.56/1.27 ($true = ('const/arith/<=' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')) @ sK1))),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f14])).
% 1.56/1.27 thf(f14,plain,(
% 1.56/1.27 (('const/realax/real_mul' @ ('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ sK0) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ sK1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_pow' @ sK0 @ Y0)))) != ('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ ('const/realax/real_pow' @ sK0 @ sK1))) & ($true = ('const/arith/<=' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')) @ sK1))),
% 1.56/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f11,f13])).
% 1.56/1.27 thf(f13,plain,(
% 1.56/1.27 ? [X0 : 'type/realax/real',X1 : 'type/nums/num'] : ((('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ ('const/realax/real_pow' @ X0 @ X1)) != ('const/realax/real_mul' @ ('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ X0) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ X1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_pow' @ X0 @ Y0))))) & (('const/arith/<=' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')) @ X1) = $true)) => ((('const/realax/real_mul' @ ('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ sK0) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ sK1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_pow' @ sK0 @ Y0)))) != ('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ ('const/realax/real_pow' @ sK0 @ sK1))) & ($true = ('const/arith/<=' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')) @ sK1)))),
% 1.56/1.27 introduced(definition,[],[choice_axiom])).
% 1.56/1.27 thf(f11,plain,(
% 1.56/1.27 ? [X0 : 'type/realax/real',X1 : 'type/nums/num'] : ((('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ ('const/realax/real_pow' @ X0 @ X1)) != ('const/realax/real_mul' @ ('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ X0) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ X1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_pow' @ X0 @ Y0))))) & (('const/arith/<=' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')) @ X1) = $true))),
% 1.56/1.27 inference(ennf_transformation,[status(thm)],[f8])).
% 1.56/1.27 thf(f8,plain,(
% 1.56/1.27 ~! [X0 : 'type/realax/real',X1 : 'type/nums/num'] : ((('const/arith/<=' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')) @ X1) = $true) => (('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ ('const/realax/real_pow' @ X0 @ X1)) = ('const/realax/real_mul' @ ('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ X0) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ X1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_pow' @ X0 @ Y0))))))),
% 1.56/1.27 inference(fool_elimination,[status(thm)],[f7])).
% 1.56/1.27 thf(f7,plain,(
% 1.56/1.27 ~! [X0 : 'type/realax/real',X1 : 'type/nums/num'] : (('const/arith/<=' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')) @ X1) => (('const/realax/real_mul' @ ('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ X0) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ X1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ (^[X2 : 'type/nums/num'] : ('const/realax/real_pow' @ X0 @ X2)))) = ('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ ('const/realax/real_pow' @ X0 @ X1))))),
% 1.56/1.27 inference(rectify,[status(thm)],[f5])).
% 1.56/1.27 thf(f5,negated_conjecture,(
% 1.56/1.27 ~! [X0 : 'type/realax/real',X1 : 'type/nums/num'] : (('const/arith/<=' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')) @ X1) => (('const/realax/real_mul' @ ('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ X0) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ X1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ (^[X2 : 'type/nums/num'] : ('const/realax/real_pow' @ X0 @ X2)))) = ('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ ('const/realax/real_pow' @ X0 @ X1))))),
% 1.56/1.27 inference(negated_conjecture,[status(cth)],[f4])).
% 1.56/1.27 thf(f4,conjecture,(
% 1.56/1.27 ! [X0 : 'type/realax/real',X1 : 'type/nums/num'] : (('const/arith/<=' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')) @ X1) => (('const/realax/real_mul' @ ('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ X0) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ X1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ (^[X2 : 'type/nums/num'] : ('const/realax/real_pow' @ X0 @ X2)))) = ('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ ('const/realax/real_pow' @ X0 @ X1))))),
% 1.56/1.27 file('/export/starexec/sandbox/tmp/tmp.QrpXl7JjAY/DTF2THF_18358.p','thm/iterate/REAL_SUB_POW_L1_')).
% 1.56/1.27 thf(f20,plain,(
% 1.56/1.27 ( ! [X0 : 'type/realax/real',X1 : 'type/nums/num'] : ((('const/arith/<=' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')) @ X1) != $true) | (('const/realax/real_sub' @ ('const/realax/real_pow' @ X0 @ X1) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) = ('const/realax/real_mul' @ ('const/realax/real_sub' @ X0 @ ('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/-' @ X1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ ('const/realax/real_pow' @ X0))))) )),
% 1.56/1.27 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.56/1.27 thf(f17,plain,(
% 1.56/1.27 ( ! [X0 : 'type/realax/real',X1 : 'type/nums/num'] : ((('const/arith/<=' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')) @ X1) != $true) | (('const/realax/real_sub' @ ('const/realax/real_pow' @ X0 @ X1) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) = ('const/realax/real_mul' @ ('const/realax/real_sub' @ X0 @ ('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/-' @ X1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_pow' @ X0 @ Y0)))))) )),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f12])).
% 1.56/1.27 thf(f12,plain,(
% 1.56/1.27 ! [X0 : 'type/realax/real',X1 : 'type/nums/num'] : ((('const/realax/real_sub' @ ('const/realax/real_pow' @ X0 @ X1) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) = ('const/realax/real_mul' @ ('const/realax/real_sub' @ X0 @ ('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/-' @ X1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_pow' @ X0 @ Y0))))) | (('const/arith/<=' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')) @ X1) != $true))),
% 1.56/1.27 inference(ennf_transformation,[status(thm)],[f10])).
% 1.56/1.27 thf(f10,plain,(
% 1.56/1.27 ! [X0 : 'type/realax/real',X1 : 'type/nums/num'] : ((('const/arith/<=' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')) @ X1) = $true) => (('const/realax/real_sub' @ ('const/realax/real_pow' @ X0 @ X1) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) = ('const/realax/real_mul' @ ('const/realax/real_sub' @ X0 @ ('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/-' @ X1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_pow' @ X0 @ Y0))))))),
% 1.56/1.27 inference(fool_elimination,[status(thm)],[f9])).
% 1.56/1.27 thf(f9,plain,(
% 1.56/1.27 ! [X0 : 'type/realax/real',X1 : 'type/nums/num'] : (('const/arith/<=' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')) @ X1) => (('const/realax/real_mul' @ ('const/realax/real_sub' @ X0 @ ('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/-' @ X1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ (^[X2 : 'type/nums/num'] : ('const/realax/real_pow' @ X0 @ X2)))) = ('const/realax/real_sub' @ ('const/realax/real_pow' @ X0 @ X1) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))))),
% 1.56/1.27 inference(rectify,[status(thm)],[f2])).
% 1.56/1.27 thf(f2,axiom,(
% 1.56/1.27 ! [X0 : 'type/realax/real',X1 : 'type/nums/num'] : (('const/arith/<=' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')) @ X1) => (('const/realax/real_mul' @ ('const/realax/real_sub' @ X0 @ ('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/-' @ X1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ (^[X2 : 'type/nums/num'] : ('const/realax/real_pow' @ X0 @ X2)))) = ('const/realax/real_sub' @ ('const/realax/real_pow' @ X0 @ X1) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))))),
% 1.56/1.27 file('/export/starexec/sandbox/tmp/tmp.QrpXl7JjAY/DTF2THF_18358.p','thm/iterate/REAL_SUB_POW_R1_')).
% 1.56/1.27 thf(f22,plain,(
% 1.56/1.27 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_mul' @ ('const/realax/real_sub' @ X1 @ X0) @ X2) = ('const/realax/real_neg' @ ('const/realax/real_mul' @ ('const/realax/real_sub' @ X0 @ X1) @ X2)))) )),
% 1.56/1.27 inference(superposition,[status(thm)],[f19,f18])).
% 1.56/1.27 thf(f19,plain,(
% 1.56/1.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_mul' @ ('const/realax/real_neg' @ X0) @ X1) = ('const/realax/real_neg' @ ('const/realax/real_mul' @ X0 @ X1)))) )),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f1])).
% 1.56/1.27 thf(f1,axiom,(
% 1.56/1.27 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_mul' @ ('const/realax/real_neg' @ X0) @ X1) = ('const/realax/real_neg' @ ('const/realax/real_mul' @ X0 @ X1)))),
% 1.56/1.27 file('/export/starexec/sandbox/tmp/tmp.QrpXl7JjAY/DTF2THF_18358.p','thm/calc_int/REAL_MUL_LNEG_')).
% 1.56/1.27 thf(f21,plain,(
% 1.56/1.27 (('const/realax/real_mul' @ ('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ sK0) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ sK1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ ('const/realax/real_pow' @ sK0))) != ('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ ('const/realax/real_pow' @ sK0 @ sK1)))),
% 1.56/1.27 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.56/1.27 thf(f16,plain,(
% 1.56/1.27 (('const/realax/real_mul' @ ('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ sK0) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ sK1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_pow' @ sK0 @ Y0)))) != ('const/realax/real_sub' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ ('const/realax/real_pow' @ sK0 @ sK1)))),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f14])).
% 1.56/1.27 % SZS output end Proof for DTF2THF_18358
% 1.56/1.27 % (18457)------------------------------
% 1.56/1.27 % (18457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.27 % (18457)Termination reason: Refutation
% 1.56/1.27
% 1.56/1.27 % (18457)Memory used [KB]: 5628
% 1.56/1.27 % (18457)Time elapsed: 0.009 s
% 1.56/1.27 % (18457)Instructions burned: 19 (million)
% 1.56/1.27 % (18457)------------------------------
% 1.56/1.27 % (18457)------------------------------
% 1.56/1.27 % (18454)Success in time 0.019 s
%------------------------------------------------------------------------------