%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA122^1 : 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 : n022.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 1.72s 1.49s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 18 unt; 0 typ; 2 def)
% Number of atoms : 265 ( 109 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 627 ( 63 ~; 67 |; 0 &; 479 @)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 63 ( 63 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 20 usr; 8 con; 0-4 aty)
% ( 7 !!; 8 ??; 0 @@+; 0 @@-)
% Number of variables : 144 ( 44 ^; 96 !; 4 ?; 144 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(type_def_6,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_pow': 'type/realax/real' > 'type/nums/num' > 'type/realax/real' ).
thf(func_def_3,type,
'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
thf(func_def_4,type,
'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_5,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_6,type,
'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_7,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_8,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_9,type,
'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
thf(func_def_10,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_21,type,
sK0: 'type/realax/real' ).
thf(func_def_23,type,
sK2: ( 'type/realax/real' > 'type/realax/real' ) > 'type/nums/num' > 'type/realax/real' ).
thf(func_def_24,type,
sK3: ( 'type/realax/real' > 'type/realax/real' ) > 'type/nums/num' ).
thf(func_def_25,type,
sK4: ( 'type/nums/num' > 'type/realax/real' ) > ( 'type/realax/real' > 'type/realax/real' ) > 'type/nums/num' > 'type/realax/real' ).
thf(func_def_26,type,
ph5:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
sK6: 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_29,type,
sK7: 'type/nums/num' > ( 'type/realax/real' > 'type/realax/real' ) > 'type/nums/num' ).
thf(func_def_30,type,
sK8: 'type/nums/num' > 'type/nums/num' ).
thf(func_def_31,type,
sK9: 'type/realax/real' > ( 'type/realax/real' > 'type/realax/real' ) > ( 'type/realax/real' > 'type/realax/real' ) > 'type/realax/real' > 'type/nums/num' ).
thf(f159,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f118,f136,f148]) ).
thf(f148,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[status(thm)],[f147]) ).
thf(f147,plain,
( $false
| ~ spl1_1 ),
inference(equality_resolution,[status(thm)],[f142]) ).
thf(f142,plain,
( ! [X0: 'type/nums/num' > 'type/realax/real'] :
( ( X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= sK0 )
| ~ spl1_1 ),
inference(equality_resolution,[status(thm)],[f141]) ).
thf(f141,plain,
( ! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/realax/real'] :
( ( sK0 != X1 )
| ( ( X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= X1 ) )
| ~ spl1_1 ),
inference(beta_eta_normalization,[status(thm)],[f140]) ).
thf(f140,plain,
( ! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/realax/real'] :
( ( ( X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= X1 )
| ( ( ^ [Y0: 'type/realax/real'] : sK0
@ ( sK4 @ X0
@ ^ [Y0: 'type/realax/real'] : sK0
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
!= X1 ) )
| ~ spl1_1 ),
inference(trivial_inequality_removal,[status(thm)],[f139]) ).
thf(f139,plain,
( ! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/realax/real'] :
( ( $true != $true )
| ( ( ^ [Y0: 'type/realax/real'] : sK0
@ ( sK4 @ X0
@ ^ [Y0: 'type/realax/real'] : sK0
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
!= X1 )
| ( ( X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= X1 ) )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f17,f113]) ).
thf(f113,plain,
( ! [X2: 'type/realax/real',X0: 'type/realax/real' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X0 )
= $true )
| ( ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= X2 )
| ( ( X0 @ ( sK4 @ X1 @ X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
!= X2 ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f112]) ).
thf(f112,definition,
( spl1_1
<=> ! [X2: 'type/realax/real',X0: 'type/realax/real' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X0 )
= $true )
| ( ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= X2 )
| ( ( X0 @ ( sK4 @ X1 @ X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
!= X2 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f17,plain,
( $true
!= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : sK0 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( $true
!= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f11,f12]) ).
thf(f12,plain,
( ? [X0: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : X0 )
!= $true )
=> ( $true
!= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
? [X0: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : X0 )
!= $true ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
~ ! [X0: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X0: 'type/realax/real'] :
( 'const/iterate/polynomial_function'
@ ^ [X1: 'type/realax/real'] : X0 ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ! [X0: 'type/realax/real'] :
( 'const/iterate/polynomial_function'
@ ^ [X1: 'type/realax/real'] : X0 ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
! [X0: 'type/realax/real'] :
( 'const/iterate/polynomial_function'
@ ^ [X1: 'type/realax/real'] : X0 ),
file('/export/starexec/sandbox/tmp/tmp.09rWDTPhcM/DTF2THF_2760.p','thm/iterate/POLYNOMIAL_FUNCTION_CONST_') ).
thf(f136,plain,
( spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f126,f115,f112]) ).
thf(f115,definition,
( spl1_2
<=> ( $true
= ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( sK8 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f126,plain,
( ! [X2: 'type/realax/real',X0: 'type/realax/real' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real'] :
( ( ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= X2 )
| ( ( X0 @ ( sK4 @ X1 @ X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
!= X2 )
| ( ( 'const/iterate/polynomial_function' @ X0 )
= $true ) )
| ~ spl1_2 ),
inference(trivial_inequality_removal,[status(thm)],[f125]) ).
thf(f125,plain,
( ! [X2: 'type/realax/real',X0: 'type/realax/real' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real'] :
( ( ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= X2 )
| ( ( 'const/iterate/polynomial_function' @ X0 )
= $true )
| ( ( X0 @ ( sK4 @ X1 @ X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
!= X2 )
| ( $true = $false ) )
| ~ spl1_2 ),
inference(duplicate_literal_removal,[status(thm)],[f120]) ).
thf(f120,plain,
( ! [X2: 'type/realax/real',X0: 'type/realax/real' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X0 )
= $true )
| ( $true = $false )
| ( $true = $false )
| ( ( X0 @ ( sK4 @ X1 @ X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
!= X2 )
| ( ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= X2 ) )
| ~ spl1_2 ),
inference(superposition,[status(thm)],[f108,f117]) ).
thf(f117,plain,
( ( $true
= ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( sK8 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f115]) ).
thf(f108,plain,
! [X2: 'type/realax/real' > 'type/realax/real',X3: 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real',X1: 'type/realax/real'] :
( ( $false
= ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( sK8 @ X3 ) ) )
| ( $false
= ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ X3 @ ( sK8 @ X3 ) ) )
| ( $true
= ( 'const/iterate/polynomial_function' @ X2 ) )
| ( ( X2 @ ( sK4 @ X0 @ X2 @ X3 ) )
!= X1 )
| ( ( X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
! [X2: 'type/realax/real' > 'type/realax/real',X3: 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/iterate/polynomial_function' @ X2 ) )
| ( ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( sK8 @ X3 ) )
!= ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ X3 @ ( sK8 @ X3 ) ) )
| ( ( X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= X1 )
| ( ( X2 @ ( sK4 @ X0 @ X2 @ X3 ) )
!= X1 ) ),
inference(negative_extensionality,[status(thm)],[f95]) ).
thf(f95,plain,
! [X2: 'type/realax/real' > 'type/realax/real',X3: 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ X3 ) )
| ( $true
= ( 'const/iterate/polynomial_function' @ X2 ) )
| ( ( X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= X1 )
| ( ( X2 @ ( sK4 @ X0 @ X2 @ X3 ) )
!= X1 ) ),
inference(constrained_superposition,[status(thm)],[f68,f14]) ).
thf(f14,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.09rWDTPhcM/DTF2THF_2760.p','thm/realarith/REAL_MUL_RID_') ).
thf(f68,plain,
! [X2: 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( ( X1 @ ( sK4 @ X0 @ X1 @ X2 ) )
!= ( 'const/realax/real_mul' @ ( X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ X2 )
!= ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
| ( ( 'const/iterate/polynomial_function' @ X1 )
= $true ) ),
inference(superposition,[status(thm)],[f67,f16]) ).
thf(f16,plain,
! [X0: 'type/realax/real'] :
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
= ( 'const/realax/real_pow' @ X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: 'type/realax/real'] :
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
= ( 'const/realax/real_pow' @ X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
file('/export/starexec/sandbox/tmp/tmp.09rWDTPhcM/DTF2THF_2760.p','thm/realax/real_pow_0') ).
thf(f67,plain,
! [X2: 'type/realax/real' > 'type/realax/real',X3: 'type/nums/num' > 'type/realax/real',X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/realax/real_mul' @ ( X3 @ X1 ) @ ( 'const/realax/real_pow' @ ( sK4 @ X3 @ X2 @ X0 ) @ X1 ) )
!= ( X2 @ ( sK4 @ X3 @ X2 @ X0 ) ) )
| ( ( 'const/iterate/..' @ X1 @ X1 )
!= ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ X0 ) )
| ( $true
= ( 'const/iterate/polynomial_function' @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f66]) ).
thf(f66,plain,
! [X2: 'type/realax/real' > 'type/realax/real',X3: 'type/nums/num' > 'type/realax/real',X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( $true
= ( 'const/iterate/polynomial_function' @ X2 ) )
| ( ( X2 @ ( sK4 @ X3 @ X2 @ X0 ) )
!= ( ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X3 @ Y0 ) @ ( 'const/realax/real_pow' @ ( sK4 @ X3 @ X2 @ X0 ) @ Y0 ) )
@ X1 ) )
| ( ( 'const/iterate/..' @ X1 @ X1 )
!= ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ X0 ) ) ),
inference(equality_resolution,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: 'type/nums/num',X3: 'type/nums/num' > 'type/realax/real',X0: 'type/nums/num' > 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real',X4: 'type/nums/num'] :
( ( ( ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X0 @ Y0 ) @ ( 'const/realax/real_pow' @ ( sK4 @ X0 @ X1 @ X2 ) @ Y0 ) ) )
!= X3 )
| ( ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ X2 )
!= ( 'const/iterate/..' @ X4 @ X4 ) )
| ( ( 'const/iterate/polynomial_function' @ X1 )
= $true )
| ( ( X1 @ ( sK4 @ X0 @ X1 @ X2 ) )
!= ( X3 @ X4 ) ) ),
inference(constrained_superposition,[status(thm)],[f34,f15]) ).
thf(f15,plain,
! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X1 ) @ X0 )
= ( X0 @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X1 ) @ X0 )
= ( X0 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.09rWDTPhcM/DTF2THF_2760.p','thm/iterate/SUM_SING_NUMSEG_') ).
thf(f34,plain,
! [X2: 'type/nums/num',X0: 'type/realax/real' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real'] :
( ( ( X0 @ ( sK4 @ X1 @ X0 @ X2 ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ X2 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X1 @ Y0 ) @ ( 'const/realax/real_pow' @ ( sK4 @ X1 @ X0 @ X2 ) @ Y0 ) ) ) )
| ( ( 'const/iterate/polynomial_function' @ X0 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: 'type/nums/num',X0: 'type/realax/real' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X0 )
= $true )
| ( ( ( X0 @ ( sK4 @ X1 @ X0 @ X2 ) )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ X2 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X1 @ Y0 ) @ ( 'const/realax/real_pow' @ ( sK4 @ X1 @ X0 @ X2 ) @ Y0 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: 'type/nums/num',X0: 'type/realax/real' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X0 )
= $true )
| ( ( ^ [Y0: 'type/realax/real'] :
( ( X0 @ Y0 )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ X2 )
@ ^ [Y1: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X1 @ Y1 ) @ ( 'const/realax/real_pow' @ Y0 @ Y1 ) ) ) )
@ ( sK4 @ X1 @ X0 @ X2 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: 'type/nums/num',X0: 'type/realax/real' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real'] :
( ( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( X0 @ Y0 )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ X2 )
@ ^ [Y1: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X1 @ Y1 ) @ ( 'const/realax/real_pow' @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( 'const/iterate/polynomial_function' @ X0 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: 'type/nums/num',X0: 'type/realax/real' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real'] :
( ( $false
= ( ^ [Y0: 'type/nums/num'] :
( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( X0 @ Y1 )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ Y0 )
@ ^ [Y2: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X1 @ Y2 ) @ ( 'const/realax/real_pow' @ Y1 @ Y2 ) ) ) ) )
@ X2 ) )
| ( ( 'const/iterate/polynomial_function' @ X0 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X0 )
= $true )
| ( $false
= ( ?? @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( X0 @ Y1 )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ Y0 )
@ ^ [Y2: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X1 @ Y2 ) @ ( 'const/realax/real_pow' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X0 )
= $true )
| ( ( ^ [Y0: 'type/nums/num' > 'type/realax/real'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] :
( !! @ 'type/realax/real'
@ ^ [Y2: 'type/realax/real'] :
( ( X0 @ Y2 )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ Y1 )
@ ^ [Y3: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( Y0 @ Y3 ) @ ( 'const/realax/real_pow' @ Y2 @ Y3 ) ) ) ) ) )
@ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: 'type/realax/real' > 'type/realax/real'] :
( ( ( ?? @ ( 'type/nums/num' > 'type/realax/real' )
@ ^ [Y0: 'type/nums/num' > 'type/realax/real'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] :
( !! @ 'type/realax/real'
@ ^ [Y2: 'type/realax/real'] :
( ( X0 @ Y2 )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ Y1 )
@ ^ [Y3: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( Y0 @ Y3 ) @ ( 'const/realax/real_pow' @ Y2 @ Y3 ) ) ) ) ) ) )
= $false )
| ( ( 'const/iterate/polynomial_function' @ X0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ X0 )
= ( ?? @ ( 'type/nums/num' > 'type/realax/real' )
@ ^ [Y0: 'type/nums/num' > 'type/realax/real'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] :
( !! @ 'type/realax/real'
@ ^ [Y2: 'type/realax/real'] :
( ( X0 @ Y2 )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ Y1 )
@ ^ [Y3: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( Y0 @ Y3 ) @ ( 'const/realax/real_pow' @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ X0 )
= ( ?? @ ( 'type/nums/num' > 'type/realax/real' )
@ ^ [Y0: 'type/nums/num' > 'type/realax/real'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] :
( !! @ 'type/realax/real'
@ ^ [Y2: 'type/realax/real'] :
( ( X0 @ Y2 )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ Y1 )
@ ^ [Y3: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( Y0 @ Y3 ) @ ( 'const/realax/real_pow' @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ X0 )
= ( ? [X1: 'type/nums/num',X2: 'type/nums/num' > 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( X0 @ X3 )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ X1 )
@ ^ [X4: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X2 @ X4 ) @ ( 'const/realax/real_pow' @ X3 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.09rWDTPhcM/DTF2THF_2760.p','thm/iterate/polynomial_function_') ).
thf(f118,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f110,f115,f112]) ).
thf(f110,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X0 )
= $true )
| ( ( X0 @ ( sK4 @ X1 @ X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
!= X2 )
| ( ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= X2 )
| ( $true
= ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( sK8 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f109]) ).
thf(f109,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real'] :
( ( ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= X2 )
| ( $true != $true )
| ( ( 'const/iterate/polynomial_function' @ X0 )
= $true )
| ( ( X0 @ ( sK4 @ X1 @ X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
!= X2 )
| ( $true
= ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( sK8 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ) ),
inference(equality_factoring,[status(thm)],[f107]) ).
thf(f107,plain,
! [X2: 'type/realax/real' > 'type/realax/real',X3: 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( sK8 @ X3 ) ) )
| ( $true
= ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ X3 @ ( sK8 @ X3 ) ) )
| ( $true
= ( 'const/iterate/polynomial_function' @ X2 ) )
| ( ( X2 @ ( sK4 @ X0 @ X2 @ X3 ) )
!= X1 )
| ( ( X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA122^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n022.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 03:51:21 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : ANA122^1 : TPTP v9.2.1. Released v7.0.0.
% 0.19/0.46 % Domain : Analysis
% 0.19/0.46 % Problem : POLYNOMIAL_FUNCTION_CONST
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Kal16]
% 0.19/0.46 % Names : POLYNOMIAL_FUNCTION_CONST_.p [Kal16]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.00 v7.2.0, 0.25 v7.1.0
% 0.19/0.46 % Syntax : Number of formulae : 16 ( 5 unt; 11 typ; 0 def)
% 0.19/0.46 % Number of atoms : 9 ( 5 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.19/0.46 % Number of connectives : 31 ( 0 ~; 0 |; 0 &; 31 @)
% 0.19/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 4 ( 3 avg)
% 0.19/0.46 % Number of types : 3 ( 2 usr)
% 0.19/0.46 % Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 10 ( 9 usr; 1 con; 0-3 aty)
% 0.19/0.46 % Number of variables : 12 ( 2 ^; 7 !; 2 ?; 12 :)
% 0.19/0.46 % ( 1 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.46 % SPC : TH1_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : Exported from core HOL Light.
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf('thf_type_type/realax/real',type,
% 0.19/0.46 'type/realax/real': $tType ).
% 0.19/0.46
% 0.19/0.46 thf('thf_type_type/nums/num',type,
% 0.19/0.46 'type/nums/num': $tType ).
% 0.19/0.46
% 0.19/0.46 thf('thf_const_const/realax/real_pow',type,
% 0.19/0.46 'const/realax/real_pow': 'type/realax/real' > 'type/nums/num' > 'type/realax/real' ).
% 0.19/0.46
% 0.19/0.46 thf('thf_const_const/realax/real_of_num',type,
% 0.19/0.46 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
% 0.19/0.46
% 0.19/0.46 thf('thf_const_const/realax/real_mul',type,
% 0.19/0.46 'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 0.19/0.46
% 0.19/0.46 thf('thf_const_const/nums/NUMERAL',type,
% 0.19/0.46 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 0.19/0.46
% 0.19/0.46 thf('thf_const_const/nums/BIT1',type,
% 0.19/0.46 'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
% 0.19/0.46
% 0.19/0.46 thf('thf_const_const/nums/_0',type,
% 0.19/0.46 'const/nums/_0': 'type/nums/num' ).
% 0.19/0.46
% 0.19/0.46 thf('thf_const_const/iterate/sum',type,
% 0.19/0.46 'const/iterate/sum':
% 0.19/0.46 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 0.19/0.46
% 0.19/0.46 thf('thf_const_const/iterate/polynomial_function',type,
% 0.19/0.46 'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
% 0.19/0.46
% 0.19/0.46 thf('thf_const_const/iterate/..',type,
% 0.19/0.46 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
% 0.19/0.46
% 0.19/0.46 thf('thm/realarith/REAL_MUL_RID_',axiom,
% 0.19/0.46 ! [A: 'type/realax/real'] :
% 0.19/0.46 ( ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
% 0.19/0.46 = A ) ).
% 0.19/0.46
% 0.19/0.46 thf('thm/realax/real_pow_0',axiom,
% 0.19/0.46 ! [A: 'type/realax/real'] :
% 0.19/0.46 ( ( 'const/realax/real_pow' @ A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
% 0.19/0.46 = ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf('thm/iterate/SUM_SING_NUMSEG_',axiom,
% 0.19/0.46 ! [A: 'type/nums/num' > 'type/realax/real',A0: 'type/nums/num'] :
% 0.19/0.46 ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A0 @ A0 ) @ A )
% 0.19/0.46 = ( A @ A0 ) ) ).
% 0.19/0.46
% 0.19/0.46 thf('thm/iterate/polynomial_function_',axiom,
% 0.19/0.46 ! [A: 'type/realax/real' > 'type/realax/real'] :
% 0.19/0.46 ( ( 'const/iterate/polynomial_function' @ A )
% 0.19/0.46 = ( ? [A0: 'type/nums/num',A1: 'type/nums/num' > 'type/realax/real'] :
% 0.19/0.46 ! [A2: 'type/realax/real'] :
% 0.19/0.46 ( ( A @ A2 )
% 0.19/0.46 = ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ A0 )
% 0.19/0.46 @ ^ [A3: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( A1 @ A3 ) @ ( 'const/realax/real_pow' @ A2 @ A3 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf('thm/iterate/POLYNOMIAL_FUNCTION_CONST_',conjecture,
% 0.19/0.46 ! [A: 'type/realax/real'] :
% 0.19/0.46 ( 'const/iterate/polynomial_function'
% 0.19/0.46 @ ^ [A0: 'type/realax/real'] : A ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.72/1.42 ---- Embedded in THF ---
% 1.72/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.72/1.42 %%% Generated on Tue Feb 24 03:51:22 EST 2026
% 1.72/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.72/1.42 %%% Logic specification used:
% 1.72/1.42 %%% thf(spec, logic, $$dhol).
% 1.72/1.42
% 1.72/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.09rWDTPhcM/DTF2DTF2760.p
% See solution above
% 1.72/1.42 ------------------------
% 1.72/1.43 ---- Cleaned THF ---
% 1.72/1.43 thf('thf_type_type/realax/real',type,
% 1.72/1.43 'type/realax/real': $tType ).
% 1.72/1.43
% 1.72/1.43 thf('thf_type_type/nums/num',type,
% 1.72/1.43 'type/nums/num': $tType ).
% 1.72/1.43
% 1.72/1.43 thf('thf_const_const/realax/real_pow',type,
% 1.72/1.43 'const/realax/real_pow': 'type/realax/real' > 'type/nums/num' > 'type/realax/real' ).
% 1.72/1.43
% 1.72/1.43 thf('thf_const_const/realax/real_of_num',type,
% 1.72/1.43 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
% 1.72/1.43
% 1.72/1.43 thf('thf_const_const/realax/real_mul',type,
% 1.72/1.43 'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 1.72/1.43
% 1.72/1.43 thf('thf_const_const/nums/NUMERAL',type,
% 1.72/1.43 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 1.72/1.43
% 1.72/1.43 thf('thf_const_const/nums/BIT1',type,
% 1.72/1.43 'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
% 1.72/1.43
% 1.72/1.43 thf('thf_const_const/nums/_0',type,
% 1.72/1.43 'const/nums/_0': 'type/nums/num' ).
% 1.72/1.43
% 1.72/1.43 thf('thf_const_const/iterate/sum',type,
% 1.72/1.43 'const/iterate/sum':
% 1.72/1.43 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 1.72/1.43
% 1.72/1.43 thf('thf_const_const/iterate/polynomial_function',type,
% 1.72/1.43 'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
% 1.72/1.43
% 1.72/1.43 thf('thf_const_const/iterate/..',type,
% 1.72/1.43 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
% 1.72/1.43
% 1.72/1.43 thf('thm/realarith/REAL_MUL_RID_',axiom,
% 1.72/1.43 ! [A: 'type/realax/real'] :
% 1.72/1.43 ( ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
% 1.72/1.43 = A ) ).
% 1.72/1.43
% 1.72/1.43 thf('thm/realax/real_pow_0',axiom,
% 1.72/1.43 ! [A: 'type/realax/real'] :
% 1.72/1.43 ( ( 'const/realax/real_pow' @ A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
% 1.72/1.43 = ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ).
% 1.72/1.43
% 1.72/1.43 thf('thm/iterate/SUM_SING_NUMSEG_',axiom,
% 1.72/1.43 ! [A: 'type/nums/num' > 'type/realax/real',A0: 'type/nums/num'] :
% 1.72/1.43 ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A0 @ A0 ) @ A )
% 1.72/1.43 = ( A @ A0 ) ) ).
% 1.72/1.43
% 1.72/1.43 thf('thm/iterate/polynomial_function_',axiom,
% 1.72/1.43 ! [A: 'type/realax/real' > 'type/realax/real'] :
% 1.72/1.43 ( ( 'const/iterate/polynomial_function' @ A )
% 1.72/1.43 = ( ? [A0: 'type/nums/num',A1: 'type/nums/num' > 'type/realax/real'] :
% 1.72/1.43 ! [A2: 'type/realax/real'] :
% 1.72/1.43 ( ( A @ A2 )
% 1.72/1.43 = ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ A0 )
% 1.72/1.43 @ ^ [A3: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( A1 @ A3 ) @ ( 'const/realax/real_pow' @ A2 @ A3 ) ) ) ) ) ) ).
% 1.72/1.43
% 1.72/1.43 thf('thm/iterate/POLYNOMIAL_FUNCTION_CONST_',conjecture,
% 1.72/1.43 ! [A: 'type/realax/real'] :
% 1.72/1.43 ( 'const/iterate/polynomial_function'
% 1.72/1.43 @ ^ [A0: 'type/realax/real'] : A ) ).
% 1.72/1.43 ------------------------
% 1.72/1.45 % (2858)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_2760 for (2999ds/4Mi)
% 1.72/1.45 % (2857)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2760 for (2999ds/183Mi)
% 1.72/1.45 % (2859)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_2760 for (2999ds/27Mi)
% 1.72/1.45 % (2860)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2760 for (2999ds/2Mi)
% 1.72/1.45 % (2861)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_2760 for (2999ds/2Mi)
% 1.72/1.45 % (2862)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_2760 for (2999ds/275Mi)
% 1.72/1.45 % (2863)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2760 for (2999ds/18Mi)
% 1.72/1.45 % (2862)Refutation not found, incomplete strategy
% 1.72/1.45 % (2862)------------------------------
% 1.72/1.45 % (2862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.45 % (2862)Termination reason: Refutation not found, incomplete strategy
% 1.72/1.45
% 1.72/1.45
% 1.72/1.45 % (2862)Memory used [KB]: 5373
% 1.72/1.45 % (2862)Time elapsed: 0.002 s
% 1.72/1.45 % (2862)Instructions burned: 1 (million)
% 1.72/1.45 % (2862)------------------------------
% 1.72/1.45 % (2862)------------------------------
% 1.72/1.45 % (2860)Instruction limit reached!
% 1.72/1.45 % (2860)------------------------------
% 1.72/1.45 % (2860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.45 % (2860)Termination reason: Unknown
% 1.72/1.45 % (2860)Termination phase: Saturation
% 1.72/1.45 % (2861)Instruction limit reached!
% 1.72/1.45 % (2861)------------------------------
% 1.72/1.45 % (2861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.45 % (2861)Termination reason: Unknown
% 1.72/1.45 % (2861)Termination phase: Saturation
% 1.72/1.45
% 1.72/1.45 % (2861)Memory used [KB]: 5500
% 1.72/1.45 % (2861)Time elapsed: 0.003 s
% 1.72/1.45 % (2861)Instructions burned: 3 (million)
% 1.72/1.45 % (2861)------------------------------
% 1.72/1.45 % (2861)------------------------------
% 1.72/1.45
% 1.72/1.45 % (2860)Memory used [KB]: 5500
% 1.72/1.45 % (2860)Time elapsed: 0.003 s
% 1.72/1.45 % (2860)Instructions burned: 3 (million)
% 1.72/1.45 % (2860)------------------------------
% 1.72/1.45 % (2860)------------------------------
% 1.72/1.45 % (2858)Instruction limit reached!
% 1.72/1.45 % (2858)------------------------------
% 1.72/1.45 % (2858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.45 % (2858)Termination reason: Unknown
% 1.72/1.45 % (2858)Termination phase: Saturation
% 1.72/1.45
% 1.72/1.45 % (2858)Memory used [KB]: 5500
% 1.72/1.45 % (2858)Time elapsed: 0.004 s
% 1.72/1.45 % (2858)Instructions burned: 4 (million)
% 1.72/1.45 % (2858)------------------------------
% 1.72/1.45 % (2858)------------------------------
% 1.72/1.46 % (2859)Refutation not found, incomplete strategy
% 1.72/1.46 % (2859)------------------------------
% 1.72/1.46 % (2859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.46 % (2859)Termination reason: Refutation not found, incomplete strategy
% 1.72/1.46
% 1.72/1.46
% 1.72/1.46 % (2859)Memory used [KB]: 5500
% 1.72/1.46 % (2859)Time elapsed: 0.007 s
% 1.72/1.46 % (2859)Instructions burned: 9 (million)
% 1.72/1.46 % (2859)------------------------------
% 1.72/1.46 % (2859)------------------------------
% 1.72/1.46 % (2863)Instruction limit reached!
% 1.72/1.46 % (2863)------------------------------
% 1.72/1.46 % (2863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.46 % (2863)Termination reason: Unknown
% 1.72/1.46 % (2863)Termination phase: Saturation
% 1.72/1.46
% 1.72/1.46 % (2863)Memory used [KB]: 5628
% 1.72/1.46 % (2863)Time elapsed: 0.011 s
% 1.72/1.46 % (2863)Instructions burned: 18 (million)
% 1.72/1.46 % (2863)------------------------------
% 1.72/1.46 % (2863)------------------------------
% 1.72/1.47 % (2864)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2760 for (2999ds/3Mi)
% 1.72/1.47 % (2865)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_2760 for (2999ds/37Mi)
% 1.72/1.47 % (2866)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_2760 for (2999ds/15Mi)
% 1.72/1.47 % (2867)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2760 for (2999ds/3Mi)
% 1.72/1.47 % (2864)Instruction limit reached!
% 1.72/1.47 % (2864)------------------------------
% 1.72/1.47 % (2864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.47 % (2864)Termination reason: Unknown
% 1.72/1.47 % (2864)Termination phase: Saturation
% 1.72/1.47
% 1.72/1.47 % (2864)Memory used [KB]: 5500
% 1.72/1.47 % (2864)Time elapsed: 0.003 s
% 1.72/1.47 % (2864)Instructions burned: 3 (million)
% 1.72/1.47 % (2864)------------------------------
% 1.72/1.47 % (2864)------------------------------
% 1.72/1.47 % (2867)Instruction limit reached!
% 1.72/1.47 % (2867)------------------------------
% 1.72/1.47 % (2867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.47 % (2867)Termination reason: Unknown
% 1.72/1.47 % (2867)Termination phase: Saturation
% 1.72/1.47
% 1.72/1.47 % (2867)Memory used [KB]: 5500
% 1.72/1.47 % (2867)Time elapsed: 0.003 s
% 1.72/1.47 % (2867)Instructions burned: 3 (million)
% 1.72/1.47 % (2867)------------------------------
% 1.72/1.47 % (2867)------------------------------
% 1.72/1.47 % (2868)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_2760 for (2999ds/1041Mi)
% 1.72/1.47 % (2866)Refutation not found, incomplete strategy
% 1.72/1.47 % (2866)------------------------------
% 1.72/1.47 % (2866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.47 % (2866)Termination reason: Refutation not found, incomplete strategy
% 1.72/1.47
% 1.72/1.47
% 1.72/1.47 % (2866)Memory used [KB]: 5500
% 1.72/1.47 % (2866)Time elapsed: 0.006 s
% 1.72/1.47 % (2866)Instructions burned: 8 (million)
% 1.72/1.47 % (2866)------------------------------
% 1.72/1.47 % (2866)------------------------------
% 1.72/1.48 % (2869)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_2760 for (2999ds/7Mi)
% 1.72/1.48 % (2869)Instruction limit reached!
% 1.72/1.48 % (2869)------------------------------
% 1.72/1.48 % (2869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.48 % (2869)Termination reason: Unknown
% 1.72/1.48 % (2869)Termination phase: Saturation
% 1.72/1.48
% 1.72/1.48 % (2869)Memory used [KB]: 1023
% 1.72/1.48 % (2869)Time elapsed: 0.006 s
% 1.72/1.48 % (2869)Instructions burned: 8 (million)
% 1.72/1.48 % (2869)------------------------------
% 1.72/1.48 % (2869)------------------------------
% 1.72/1.48 % (2870)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_2760 for (2999ds/16Mi)
% 1.72/1.49 % (2871)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_2760 for (2999ds/3Mi)
% 1.72/1.49 % (2865)Instruction limit reached!
% 1.72/1.49 % (2865)------------------------------
% 1.72/1.49 % (2865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.49 % (2865)Termination reason: Unknown
% 1.72/1.49 % (2865)Termination phase: Saturation
% 1.72/1.49
% 1.72/1.49 % (2865)Memory used [KB]: 5884
% 1.72/1.49 % (2865)Time elapsed: 0.020 s
% 1.72/1.49 % (2865)Instructions burned: 37 (million)
% 1.72/1.49 % (2865)------------------------------
% 1.72/1.49 % (2865)------------------------------
% 1.72/1.49 % (2871)Instruction limit reached!
% 1.72/1.49 % (2871)------------------------------
% 1.72/1.49 % (2871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.49 % (2871)Termination reason: Unknown
% 1.72/1.49 % (2871)Termination phase: Saturation
% 1.72/1.49
% 1.72/1.49 % (2871)Memory used [KB]: 5500
% 1.72/1.49 % (2871)Time elapsed: 0.003 s
% 1.72/1.49 % (2871)Instructions burned: 3 (million)
% 1.72/1.49 % (2871)------------------------------
% 1.72/1.49 % (2871)------------------------------
% 1.72/1.49 % (2857)First to succeed.
% 1.72/1.49 % (2872)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_2760 for (2999ds/3Mi)
% 1.72/1.49 % (2872)Instruction limit reached!
% 1.72/1.49 % (2872)------------------------------
% 1.72/1.49 % (2872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.49 % (2872)Termination reason: Unknown
% 1.72/1.49 % (2872)Termination phase: Saturation
% 1.72/1.49
% 1.72/1.49 % (2872)Memory used [KB]: 1023
% 1.72/1.49 % (2872)Time elapsed: 0.003 s
% 1.72/1.49 % (2872)Instructions burned: 3 (million)
% 1.72/1.49 % (2872)------------------------------
% 1.72/1.49 % (2872)------------------------------
% 1.72/1.49 % (2857)Refutation found. Thanks to Tanya!
% 1.72/1.49 % SZS status Theorem for DTF2THF_2760
% 1.72/1.49 % SZS output start Proof for DTF2THF_2760
% 1.72/1.49 thf(type_def_5, type, 'type/realax/real': $tType).
% 1.72/1.49 thf(type_def_6, type, 'type/nums/num': $tType).
% 1.72/1.49 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.72/1.49 thf(func_def_1, type, 'type/nums/num': $tType).
% 1.72/1.49 thf(func_def_2, type, 'const/realax/real_pow': 'type/realax/real' > 'type/nums/num' > 'type/realax/real').
% 1.72/1.49 thf(func_def_3, type, 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real').
% 1.72/1.49 thf(func_def_4, type, 'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real').
% 1.72/1.49 thf(func_def_5, type, 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num').
% 1.72/1.49 thf(func_def_6, type, 'const/nums/BIT1': 'type/nums/num' > 'type/nums/num').
% 1.72/1.49 thf(func_def_7, type, 'const/nums/_0': 'type/nums/num').
% 1.72/1.49 thf(func_def_8, type, 'const/iterate/sum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real')).
% 1.72/1.49 thf(func_def_9, type, 'const/iterate/polynomial_function': ('type/realax/real' > 'type/realax/real') > $o).
% 1.72/1.49 thf(func_def_10, type, 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o).
% 1.72/1.49 thf(func_def_21, type, sK0: 'type/realax/real').
% 1.72/1.49 thf(func_def_23, type, sK2: ('type/realax/real' > 'type/realax/real') > 'type/nums/num' > 'type/realax/real').
% 1.72/1.49 thf(func_def_24, type, sK3: ('type/realax/real' > 'type/realax/real') > 'type/nums/num').
% 1.72/1.49 thf(func_def_25, type, sK4: ('type/nums/num' > 'type/realax/real') > ('type/realax/real' > 'type/realax/real') > 'type/nums/num' > 'type/realax/real').
% 1.72/1.49 thf(func_def_26, type, ph5: !>[X0: $tType]:(X0)).
% 1.72/1.49 thf(func_def_27, type, sK6: 'type/nums/num' > 'type/nums/num' > 'type/nums/num').
% 1.72/1.49 thf(func_def_29, type, sK7: 'type/nums/num' > ('type/realax/real' > 'type/realax/real') > 'type/nums/num').
% 1.72/1.49 thf(func_def_30, type, sK8: 'type/nums/num' > 'type/nums/num').
% 1.72/1.49 thf(func_def_31, type, sK9: 'type/realax/real' > ('type/realax/real' > 'type/realax/real') > ('type/realax/real' > 'type/realax/real') > 'type/realax/real' > 'type/nums/num').
% 1.72/1.49 thf(f159,plain,(
% 1.72/1.49 $false),
% 1.72/1.49 inference(avatar_sat_refutation,[status(thm)],[f118,f136,f148])).
% 1.72/1.49 thf(f148,plain,(
% 1.72/1.49 ~spl1_1),
% 1.72/1.49 inference(avatar_contradiction_clause,[status(thm)],[f147])).
% 1.72/1.49 thf(f147,plain,(
% 1.72/1.49 $false | ~spl1_1),
% 1.72/1.49 inference(equality_resolution,[status(thm)],[f142])).
% 1.72/1.49 thf(f142,plain,(
% 1.72/1.49 ( ! [X0 : 'type/nums/num' > 'type/realax/real'] : (((X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != sK0)) ) | ~spl1_1),
% 1.72/1.49 inference(equality_resolution,[status(thm)],[f141])).
% 1.72/1.49 thf(f141,plain,(
% 1.72/1.49 ( ! [X0 : 'type/nums/num' > 'type/realax/real',X1 : 'type/realax/real'] : ((sK0 != X1) | ((X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != X1)) ) | ~spl1_1),
% 1.72/1.49 inference(beta_eta_normalization,[status(thm)],[f140])).
% 1.72/1.49 thf(f140,plain,(
% 1.72/1.49 ( ! [X0 : 'type/nums/num' > 'type/realax/real',X1 : 'type/realax/real'] : (((X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != X1) | (((^[Y0 : 'type/realax/real']: (sK0)) @ (sK4 @ X0 @ (^[Y0 : 'type/realax/real']: (sK0)) @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != X1)) ) | ~spl1_1),
% 1.72/1.49 inference(trivial_inequality_removal,[status(thm)],[f139])).
% 1.72/1.49 thf(f139,plain,(
% 1.72/1.49 ( ! [X0 : 'type/nums/num' > 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | (((^[Y0 : 'type/realax/real']: (sK0)) @ (sK4 @ X0 @ (^[Y0 : 'type/realax/real']: (sK0)) @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != X1) | ((X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != X1)) ) | ~spl1_1),
% 1.72/1.49 inference(superposition,[status(thm)],[f17,f113])).
% 1.72/1.49 thf(f113,plain,(
% 1.72/1.49 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/nums/num' > 'type/realax/real'] : ((('const/iterate/polynomial_function' @ X0) = $true) | ((X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != X2) | ((X0 @ (sK4 @ X1 @ X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != X2)) ) | ~spl1_1),
% 1.72/1.49 inference(avatar_component_clause,[status(thm)],[f112])).
% 1.72/1.49 thf(f112,definition,(
% 1.72/1.49 spl1_1 <=> ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/nums/num' > 'type/realax/real'] : ((('const/iterate/polynomial_function' @ X0) = $true) | ((X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != X2) | ((X0 @ (sK4 @ X1 @ X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != X2))),
% 1.72/1.49 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.72/1.49 thf(f17,plain,(
% 1.72/1.49 ($true != ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: (sK0))))),
% 1.72/1.49 inference(cnf_transformation,[status(thm)],[f13])).
% 1.72/1.49 thf(f13,plain,(
% 1.72/1.49 ($true != ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: (sK0))))),
% 1.72/1.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f11,f12])).
% 1.72/1.49 thf(f12,plain,(
% 1.72/1.49 ? [X0 : 'type/realax/real'] : (('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: (X0))) != $true) => ($true != ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: (sK0))))),
% 1.72/1.49 introduced(definition,[],[choice_axiom])).
% 1.72/1.49 thf(f11,plain,(
% 1.72/1.49 ? [X0 : 'type/realax/real'] : (('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: (X0))) != $true)),
% 1.72/1.49 inference(ennf_transformation,[status(thm)],[f10])).
% 1.72/1.49 thf(f10,plain,(
% 1.72/1.49 ~! [X0 : 'type/realax/real'] : (('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: (X0))) = $true)),
% 1.72/1.49 inference(fool_elimination,[status(thm)],[f9])).
% 1.72/1.49 thf(f9,plain,(
% 1.72/1.49 ~! [X0 : 'type/realax/real'] : ('const/iterate/polynomial_function' @ (^[X1 : 'type/realax/real'] : (X0)))),
% 1.72/1.49 inference(rectify,[status(thm)],[f6])).
% 1.72/1.49 thf(f6,negated_conjecture,(
% 1.72/1.49 ~! [X0 : 'type/realax/real'] : ('const/iterate/polynomial_function' @ (^[X1 : 'type/realax/real'] : (X0)))),
% 1.72/1.49 inference(negated_conjecture,[status(cth)],[f5])).
% 1.72/1.49 thf(f5,conjecture,(
% 1.72/1.49 ! [X0 : 'type/realax/real'] : ('const/iterate/polynomial_function' @ (^[X1 : 'type/realax/real'] : (X0)))),
% 1.72/1.49 file('/export/starexec/sandbox/tmp/tmp.09rWDTPhcM/DTF2THF_2760.p','thm/iterate/POLYNOMIAL_FUNCTION_CONST_')).
% 1.72/1.49 thf(f136,plain,(
% 1.72/1.49 spl1_1 | ~spl1_2),
% 1.72/1.49 inference(avatar_split_clause,[status(thm)],[f126,f115,f112])).
% 1.72/1.49 thf(f115,definition,(
% 1.72/1.49 spl1_2 <=> ($true = ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ (sK8 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))),
% 1.72/1.49 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.72/1.49 thf(f126,plain,(
% 1.72/1.49 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/nums/num' > 'type/realax/real'] : (((X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != X2) | ((X0 @ (sK4 @ X1 @ X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != X2) | (('const/iterate/polynomial_function' @ X0) = $true)) ) | ~spl1_2),
% 1.72/1.49 inference(trivial_inequality_removal,[status(thm)],[f125])).
% 1.72/1.49 thf(f125,plain,(
% 1.72/1.49 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/nums/num' > 'type/realax/real'] : (((X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != X2) | (('const/iterate/polynomial_function' @ X0) = $true) | ((X0 @ (sK4 @ X1 @ X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != X2) | ($true = $false)) ) | ~spl1_2),
% 1.72/1.49 inference(duplicate_literal_removal,[status(thm)],[f120])).
% 1.72/1.49 thf(f120,plain,(
% 1.72/1.49 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/nums/num' > 'type/realax/real'] : ((('const/iterate/polynomial_function' @ X0) = $true) | ($true = $false) | ($true = $false) | ((X0 @ (sK4 @ X1 @ X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != X2) | ((X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != X2)) ) | ~spl1_2),
% 1.72/1.49 inference(superposition,[status(thm)],[f108,f117])).
% 1.72/1.49 thf(f117,plain,(
% 1.72/1.49 ($true = ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ (sK8 @ ('const/nums/NUMERAL' @ 'const/nums/_0')))) | ~spl1_2),
% 1.72/1.49 inference(avatar_component_clause,[status(thm)],[f115])).
% 1.72/1.49 thf(f108,plain,(
% 1.72/1.49 ( ! [X2 : 'type/realax/real' > 'type/realax/real',X3 : 'type/nums/num',X0 : 'type/nums/num' > 'type/realax/real',X1 : 'type/realax/real'] : (($false = ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ (sK8 @ X3))) | ($false = ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X3 @ (sK8 @ X3))) | ($true = ('const/iterate/polynomial_function' @ X2)) | ((X2 @ (sK4 @ X0 @ X2 @ X3)) != X1) | ((X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != X1)) )),
% 1.72/1.49 inference(binary_proxy_clausification,[status(thm)],[f106])).
% 1.72/1.49 thf(f106,plain,(
% 1.72/1.49 ( ! [X2 : 'type/realax/real' > 'type/realax/real',X3 : 'type/nums/num',X0 : 'type/nums/num' > 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/iterate/polynomial_function' @ X2)) | (('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ (sK8 @ X3)) != ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X3 @ (sK8 @ X3))) | ((X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != X1) | ((X2 @ (sK4 @ X0 @ X2 @ X3)) != X1)) )),
% 1.72/1.49 inference(negative_extensionality,[status(thm)],[f95])).
% 1.72/1.49 thf(f95,plain,(
% 1.72/1.49 ( ! [X2 : 'type/realax/real' > 'type/realax/real',X3 : 'type/nums/num',X0 : 'type/nums/num' > 'type/realax/real',X1 : 'type/realax/real'] : ((('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X3)) | ($true = ('const/iterate/polynomial_function' @ X2)) | ((X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != X1) | ((X2 @ (sK4 @ X0 @ X2 @ X3)) != X1)) )),
% 1.72/1.49 inference(constrained_superposition,[status(thm)],[f68,f14])).
% 1.72/1.49 thf(f14,plain,(
% 1.72/1.49 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_mul' @ X0 @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) = X0)) )),
% 1.72/1.49 inference(cnf_transformation,[status(thm)],[f1])).
% 1.72/1.49 thf(f1,axiom,(
% 1.72/1.49 ! [X0 : 'type/realax/real'] : (('const/realax/real_mul' @ X0 @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) = X0)),
% 1.72/1.49 file('/export/starexec/sandbox/tmp/tmp.09rWDTPhcM/DTF2THF_2760.p','thm/realarith/REAL_MUL_RID_')).
% 1.72/1.49 thf(f68,plain,(
% 1.72/1.49 ( ! [X2 : 'type/nums/num',X0 : 'type/nums/num' > 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : (((X1 @ (sK4 @ X0 @ X1 @ X2)) != ('const/realax/real_mul' @ (X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) | (('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X2) != ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) | (('const/iterate/polynomial_function' @ X1) = $true)) )),
% 1.72/1.49 inference(superposition,[status(thm)],[f67,f16])).
% 1.72/1.49 thf(f16,plain,(
% 1.72/1.49 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) = ('const/realax/real_pow' @ X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')))) )),
% 1.72/1.49 inference(cnf_transformation,[status(thm)],[f2])).
% 1.72/1.49 thf(f2,axiom,(
% 1.72/1.49 ! [X0 : 'type/realax/real'] : (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) = ('const/realax/real_pow' @ X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 1.72/1.49 file('/export/starexec/sandbox/tmp/tmp.09rWDTPhcM/DTF2THF_2760.p','thm/realax/real_pow_0')).
% 1.72/1.49 thf(f67,plain,(
% 1.72/1.49 ( ! [X2 : 'type/realax/real' > 'type/realax/real',X3 : 'type/nums/num' > 'type/realax/real',X0 : 'type/nums/num',X1 : 'type/nums/num'] : ((('const/realax/real_mul' @ (X3 @ X1) @ ('const/realax/real_pow' @ (sK4 @ X3 @ X2 @ X0) @ X1)) != (X2 @ (sK4 @ X3 @ X2 @ X0))) | (('const/iterate/..' @ X1 @ X1) != ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X0)) | ($true = ('const/iterate/polynomial_function' @ X2))) )),
% 1.72/1.49 inference(beta_eta_normalization,[status(thm)],[f66])).
% 1.72/1.49 thf(f66,plain,(
% 1.72/1.49 ( ! [X2 : 'type/realax/real' > 'type/realax/real',X3 : 'type/nums/num' > 'type/realax/real',X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($true = ('const/iterate/polynomial_function' @ X2)) | ((X2 @ (sK4 @ X3 @ X2 @ X0)) != ((^[Y0 : 'type/nums/num']: ('const/realax/real_mul' @ (X3 @ Y0) @ ('const/realax/real_pow' @ (sK4 @ X3 @ X2 @ X0) @ Y0))) @ X1)) | (('const/iterate/..' @ X1 @ X1) != ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X0))) )),
% 1.72/1.49 inference(equality_resolution,[status(thm)],[f55])).
% 1.72/1.49 thf(f55,plain,(
% 1.72/1.49 ( ! [X2 : 'type/nums/num',X3 : 'type/nums/num' > 'type/realax/real',X0 : 'type/nums/num' > 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real',X4 : 'type/nums/num'] : (((^[Y0 : 'type/nums/num']: ('const/realax/real_mul' @ (X0 @ Y0) @ ('const/realax/real_pow' @ (sK4 @ X0 @ X1 @ X2) @ Y0))) != X3) | (('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X2) != ('const/iterate/..' @ X4 @ X4)) | (('const/iterate/polynomial_function' @ X1) = $true) | ((X1 @ (sK4 @ X0 @ X1 @ X2)) != (X3 @ X4))) )),
% 1.72/1.49 inference(constrained_superposition,[status(thm)],[f34,f15])).
% 1.72/1.49 thf(f15,plain,(
% 1.72/1.49 ( ! [X0 : 'type/nums/num' > 'type/realax/real',X1 : 'type/nums/num'] : ((('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X1) @ X0) = (X0 @ X1))) )),
% 1.72/1.49 inference(cnf_transformation,[status(thm)],[f3])).
% 1.72/1.49 thf(f3,axiom,(
% 1.72/1.49 ! [X0 : 'type/nums/num' > 'type/realax/real',X1 : 'type/nums/num'] : (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X1) @ X0) = (X0 @ X1))),
% 1.72/1.49 file('/export/starexec/sandbox/tmp/tmp.09rWDTPhcM/DTF2THF_2760.p','thm/iterate/SUM_SING_NUMSEG_')).
% 1.72/1.49 thf(f34,plain,(
% 1.72/1.49 ( ! [X2 : 'type/nums/num',X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/nums/num' > 'type/realax/real'] : (((X0 @ (sK4 @ X1 @ X0 @ X2)) != ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X2) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_mul' @ (X1 @ Y0) @ ('const/realax/real_pow' @ (sK4 @ X1 @ X0 @ X2) @ Y0))))) | (('const/iterate/polynomial_function' @ X0) = $true)) )),
% 1.72/1.49 inference(equality_proxy_clausification,[status(thm)],[f33])).
% 1.72/1.49 thf(f33,plain,(
% 1.72/1.49 ( ! [X2 : 'type/nums/num',X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/nums/num' > 'type/realax/real'] : ((('const/iterate/polynomial_function' @ X0) = $true) | (((X0 @ (sK4 @ X1 @ X0 @ X2)) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X2) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_mul' @ (X1 @ Y0) @ ('const/realax/real_pow' @ (sK4 @ X1 @ X0 @ X2) @ Y0))))) = $false)) )),
% 1.72/1.49 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.72/1.49 thf(f32,plain,(
% 1.72/1.49 ( ! [X2 : 'type/nums/num',X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/nums/num' > 'type/realax/real'] : ((('const/iterate/polynomial_function' @ X0) = $true) | (((^[Y0 : 'type/realax/real']: ((X0 @ Y0) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X2) @ (^[Y1 : 'type/nums/num']: ('const/realax/real_mul' @ (X1 @ Y1) @ ('const/realax/real_pow' @ Y0 @ Y1)))))) @ (sK4 @ X1 @ X0 @ X2)) = $false)) )),
% 1.72/1.49 inference(sigma_clausification,[status(thm)],[f31])).
% 1.72/1.49 thf(f31,plain,(
% 1.72/1.49 ( ! [X2 : 'type/nums/num',X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/nums/num' > 'type/realax/real'] : (((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: ((X0 @ Y0) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X2) @ (^[Y1 : 'type/nums/num']: ('const/realax/real_mul' @ (X1 @ Y1) @ ('const/realax/real_pow' @ Y0 @ Y1))))))) = $false) | (('const/iterate/polynomial_function' @ X0) = $true)) )),
% 1.72/1.49 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.72/1.49 thf(f30,plain,(
% 1.72/1.49 ( ! [X2 : 'type/nums/num',X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/nums/num' > 'type/realax/real'] : (($false = ((^[Y0 : 'type/nums/num']: (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: ((X0 @ Y1) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ Y0) @ (^[Y2 : 'type/nums/num']: ('const/realax/real_mul' @ (X1 @ Y2) @ ('const/realax/real_pow' @ Y1 @ Y2)))))))) @ X2)) | (('const/iterate/polynomial_function' @ X0) = $true)) )),
% 1.72/1.49 inference(pi_clausification,[status(thm)],[f29])).
% 1.72/1.49 thf(f29,plain,(
% 1.72/1.49 ( ! [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/nums/num' > 'type/realax/real'] : ((('const/iterate/polynomial_function' @ X0) = $true) | ($false = (?? @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: ((X0 @ Y1) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ Y0) @ (^[Y2 : 'type/nums/num']: ('const/realax/real_mul' @ (X1 @ Y2) @ ('const/realax/real_pow' @ Y1 @ Y2))))))))))) )),
% 1.72/1.49 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.72/1.49 thf(f28,plain,(
% 1.72/1.49 ( ! [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/nums/num' > 'type/realax/real'] : ((('const/iterate/polynomial_function' @ X0) = $true) | (((^[Y0 : 'type/nums/num' > 'type/realax/real']: (?? @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: (!! @ 'type/realax/real' @ (^[Y2 : 'type/realax/real']: ((X0 @ Y2) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ Y1) @ (^[Y3 : 'type/nums/num']: ('const/realax/real_mul' @ (Y0 @ Y3) @ ('const/realax/real_pow' @ Y2 @ Y3)))))))))) @ X1) = $false)) )),
% 1.72/1.49 inference(pi_clausification,[status(thm)],[f19])).
% 1.72/1.49 thf(f19,plain,(
% 1.72/1.49 ( ! [X0 : 'type/realax/real' > 'type/realax/real'] : (((?? @ ('type/nums/num' > 'type/realax/real') @ (^[Y0 : 'type/nums/num' > 'type/realax/real']: (?? @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: (!! @ 'type/realax/real' @ (^[Y2 : 'type/realax/real']: ((X0 @ Y2) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ Y1) @ (^[Y3 : 'type/nums/num']: ('const/realax/real_mul' @ (Y0 @ Y3) @ ('const/realax/real_pow' @ Y2 @ Y3))))))))))) = $false) | (('const/iterate/polynomial_function' @ X0) = $true)) )),
% 1.72/1.49 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.72/1.49 thf(f18,plain,(
% 1.72/1.49 ( ! [X0 : 'type/realax/real' > 'type/realax/real'] : ((('const/iterate/polynomial_function' @ X0) = (?? @ ('type/nums/num' > 'type/realax/real') @ (^[Y0 : 'type/nums/num' > 'type/realax/real']: (?? @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: (!! @ 'type/realax/real' @ (^[Y2 : 'type/realax/real']: ((X0 @ Y2) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ Y1) @ (^[Y3 : 'type/nums/num']: ('const/realax/real_mul' @ (Y0 @ Y3) @ ('const/realax/real_pow' @ Y2 @ Y3))))))))))))) )),
% 1.72/1.49 inference(cnf_transformation,[status(thm)],[f8])).
% 1.72/1.49 thf(f8,plain,(
% 1.72/1.49 ! [X0 : 'type/realax/real' > 'type/realax/real'] : (('const/iterate/polynomial_function' @ X0) = (?? @ ('type/nums/num' > 'type/realax/real') @ (^[Y0 : 'type/nums/num' > 'type/realax/real']: (?? @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: (!! @ 'type/realax/real' @ (^[Y2 : 'type/realax/real']: ((X0 @ Y2) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ Y1) @ (^[Y3 : 'type/nums/num']: ('const/realax/real_mul' @ (Y0 @ Y3) @ ('const/realax/real_pow' @ Y2 @ Y3))))))))))))),
% 1.72/1.49 inference(fool_elimination,[status(thm)],[f4])).
% 1.72/1.49 thf(f4,axiom,(
% 1.72/1.49 ! [X0 : 'type/realax/real' > 'type/realax/real'] : (('const/iterate/polynomial_function' @ X0) = ? [X1 : 'type/nums/num',X2 : 'type/nums/num' > 'type/realax/real'] : ! [X3 : 'type/realax/real'] : ((X0 @ X3) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X1) @ (^[X4 : 'type/nums/num'] : ('const/realax/real_mul' @ (X2 @ X4) @ ('const/realax/real_pow' @ X3 @ X4))))))),
% 1.72/1.49 file('/export/starexec/sandbox/tmp/tmp.09rWDTPhcM/DTF2THF_2760.p','thm/iterate/polynomial_function_')).
% 1.72/1.49 thf(f118,plain,(
% 1.72/1.49 spl1_1 | spl1_2),
% 1.72/1.49 inference(avatar_split_clause,[status(thm)],[f110,f115,f112])).
% 1.72/1.49 thf(f110,plain,(
% 1.72/1.49 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/nums/num' > 'type/realax/real'] : ((('const/iterate/polynomial_function' @ X0) = $true) | ((X0 @ (sK4 @ X1 @ X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != X2) | ((X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != X2) | ($true = ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ (sK8 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))) )),
% 1.72/1.49 inference(trivial_inequality_removal,[status(thm)],[f109])).
% 1.72/1.49 thf(f109,plain,(
% 1.72/1.49 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/nums/num' > 'type/realax/real'] : (((X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != X2) | ($true != $true) | (('const/iterate/polynomial_function' @ X0) = $true) | ((X0 @ (sK4 @ X1 @ X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != X2) | ($true = ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ (sK8 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))) )),
% 1.72/1.49 inference(equality_factoring,[status(thm)],[f107])).
% 1.72/1.49 thf(f107,plain,(
% 1.72/1.49 ( ! [X2 : 'type/realax/real' > 'type/realax/real',X3 : 'type/nums/num',X0 : 'type/nums/num' > 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ (sK8 @ X3))) | ($true = ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X3 @ (sK8 @ X3))) | ($true = ('const/iterate/polynomial_function' @ X2)) | ((X2 @ (sK4 @ X0 @ X2 @ X3)) != X1) | ((X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != X1)) )),
% 1.72/1.49 inference(binary_proxy_clausification,[status(thm)],[f106])).
% 1.72/1.49 % SZS output end Proof for DTF2THF_2760
% 1.72/1.49 % (2857)------------------------------
% 1.72/1.49 % (2857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.49 % (2857)Termination reason: Refutation
% 1.72/1.49
% 1.72/1.49 % (2857)Memory used [KB]: 6140
% 1.72/1.49 % (2857)Time elapsed: 0.042 s
% 1.72/1.49 % (2857)Instructions burned: 78 (million)
% 1.72/1.49 % (2857)------------------------------
% 1.72/1.49 % (2857)------------------------------
% 1.72/1.49 % (2856)Success in time 0.05 s
%------------------------------------------------------------------------------