%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA118^1 : 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 : n015.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 1.77s 1.49s
% Output : Refutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 99 ( 56 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 903 ( 37 ~; 20 |; 4 &; 834 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 62 ( 18 ^; 40 !; 4 ?; 62 :)
% 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_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_6,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_7,type,
'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_8,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_9,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_10,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_11,type,
'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_12,type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_18,type,
sK0: 'type/realax/real' ).
thf(func_def_19,type,
sK1: 'type/nums/num' ).
thf(func_def_21,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
sK4: 'type/realax/real' > 'type/realax/real' > 'type/nums/num' ).
thf(f42,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f41,f15]) ).
thf(f15,plain,
! [X0: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ X0 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= X0 ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ X0 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= X0 ),
file('/export/starexec/sandbox/tmp/tmp.0FPpoGFYUw/DTF2THF_23538.p','thm/realarith/REAL_MUL_RID_') ).
thf(f41,plain,
( ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ sK0 @ ( sK4 @ sK0 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( 'const/realax/real_pow' @ sK0 @ ( sK4 @ sK0 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ sK0 @ ( sK4 @ sK0 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( 'const/realax/real_pow' @ sK0 @ ( sK4 @ sK0 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( sK0 != sK0 ) ),
inference(equality_resolution,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ sK1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ sK0 @ sK1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( 'const/realax/real_pow' @ sK0 @ ( sK4 @ X0 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ X0 @ ( sK4 @ X0 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( sK0 != X0 ) ),
inference(forward_demodulation,[status(thm)],[f28,f18]) ).
thf(f18,plain,
! [X0: 'type/nums/num'] :
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
= ( 'const/realax/real_pow' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: 'type/nums/num'] :
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
= ( 'const/realax/real_pow' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.0FPpoGFYUw/DTF2THF_23538.p','thm/real/REAL_POW_ONE_') ).
thf(f28,plain,
! [X0: 'type/realax/real'] :
( ( sK0 != X0 )
| ( ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ X0 @ ( sK4 @ X0 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) @ ( 'const/realax/real_pow' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/arith/-' @ ( 'const/arith/-' @ sK1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( sK4 @ X0 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
!= ( 'const/realax/real_pow' @ sK0 @ ( sK4 @ X0 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ sK1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ sK0 @ sK1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: 'type/realax/real'] :
( ( sK0 != X0 )
| ( ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ X0 @ ( sK4 @ X0 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) @ ( 'const/realax/real_pow' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/arith/-' @ ( 'const/arith/-' @ sK1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( sK4 @ X0 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
!= ( 'const/realax/real_pow' @ sK0 @ ( sK4 @ X0 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ sK1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ sK0 @ sK1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
!= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ),
inference(superposition,[status(thm)],[f25,f18]) ).
thf(f25,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X1 @ sK1 ) @ ( 'const/realax/real_pow' @ X0 @ sK1 ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ sK0 @ sK1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( sK0 != X1 )
| ( ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ X1 @ ( sK4 @ X1 @ X0 ) ) @ ( 'const/realax/real_pow' @ X0 @ ( 'const/arith/-' @ ( 'const/arith/-' @ sK1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( sK4 @ X1 @ X0 ) ) ) )
!= ( 'const/realax/real_pow' @ sK0 @ ( sK4 @ X1 @ X0 ) ) )
| ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
!= X0 ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ X1 @ Y0 ) @ ( 'const/realax/real_pow' @ X0 @ ( 'const/arith/-' @ ( 'const/arith/-' @ sK1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ Y0 ) ) )
@ ( sK4 @ X1 @ X0 ) )
!= ( 'const/realax/real_pow' @ sK0 @ ( sK4 @ X1 @ X0 ) ) )
| ( sK0 != X1 )
| ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
!= X0 )
| ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X1 @ sK1 ) @ ( 'const/realax/real_pow' @ X0 @ sK1 ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ sK0 @ sK1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ),
inference(negative_extensionality,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_pow' @ sK0 )
!= ( ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ X1 @ Y0 ) @ ( 'const/realax/real_pow' @ X0 @ ( 'const/arith/-' @ ( 'const/arith/-' @ sK1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ Y0 ) ) ) ) )
| ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X1 @ sK1 ) @ ( 'const/realax/real_pow' @ X0 @ sK1 ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ sK0 @ sK1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
!= X0 )
| ( sK0 != X1 ) ),
inference(constrained_superposition,[status(thm)],[f20,f22]) ).
thf(f22,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ X1 )
@ ( '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_mul' @ ( 'const/realax/real_pow' @ X0 @ Y0 ) @ ( 'const/realax/real_pow' @ X1 @ ( 'const/arith/-' @ ( 'const/arith/-' @ sK1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ Y0 ) ) ) ) )
= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ sK1 ) @ ( 'const/realax/real_pow' @ X1 @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ X1 )
@ ( '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_mul' @ ( 'const/realax/real_pow' @ X0 @ Y0 ) @ ( 'const/realax/real_pow' @ X1 @ ( 'const/arith/-' @ ( 'const/arith/-' @ sK1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ Y0 ) ) ) ) )
= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ sK1 ) @ ( 'const/realax/real_pow' @ X1 @ sK1 ) ) ) ),
inference(superposition,[status(thm)],[f19,f16]) ).
thf(f16,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' @ sK0 @ ( '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' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_pow' @ sK0 @ Y0 ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ sK0 @ sK1 ) @ ( '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' ) ) @ sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f13]) ).
thf(f13,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 ) )
=> ( ( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ sK0 @ ( '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' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_pow' @ sK0 @ Y0 ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ sK0 @ sK1 ) @ ( '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' ) ) @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
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)],[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' @ 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(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' @ 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.0FPpoGFYUw/DTF2THF_23538.p','thm/iterate/REAL_SUB_POW_R1_') ).
thf(f19,plain,
! [X2: 'type/nums/num',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X2 )
!= $true )
| ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ X2 ) @ ( 'const/realax/real_pow' @ X1 @ X2 ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ X1 )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ X0 @ Y0 ) @ ( 'const/realax/real_pow' @ X1 @ ( 'const/arith/-' @ ( 'const/arith/-' @ X2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X2 )
!= $true )
| ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ X2 ) @ ( 'const/realax/real_pow' @ X1 @ X2 ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ X1 )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ X0 @ Y0 ) @ ( 'const/realax/real_pow' @ X1 @ ( 'const/arith/-' @ ( 'const/arith/-' @ X2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ Y0 ) ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X2 )
= $true )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ X2 ) @ ( 'const/realax/real_pow' @ X1 @ X2 ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ X1 )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ X0 @ Y0 ) @ ( 'const/realax/real_pow' @ X1 @ ( 'const/arith/-' @ ( 'const/arith/-' @ X2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X2 )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ X2 ) @ ( 'const/realax/real_pow' @ X1 @ X2 ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ X1 )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [X3: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ X0 @ X3 ) @ ( 'const/realax/real_pow' @ X1 @ ( 'const/arith/-' @ ( 'const/arith/-' @ X2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X2 )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ X2 ) @ ( 'const/realax/real_pow' @ X1 @ X2 ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ X1 )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [X3: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ X0 @ X3 ) @ ( 'const/realax/real_pow' @ X1 @ ( 'const/arith/-' @ ( 'const/arith/-' @ X2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0FPpoGFYUw/DTF2THF_23538.p','thm/iterate/REAL_SUB_POW_') ).
thf(f20,plain,
( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ sK0 @ ( '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' @ sK0 ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ sK0 @ sK1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ sK0 @ ( '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' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_pow' @ sK0 @ Y0 ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ sK0 @ sK1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ANA118^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.30 % Computer : n015.cluster.edu
% 0.13/0.30 % Model : x86_64 x86_64
% 0.13/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.30 % Memory : 8042.1875MB
% 0.13/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.30 % CPULimit : 300
% 0.13/0.30 % WCLimit : 300
% 0.13/0.30 % DateTime : Tue Feb 24 03:51:46 EST 2026
% 0.13/0.31 % CPUTime :
% 0.13/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.40 ---- Original DTF file ---
% 0.17/0.41 thf(spec,logic,$$dhol).
% 0.17/0.41 %------------------------------------------------------------------------------
% 0.17/0.41 % File : ANA118^1 : TPTP v9.2.1. Released v7.0.0.
% 0.17/0.41 % Domain : Analysis
% 0.17/0.41 % Problem : REAL_SUB_POW_R1
% 0.17/0.41 % Version : Especial.
% 0.17/0.41 % English :
% 0.17/0.41
% 0.17/0.41 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.17/0.41 % Source : [Kal16]
% 0.17/0.41 % Names : REAL_SUB_POW_R1_.p [Kal16]
% 0.17/0.41
% 0.17/0.41 % Status : Theorem
% 0.17/0.41 % Rating : 0.33 v8.1.0, 0.25 v7.5.0, 0.00 v7.1.0
% 0.17/0.41 % Syntax : Number of formulae : 17 ( 2 unt; 13 typ; 0 def)
% 0.17/0.41 % Number of atoms : 8 ( 4 equ; 0 cnn)
% 0.17/0.41 % Maximal formula atoms : 2 ( 2 avg)
% 0.17/0.41 % Number of connectives : 81 ( 0 ~; 0 |; 0 &; 79 @)
% 0.17/0.41 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.17/0.41 % Maximal formula depth : 9 ( 5 avg)
% 0.17/0.41 % Number of types : 3 ( 2 usr)
% 0.17/0.41 % Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% 0.17/0.41 % Number of symbols : 12 ( 11 usr; 1 con; 0-3 aty)
% 0.17/0.41 % Number of variables : 10 ( 2 ^; 7 !; 0 ?; 10 :)
% 0.17/0.41 % ( 1 !>; 0 ?*; 0 @-; 0 @+)
% 0.17/0.41 % SPC : TH1_THM_EQU_NAR
% 0.17/0.41
% 0.17/0.41 % Comments : Exported from core HOL Light.
% 0.17/0.41 %------------------------------------------------------------------------------
% 0.17/0.41 thf('thf_type_type/realax/real',type,
% 0.17/0.41 'type/realax/real': $tType ).
% 0.17/0.41
% 0.17/0.41 thf('thf_type_type/nums/num',type,
% 0.17/0.41 'type/nums/num': $tType ).
% 0.17/0.41
% 0.17/0.41 thf('thf_const_const/realax/real_sub',type,
% 0.17/0.41 'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 0.17/0.41
% 0.17/0.41 thf('thf_const_const/realax/real_pow',type,
% 0.17/0.41 'const/realax/real_pow': 'type/realax/real' > 'type/nums/num' > 'type/realax/real' ).
% 0.17/0.41
% 0.17/0.41 thf('thf_const_const/realax/real_of_num',type,
% 0.17/0.41 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
% 0.17/0.41
% 0.17/0.41 thf('thf_const_const/realax/real_mul',type,
% 0.17/0.41 'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 0.17/0.41
% 0.17/0.41 thf('thf_const_const/nums/NUMERAL',type,
% 0.17/0.41 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 0.17/0.41
% 0.17/0.41 thf('thf_const_const/nums/BIT1',type,
% 0.17/0.41 'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
% 0.17/0.41
% 0.17/0.41 thf('thf_const_const/nums/_0',type,
% 0.17/0.41 'const/nums/_0': 'type/nums/num' ).
% 0.17/0.41
% 0.17/0.41 thf('thf_const_const/iterate/sum',type,
% 0.17/0.41 'const/iterate/sum':
% 0.17/0.41 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 0.17/0.41
% 0.17/0.41 thf('thf_const_const/iterate/..',type,
% 0.17/0.41 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
% 0.17/0.41
% 0.17/0.41 thf('thf_const_const/arith/-',type,
% 0.17/0.41 'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
% 0.17/0.41
% 0.17/0.41 thf('thf_const_const/arith/<=',type,
% 0.17/0.41 'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
% 0.17/0.41
% 0.17/0.41 thf('thm/realarith/REAL_MUL_RID_',axiom,
% 0.17/0.41 ! [A: 'type/realax/real'] :
% 0.17/0.41 ( ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
% 0.17/0.41 = A ) ).
% 0.17/0.41
% 0.17/0.41 thf('thm/real/REAL_POW_ONE_',axiom,
% 0.17/0.41 ! [A: 'type/nums/num'] :
% 0.17/0.41 ( ( 'const/realax/real_pow' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A )
% 0.17/0.41 = ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf('thm/iterate/REAL_SUB_POW_',axiom,
% 0.17/0.41 ! [A: 'type/realax/real',A0: 'type/realax/real',A1: 'type/nums/num'] :
% 0.17/0.41 ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ A1 )
% 0.17/0.41 => ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ A1 ) @ ( 'const/realax/real_pow' @ A0 @ A1 ) )
% 0.17/0.41 = ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ A0 )
% 0.17/0.41 @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ A1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
% 0.17/0.41 @ ^ [A2: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ A @ A2 ) @ ( 'const/realax/real_pow' @ A0 @ ( 'const/arith/-' @ ( 'const/arith/-' @ A1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A2 ) ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf('thm/iterate/REAL_SUB_POW_R1_',conjecture,
% 0.17/0.41 ! [A: 'type/realax/real',A0: 'type/nums/num'] :
% 0.17/0.41 ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ A0 )
% 0.17/0.41 => ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ A0 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
% 0.17/0.41 = ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
% 0.17/0.41 @ ( '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' ) ) ) )
% 0.17/0.41 @ ^ [A1: 'type/nums/num'] : ( 'const/realax/real_pow' @ A @ A1 ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 %------------------------------------------------------------------------------
% 0.17/0.41 ------------------------
% 1.77/1.44 ---- Embedded in THF ---
% 1.77/1.44 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.77/1.44 %%% Generated on Tue Feb 24 03:51:47 EST 2026
% 1.77/1.44 %%% using '$$dhol' embedding, version 1.3.0.
% 1.77/1.44 %%% Logic specification used:
% 1.77/1.44 %%% thf(spec, logic, $$dhol).
% 1.77/1.44
% 1.77/1.44 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.0FPpoGFYUw/DTF2DTF23538.p
% See solution above
% 1.77/1.44 ------------------------
% 1.77/1.45 ---- Cleaned THF ---
% 1.77/1.45 thf('thf_type_type/realax/real',type,
% 1.77/1.45 'type/realax/real': $tType ).
% 1.77/1.45
% 1.77/1.45 thf('thf_type_type/nums/num',type,
% 1.77/1.45 'type/nums/num': $tType ).
% 1.77/1.45
% 1.77/1.45 thf('thf_const_const/realax/real_sub',type,
% 1.77/1.45 'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 1.77/1.45
% 1.77/1.45 thf('thf_const_const/realax/real_pow',type,
% 1.77/1.45 'const/realax/real_pow': 'type/realax/real' > 'type/nums/num' > 'type/realax/real' ).
% 1.77/1.45
% 1.77/1.45 thf('thf_const_const/realax/real_of_num',type,
% 1.77/1.45 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
% 1.77/1.45
% 1.77/1.45 thf('thf_const_const/realax/real_mul',type,
% 1.77/1.45 'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 1.77/1.45
% 1.77/1.45 thf('thf_const_const/nums/NUMERAL',type,
% 1.77/1.45 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 1.77/1.45
% 1.77/1.45 thf('thf_const_const/nums/BIT1',type,
% 1.77/1.45 'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
% 1.77/1.45
% 1.77/1.45 thf('thf_const_const/nums/_0',type,
% 1.77/1.45 'const/nums/_0': 'type/nums/num' ).
% 1.77/1.45
% 1.77/1.45 thf('thf_const_const/iterate/sum',type,
% 1.77/1.45 'const/iterate/sum':
% 1.77/1.45 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 1.77/1.45
% 1.77/1.45 thf('thf_const_const/iterate/..',type,
% 1.77/1.45 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
% 1.77/1.45
% 1.77/1.45 thf('thf_const_const/arith/-',type,
% 1.77/1.45 'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
% 1.77/1.45
% 1.77/1.45 thf('thf_const_const/arith/<=',type,
% 1.77/1.45 'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
% 1.77/1.45
% 1.77/1.45 thf('thm/realarith/REAL_MUL_RID_',axiom,
% 1.77/1.45 ! [A: 'type/realax/real'] :
% 1.77/1.45 ( ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
% 1.77/1.45 = A ) ).
% 1.77/1.45
% 1.77/1.45 thf('thm/real/REAL_POW_ONE_',axiom,
% 1.77/1.45 ! [A: 'type/nums/num'] :
% 1.77/1.45 ( ( 'const/realax/real_pow' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A )
% 1.77/1.45 = ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ).
% 1.77/1.45
% 1.77/1.45 thf('thm/iterate/REAL_SUB_POW_',axiom,
% 1.77/1.45 ! [A: 'type/realax/real',A0: 'type/realax/real',A1: 'type/nums/num'] :
% 1.77/1.45 ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ A1 )
% 1.77/1.45 => ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ A1 ) @ ( 'const/realax/real_pow' @ A0 @ A1 ) )
% 1.77/1.45 = ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ A0 )
% 1.77/1.45 @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ A1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
% 1.77/1.45 @ ^ [A2: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( 'const/realax/real_pow' @ A @ A2 ) @ ( 'const/realax/real_pow' @ A0 @ ( 'const/arith/-' @ ( 'const/arith/-' @ A1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A2 ) ) ) ) ) ) ) ).
% 1.77/1.45
% 1.77/1.45 thf('thm/iterate/REAL_SUB_POW_R1_',conjecture,
% 1.77/1.45 ! [A: 'type/realax/real',A0: 'type/nums/num'] :
% 1.77/1.45 ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ A0 )
% 1.77/1.45 => ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ A0 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
% 1.77/1.45 = ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
% 1.77/1.45 @ ( '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' ) ) ) )
% 1.77/1.45 @ ^ [A1: 'type/nums/num'] : ( 'const/realax/real_pow' @ A @ A1 ) ) ) ) ) ).
% 1.77/1.45 ------------------------
% 1.77/1.48 % (23636)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23538 for (2999ds/183Mi)
% 1.77/1.48 % (23639)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23538 for (2999ds/2Mi)
% 1.77/1.48 % (23637)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_23538 for (2999ds/4Mi)
% 1.77/1.48 % (23641)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_23538 for (2999ds/275Mi)
% 1.77/1.48 % (23642)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23538 for (2999ds/18Mi)
% 1.77/1.48 % (23639)Instruction limit reached!
% 1.77/1.48 % (23639)------------------------------
% 1.77/1.48 % (23639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.48 % (23639)Termination reason: Unknown
% 1.77/1.48 % (23639)Termination phase: Property scanning
% 1.77/1.48
% 1.77/1.48 % (23639)Memory used [KB]: 895
% 1.77/1.48 % (23639)Time elapsed: 0.003 s
% 1.77/1.48 % (23639)Instructions burned: 2 (million)
% 1.77/1.48 % (23639)------------------------------
% 1.77/1.48 % (23639)------------------------------
% 1.77/1.48 % (23638)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_23538 for (2999ds/27Mi)
% 1.77/1.48 % (23640)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_23538 for (2999ds/2Mi)
% 1.77/1.48 % (23637)Instruction limit reached!
% 1.77/1.48 % (23637)------------------------------
% 1.77/1.48 % (23637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.48 % (23637)Termination reason: Unknown
% 1.77/1.48 % (23637)Termination phase: Saturation
% 1.77/1.48
% 1.77/1.48 % (23637)Memory used [KB]: 5500
% 1.77/1.48 % (23637)Time elapsed: 0.005 s
% 1.77/1.48 % (23637)Instructions burned: 5 (million)
% 1.77/1.48 % (23637)------------------------------
% 1.77/1.48 % (23637)------------------------------
% 1.77/1.48 % (23641)Refutation not found, incomplete strategy
% 1.77/1.48 % (23641)------------------------------
% 1.77/1.48 % (23641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.48 % (23641)Termination reason: Refutation not found, incomplete strategy
% 1.77/1.48
% 1.77/1.48
% 1.77/1.48 % (23641)Memory used [KB]: 5500
% 1.77/1.48 % (23641)Time elapsed: 0.004 s
% 1.77/1.48 % (23641)Instructions burned: 3 (million)
% 1.77/1.48 % (23641)------------------------------
% 1.77/1.48 % (23641)------------------------------
% 1.77/1.48 % (23640)Instruction limit reached!
% 1.77/1.48 % (23640)------------------------------
% 1.77/1.48 % (23640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.48 % (23640)Termination reason: Unknown
% 1.77/1.48 % (23640)Termination phase: Property scanning
% 1.77/1.48
% 1.77/1.48 % (23640)Memory used [KB]: 895
% 1.77/1.48 % (23640)Time elapsed: 0.003 s
% 1.77/1.48 % (23640)Instructions burned: 3 (million)
% 1.77/1.48 % (23640)------------------------------
% 1.77/1.48 % (23640)------------------------------
% 1.77/1.48 % (23638)Refutation not found, incomplete strategy
% 1.77/1.48 % (23638)------------------------------
% 1.77/1.48 % (23638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.48 % (23638)Termination reason: Refutation not found, incomplete strategy
% 1.77/1.48
% 1.77/1.48
% 1.77/1.48 % (23638)Memory used [KB]: 5500
% 1.77/1.48 % (23638)Time elapsed: 0.006 s
% 1.77/1.48 % (23638)Instructions burned: 6 (million)
% 1.77/1.48 % (23638)------------------------------
% 1.77/1.48 % (23638)------------------------------
% 1.77/1.48 % (23642)First to succeed.
% 1.77/1.49 % (23642)Refutation found. Thanks to Tanya!
% 1.77/1.49 % SZS status Theorem for DTF2THF_23538
% 1.77/1.49 % SZS output start Proof for DTF2THF_23538
% 1.77/1.49 thf(type_def_5, type, 'type/realax/real': $tType).
% 1.77/1.49 thf(type_def_7, type, 'type/nums/num': $tType).
% 1.77/1.49 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.77/1.49 thf(func_def_1, type, 'type/nums/num': $tType).
% 1.77/1.49 thf(func_def_2, type, 'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > 'type/realax/real').
% 1.77/1.49 thf(func_def_3, type, 'const/realax/real_pow': 'type/realax/real' > 'type/nums/num' > 'type/realax/real').
% 1.77/1.49 thf(func_def_4, type, 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real').
% 1.77/1.49 thf(func_def_5, type, 'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real').
% 1.77/1.49 thf(func_def_6, type, 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num').
% 1.77/1.49 thf(func_def_7, type, 'const/nums/BIT1': 'type/nums/num' > 'type/nums/num').
% 1.77/1.49 thf(func_def_8, type, 'const/nums/_0': 'type/nums/num').
% 1.77/1.49 thf(func_def_9, type, 'const/iterate/sum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real')).
% 1.77/1.49 thf(func_def_10, type, 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o).
% 1.77/1.49 thf(func_def_11, type, 'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num').
% 1.77/1.49 thf(func_def_12, type, 'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o).
% 1.77/1.49 thf(func_def_18, type, sK0: 'type/realax/real').
% 1.77/1.49 thf(func_def_19, type, sK1: 'type/nums/num').
% 1.77/1.49 thf(func_def_21, type, ph3: !>[X0: $tType]:(X0)).
% 1.77/1.49 thf(func_def_22, type, sK4: 'type/realax/real' > 'type/realax/real' > 'type/nums/num').
% 1.77/1.49 thf(f42,plain,(
% 1.77/1.49 $false),
% 1.77/1.49 inference(subsumption_resolution,[status(thm)],[f41,f15])).
% 1.77/1.49 thf(f15,plain,(
% 1.77/1.49 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_mul' @ X0 @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) = X0)) )),
% 1.77/1.49 inference(cnf_transformation,[status(thm)],[f1])).
% 1.77/1.49 thf(f1,axiom,(
% 1.77/1.49 ! [X0 : 'type/realax/real'] : (('const/realax/real_mul' @ X0 @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) = X0)),
% 1.77/1.49 file('/export/starexec/sandbox/tmp/tmp.0FPpoGFYUw/DTF2THF_23538.p','thm/realarith/REAL_MUL_RID_')).
% 1.77/1.49 thf(f41,plain,(
% 1.77/1.49 (('const/realax/real_mul' @ ('const/realax/real_pow' @ sK0 @ (sK4 @ sK0 @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) != ('const/realax/real_pow' @ sK0 @ (sK4 @ sK0 @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))))),
% 1.77/1.49 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.77/1.49 thf(f40,plain,(
% 1.77/1.49 (('const/realax/real_mul' @ ('const/realax/real_pow' @ sK0 @ (sK4 @ sK0 @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) != ('const/realax/real_pow' @ sK0 @ (sK4 @ sK0 @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))) | (sK0 != sK0)),
% 1.77/1.49 inference(equality_resolution,[status(thm)],[f38])).
% 1.77/1.49 thf(f38,plain,(
% 1.77/1.49 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_sub' @ ('const/realax/real_pow' @ X0 @ sK1) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) != ('const/realax/real_sub' @ ('const/realax/real_pow' @ sK0 @ sK1) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) | (('const/realax/real_pow' @ sK0 @ (sK4 @ X0 @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) != ('const/realax/real_mul' @ ('const/realax/real_pow' @ X0 @ (sK4 @ X0 @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) | (sK0 != X0)) )),
% 1.77/1.49 inference(forward_demodulation,[status(thm)],[f28,f18])).
% 1.77/1.49 thf(f18,plain,(
% 1.77/1.49 ( ! [X0 : 'type/nums/num'] : ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) = ('const/realax/real_pow' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ X0))) )),
% 1.77/1.49 inference(cnf_transformation,[status(thm)],[f2])).
% 1.77/1.49 thf(f2,axiom,(
% 1.77/1.49 ! [X0 : 'type/nums/num'] : (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) = ('const/realax/real_pow' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ X0))),
% 1.77/1.49 file('/export/starexec/sandbox/tmp/tmp.0FPpoGFYUw/DTF2THF_23538.p','thm/real/REAL_POW_ONE_')).
% 1.77/1.49 thf(f28,plain,(
% 1.77/1.49 ( ! [X0 : 'type/realax/real'] : ((sK0 != X0) | (('const/realax/real_mul' @ ('const/realax/real_pow' @ X0 @ (sK4 @ X0 @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) @ ('const/realax/real_pow' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ ('const/arith/-' @ ('const/arith/-' @ sK1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ (sK4 @ X0 @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))))) != ('const/realax/real_pow' @ sK0 @ (sK4 @ X0 @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))) | (('const/realax/real_sub' @ ('const/realax/real_pow' @ X0 @ sK1) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) != ('const/realax/real_sub' @ ('const/realax/real_pow' @ sK0 @ sK1) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))) )),
% 1.77/1.49 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.77/1.49 thf(f26,plain,(
% 1.77/1.49 ( ! [X0 : 'type/realax/real'] : ((sK0 != X0) | (('const/realax/real_mul' @ ('const/realax/real_pow' @ X0 @ (sK4 @ X0 @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) @ ('const/realax/real_pow' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ ('const/arith/-' @ ('const/arith/-' @ sK1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ (sK4 @ X0 @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))))) != ('const/realax/real_pow' @ sK0 @ (sK4 @ X0 @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))) | (('const/realax/real_sub' @ ('const/realax/real_pow' @ X0 @ sK1) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) != ('const/realax/real_sub' @ ('const/realax/real_pow' @ sK0 @ sK1) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) | (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) != ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) )),
% 1.77/1.49 inference(superposition,[status(thm)],[f25,f18])).
% 1.77/1.49 thf(f25,plain,(
% 1.77/1.49 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_sub' @ ('const/realax/real_pow' @ X1 @ sK1) @ ('const/realax/real_pow' @ X0 @ sK1)) != ('const/realax/real_sub' @ ('const/realax/real_pow' @ sK0 @ sK1) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) | (sK0 != X1) | (('const/realax/real_mul' @ ('const/realax/real_pow' @ X1 @ (sK4 @ X1 @ X0)) @ ('const/realax/real_pow' @ X0 @ ('const/arith/-' @ ('const/arith/-' @ sK1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ (sK4 @ X1 @ X0)))) != ('const/realax/real_pow' @ sK0 @ (sK4 @ X1 @ X0))) | (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) != X0)) )),
% 1.77/1.49 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.77/1.49 thf(f24,plain,(
% 1.77/1.49 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((((^[Y0 : 'type/nums/num']: ('const/realax/real_mul' @ ('const/realax/real_pow' @ X1 @ Y0) @ ('const/realax/real_pow' @ X0 @ ('const/arith/-' @ ('const/arith/-' @ sK1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ Y0)))) @ (sK4 @ X1 @ X0)) != ('const/realax/real_pow' @ sK0 @ (sK4 @ X1 @ X0))) | (sK0 != X1) | (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) != X0) | (('const/realax/real_sub' @ ('const/realax/real_pow' @ X1 @ sK1) @ ('const/realax/real_pow' @ X0 @ sK1)) != ('const/realax/real_sub' @ ('const/realax/real_pow' @ sK0 @ sK1) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))) )),
% 1.77/1.49 inference(negative_extensionality,[status(thm)],[f23])).
% 1.77/1.49 thf(f23,plain,(
% 1.77/1.49 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_pow' @ sK0) != (^[Y0 : 'type/nums/num']: ('const/realax/real_mul' @ ('const/realax/real_pow' @ X1 @ Y0) @ ('const/realax/real_pow' @ X0 @ ('const/arith/-' @ ('const/arith/-' @ sK1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ Y0))))) | (('const/realax/real_sub' @ ('const/realax/real_pow' @ X1 @ sK1) @ ('const/realax/real_pow' @ X0 @ sK1)) != ('const/realax/real_sub' @ ('const/realax/real_pow' @ sK0 @ sK1) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) | (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) != X0) | (sK0 != X1)) )),
% 1.77/1.49 inference(constrained_superposition,[status(thm)],[f20,f22])).
% 1.77/1.49 thf(f22,plain,(
% 1.77/1.49 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_mul' @ ('const/realax/real_sub' @ X0 @ X1) @ ('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_mul' @ ('const/realax/real_pow' @ X0 @ Y0) @ ('const/realax/real_pow' @ X1 @ ('const/arith/-' @ ('const/arith/-' @ sK1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ Y0)))))) = ('const/realax/real_sub' @ ('const/realax/real_pow' @ X0 @ sK1) @ ('const/realax/real_pow' @ X1 @ sK1)))) )),
% 1.77/1.49 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.77/1.49 thf(f21,plain,(
% 1.77/1.49 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | (('const/realax/real_mul' @ ('const/realax/real_sub' @ X0 @ X1) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ sK1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_mul' @ ('const/realax/real_pow' @ X0 @ Y0) @ ('const/realax/real_pow' @ X1 @ ('const/arith/-' @ ('const/arith/-' @ sK1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ Y0)))))) = ('const/realax/real_sub' @ ('const/realax/real_pow' @ X0 @ sK1) @ ('const/realax/real_pow' @ X1 @ sK1)))) )),
% 1.77/1.49 inference(superposition,[status(thm)],[f19,f16])).
% 1.77/1.49 thf(f16,plain,(
% 1.77/1.49 ($true = ('const/arith/<=' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')) @ sK1))),
% 1.77/1.49 inference(cnf_transformation,[status(thm)],[f14])).
% 1.77/1.49 thf(f14,plain,(
% 1.77/1.49 (('const/realax/real_mul' @ ('const/realax/real_sub' @ sK0 @ ('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')))) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_pow' @ sK0 @ Y0)))) != ('const/realax/real_sub' @ ('const/realax/real_pow' @ sK0 @ sK1) @ ('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')) @ sK1))),
% 1.77/1.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f13])).
% 1.77/1.49 thf(f13,plain,(
% 1.77/1.49 ? [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) = $true)) => ((('const/realax/real_mul' @ ('const/realax/real_sub' @ sK0 @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ sK1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_pow' @ sK0 @ Y0)))) != ('const/realax/real_sub' @ ('const/realax/real_pow' @ sK0 @ sK1) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) & ($true = ('const/arith/<=' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')) @ sK1)))),
% 1.77/1.49 introduced(definition,[],[choice_axiom])).
% 1.77/1.49 thf(f12,plain,(
% 1.77/1.49 ? [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))),
% 1.77/1.49 inference(ennf_transformation,[status(thm)],[f10])).
% 1.77/1.49 thf(f10,plain,(
% 1.77/1.49 ~! [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))))))),
% 1.77/1.49 inference(fool_elimination,[status(thm)],[f9])).
% 1.77/1.49 thf(f9,plain,(
% 1.77/1.49 ~! [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'))))))),
% 1.77/1.49 inference(rectify,[status(thm)],[f5])).
% 1.77/1.49 thf(f5,negated_conjecture,(
% 1.77/1.49 ~! [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'))))))),
% 1.77/1.49 inference(negated_conjecture,[status(cth)],[f4])).
% 1.77/1.49 thf(f4,conjecture,(
% 1.77/1.49 ! [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'))))))),
% 1.77/1.49 file('/export/starexec/sandbox/tmp/tmp.0FPpoGFYUw/DTF2THF_23538.p','thm/iterate/REAL_SUB_POW_R1_')).
% 1.77/1.49 thf(f19,plain,(
% 1.77/1.49 ( ! [X2 : 'type/nums/num',X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/arith/<=' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')) @ X2) != $true) | (('const/realax/real_sub' @ ('const/realax/real_pow' @ X0 @ X2) @ ('const/realax/real_pow' @ X1 @ X2)) = ('const/realax/real_mul' @ ('const/realax/real_sub' @ X0 @ X1) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ X2 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_mul' @ ('const/realax/real_pow' @ X0 @ Y0) @ ('const/realax/real_pow' @ X1 @ ('const/arith/-' @ ('const/arith/-' @ X2 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ Y0)))))))) )),
% 1.77/1.49 inference(cnf_transformation,[status(thm)],[f11])).
% 1.77/1.49 thf(f11,plain,(
% 1.77/1.49 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/nums/num'] : ((('const/arith/<=' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')) @ X2) != $true) | (('const/realax/real_sub' @ ('const/realax/real_pow' @ X0 @ X2) @ ('const/realax/real_pow' @ X1 @ X2)) = ('const/realax/real_mul' @ ('const/realax/real_sub' @ X0 @ X1) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ X2 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_mul' @ ('const/realax/real_pow' @ X0 @ Y0) @ ('const/realax/real_pow' @ X1 @ ('const/arith/-' @ ('const/arith/-' @ X2 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ Y0))))))))),
% 1.77/1.49 inference(ennf_transformation,[status(thm)],[f8])).
% 1.77/1.49 thf(f8,plain,(
% 1.77/1.49 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/nums/num'] : ((('const/arith/<=' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')) @ X2) = $true) => (('const/realax/real_sub' @ ('const/realax/real_pow' @ X0 @ X2) @ ('const/realax/real_pow' @ X1 @ X2)) = ('const/realax/real_mul' @ ('const/realax/real_sub' @ X0 @ X1) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ X2 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_mul' @ ('const/realax/real_pow' @ X0 @ Y0) @ ('const/realax/real_pow' @ X1 @ ('const/arith/-' @ ('const/arith/-' @ X2 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ Y0))))))))),
% 1.77/1.49 inference(fool_elimination,[status(thm)],[f7])).
% 1.77/1.49 thf(f7,plain,(
% 1.77/1.49 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/nums/num'] : (('const/arith/<=' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')) @ X2) => (('const/realax/real_sub' @ ('const/realax/real_pow' @ X0 @ X2) @ ('const/realax/real_pow' @ X1 @ X2)) = ('const/realax/real_mul' @ ('const/realax/real_sub' @ X0 @ X1) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ X2 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ (^[X3 : 'type/nums/num'] : ('const/realax/real_mul' @ ('const/realax/real_pow' @ X0 @ X3) @ ('const/realax/real_pow' @ X1 @ ('const/arith/-' @ ('const/arith/-' @ X2 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ X3))))))))),
% 1.77/1.49 inference(rectify,[status(thm)],[f3])).
% 1.77/1.49 thf(f3,axiom,(
% 1.77/1.49 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/nums/num'] : (('const/arith/<=' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')) @ X2) => (('const/realax/real_sub' @ ('const/realax/real_pow' @ X0 @ X2) @ ('const/realax/real_pow' @ X1 @ X2)) = ('const/realax/real_mul' @ ('const/realax/real_sub' @ X0 @ X1) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ X2 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) @ (^[X3 : 'type/nums/num'] : ('const/realax/real_mul' @ ('const/realax/real_pow' @ X0 @ X3) @ ('const/realax/real_pow' @ X1 @ ('const/arith/-' @ ('const/arith/-' @ X2 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ X3))))))))),
% 1.77/1.49 file('/export/starexec/sandbox/tmp/tmp.0FPpoGFYUw/DTF2THF_23538.p','thm/iterate/REAL_SUB_POW_')).
% 1.77/1.49 thf(f20,plain,(
% 1.77/1.49 (('const/realax/real_mul' @ ('const/realax/real_sub' @ sK0 @ ('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' @ sK0))) != ('const/realax/real_sub' @ ('const/realax/real_pow' @ sK0 @ sK1) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))),
% 1.77/1.49 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.77/1.49 thf(f17,plain,(
% 1.77/1.49 (('const/realax/real_mul' @ ('const/realax/real_sub' @ sK0 @ ('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')))) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_pow' @ sK0 @ Y0)))) != ('const/realax/real_sub' @ ('const/realax/real_pow' @ sK0 @ sK1) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))),
% 1.77/1.49 inference(cnf_transformation,[status(thm)],[f14])).
% 1.77/1.49 % SZS output end Proof for DTF2THF_23538
% 1.77/1.49 % (23642)------------------------------
% 1.77/1.49 % (23642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.49 % (23642)Termination reason: Refutation
% 1.77/1.49
% 1.77/1.49 % (23642)Memory used [KB]: 5628
% 1.77/1.49 % (23642)Time elapsed: 0.012 s
% 1.77/1.49 % (23642)Instructions burned: 12 (million)
% 1.77/1.49 % (23642)------------------------------
% 1.77/1.49 % (23642)------------------------------
% 1.77/1.49 % (23635)Success in time 0.025 s
%------------------------------------------------------------------------------