%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA127^1 : 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 : n026.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 08:38:56 AM UTC 2026
% Result : Theorem 1.70s 1.48s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 263 ( 88 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 476 ( 61 ~; 48 |; 17 &; 340 @)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 9 con; 0-3 aty)
% Number of variables : 120 ( 64 ^; 50 !; 6 ?; 120 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_2,type,
'const/realax/real_neg': 'type/realax/real' > 'type/realax/real' ).
thf(func_def_3,type,
'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_4,type,
'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
thf(func_def_10,type,
sK0: 'type/realax/real' > 'type/realax/real' ).
thf(func_def_11,type,
sK1: 'type/realax/real' > 'type/realax/real' ).
thf(func_def_13,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK4: ( 'type/realax/real' > 'type/realax/real' ) > 'type/realax/real' ).
thf(func_def_15,type,
sK5: ( 'type/realax/real' > 'type/realax/real' ) > 'type/realax/real' ).
thf(func_def_16,type,
sK6: 'type/realax/real' ).
thf(func_def_17,type,
sK7: 'type/realax/real' ).
thf(func_def_18,type,
sK8: ( 'type/realax/real' > 'type/realax/real' ) > ( 'type/realax/real' > 'type/realax/real' ) > 'type/realax/real' ).
thf(func_def_19,type,
sK9: ( 'type/realax/real' > 'type/realax/real' ) > 'type/realax/real' ).
thf(func_def_20,type,
sK10: ( 'type/realax/real' > 'type/realax/real' ) > ( 'type/realax/real' > 'type/realax/real' ) > 'type/realax/real' ).
thf(func_def_21,type,
sK11: ( 'type/realax/real' > 'type/realax/real' ) > ( 'type/realax/real' > 'type/realax/real' ) > ( 'type/realax/real' > 'type/realax/real' ) > 'type/realax/real' ).
thf(func_def_22,type,
sK12: ( 'type/realax/real' > 'type/realax/real' ) > ( 'type/realax/real' > 'type/realax/real' ) > 'type/realax/real' ).
thf(func_def_23,type,
sK13: ( 'type/realax/real' > 'type/realax/real' ) > 'type/realax/real' ).
thf(func_def_24,type,
sK14: 'type/realax/real' ).
thf(func_def_25,type,
sK15: 'type/realax/real' ).
thf(func_def_26,type,
sK16: ( 'type/realax/real' > 'type/realax/real' ) > 'type/realax/real' ).
thf(func_def_27,type,
sK17: ( 'type/realax/real' > 'type/realax/real' ) > 'type/realax/real' ).
thf(func_def_28,type,
sK18: 'type/realax/real' ).
thf(f291,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f207,f251,f290]) ).
thf(f290,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f289]) ).
thf(f289,plain,
( $false
| ~ spl2_2 ),
inference(subsumption_resolution,[status(thm)],[f287,f18]) ).
thf(f18,plain,
( $true
= ( 'const/iterate/polynomial_function' @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $true
!= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_sub' @ ( sK0 @ Y0 ) @ ( sK1 @ Y0 ) ) ) )
& ( ( 'const/iterate/polynomial_function' @ sK1 )
= $true )
& ( $true
= ( 'const/iterate/polynomial_function' @ sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f15,f16]) ).
thf(f16,plain,
( ? [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( $true
!= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_sub' @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) )
& ( ( 'const/iterate/polynomial_function' @ X1 )
= $true )
& ( ( 'const/iterate/polynomial_function' @ X0 )
= $true ) )
=> ( ( $true
!= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_sub' @ ( sK0 @ Y0 ) @ ( sK1 @ Y0 ) ) ) )
& ( ( 'const/iterate/polynomial_function' @ sK1 )
= $true )
& ( $true
= ( 'const/iterate/polynomial_function' @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
? [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( $true
!= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_sub' @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) )
& ( ( 'const/iterate/polynomial_function' @ X1 )
= $true )
& ( ( 'const/iterate/polynomial_function' @ X0 )
= $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
? [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( $true
!= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_sub' @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) )
& ( ( 'const/iterate/polynomial_function' @ X0 )
= $true )
& ( ( 'const/iterate/polynomial_function' @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
~ ! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( ( ( 'const/iterate/polynomial_function' @ X0 )
= $true )
& ( ( 'const/iterate/polynomial_function' @ X1 )
= $true ) )
=> ( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_sub' @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X0 )
& ( 'const/iterate/polynomial_function' @ X1 ) )
=> ( 'const/iterate/polynomial_function'
@ ^ [X2: 'type/realax/real'] : ( 'const/realax/real_sub' @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X0 )
& ( 'const/iterate/polynomial_function' @ X1 ) )
=> ( 'const/iterate/polynomial_function'
@ ^ [X2: 'type/realax/real'] : ( 'const/realax/real_sub' @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X0 )
& ( 'const/iterate/polynomial_function' @ X1 ) )
=> ( 'const/iterate/polynomial_function'
@ ^ [X2: 'type/realax/real'] : ( 'const/realax/real_sub' @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PRKencDl8S/DTF2THF_23358.p','thm/iterate/POLYNOMIAL_FUNCTION_SUB_') ).
thf(f287,plain,
( ( $true
!= ( 'const/iterate/polynomial_function' @ sK0 ) )
| ~ spl2_2 ),
inference(beta_eta_normalization,[status(thm)],[f286]) ).
thf(f286,plain,
( ( $true
!= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] :
( sK0
@ ( ^ [Y1: 'type/realax/real'] : Y1
@ Y0 ) ) ) )
| ~ spl2_2 ),
inference(equality_resolution,[status(thm)],[f206]) ).
thf(f206,plain,
( ! [X0: 'type/realax/real' > 'type/realax/real'] :
( ( ( X0
@ ( sK10
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK1 @ Y0 ) )
@ X0 ) )
!= ( sK0
@ ( sK10
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK1 @ Y0 ) )
@ X0 ) ) )
| ( ( 'const/iterate/polynomial_function' @ X0 )
!= $true ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f205]) ).
thf(f205,definition,
( spl2_2
<=> ! [X0: 'type/realax/real' > 'type/realax/real'] :
( ( ( X0
@ ( sK10
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK1 @ Y0 ) )
@ X0 ) )
!= ( sK0
@ ( sK10
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK1 @ Y0 ) )
@ X0 ) ) )
| ( ( 'const/iterate/polynomial_function' @ X0 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f251,plain,
spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f250]) ).
thf(f250,plain,
( $false
| spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f241]) ).
thf(f241,plain,
( ( $false = $true )
| spl2_1 ),
inference(superposition,[status(thm)],[f19,f233]) ).
thf(f233,plain,
( ( ( 'const/iterate/polynomial_function' @ sK1 )
= $false )
| spl2_1 ),
inference(beta_eta_normalization,[status(thm)],[f232]) ).
thf(f232,plain,
( ( $false
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] :
( sK1
@ ( ^ [Y1: 'type/realax/real'] : Y1
@ Y0 ) ) ) )
| spl2_1 ),
inference(equality_resolution,[status(thm)],[f228]) ).
thf(f228,plain,
( ! [X0: 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/realax/real_neg' @ ( X0 @ ( sK16 @ X0 ) ) )
!= ( 'const/realax/real_neg' @ ( sK1 @ ( sK16 @ X0 ) ) ) )
| ( ( 'const/iterate/polynomial_function' @ X0 )
= $false ) )
| spl2_1 ),
inference(beta_eta_normalization,[status(thm)],[f227]) ).
thf(f227,plain,
( ! [X0: 'type/realax/real' > 'type/realax/real'] :
( ( ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK1 @ Y0 ) )
@ ( sK16 @ X0 ) )
!= ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( X0 @ Y0 ) )
@ ( sK16 @ X0 ) ) )
| ( ( 'const/iterate/polynomial_function' @ X0 )
= $false ) )
| spl2_1 ),
inference(negative_extensionality,[status(thm)],[f222]) ).
thf(f222,plain,
( ! [X0: 'type/realax/real' > 'type/realax/real'] :
( ( ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( X0 @ Y0 ) ) )
!= ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK1 @ Y0 ) ) ) )
| ( ( 'const/iterate/polynomial_function' @ X0 )
= $false ) )
| spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f210]) ).
thf(f210,plain,
( ! [X0: 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X0 )
= $false )
| ( ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( X0 @ Y0 ) ) )
!= ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK1 @ Y0 ) ) ) )
| ( $true != $true ) )
| spl2_1 ),
inference(constrained_superposition,[status(thm)],[f203,f25]) ).
thf(f25,plain,
! [X0: 'type/realax/real' > 'type/realax/real'] :
( ( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( X0 @ Y0 ) ) ) )
| ( ( 'const/iterate/polynomial_function' @ X0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ X0 )
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( X0 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ X0 )
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( X0 @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function'
@ ^ [X1: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( X0 @ X1 ) ) )
= ( 'const/iterate/polynomial_function' @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.PRKencDl8S/DTF2THF_23358.p','thm/iterate/POLYNOMIAL_FUNCTION_NEG_') ).
thf(f203,plain,
( ( $true
!= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK1 @ Y0 ) ) ) )
| spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f201]) ).
thf(f201,definition,
( spl2_1
<=> ( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK1 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f19,plain,
( ( 'const/iterate/polynomial_function' @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f207,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f198,f205,f201]) ).
thf(f198,plain,
! [X0: 'type/realax/real' > 'type/realax/real'] :
( ( $true
!= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK1 @ Y0 ) ) ) )
| ( ( X0
@ ( sK10
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK1 @ Y0 ) )
@ X0 ) )
!= ( sK0
@ ( sK10
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK1 @ Y0 ) )
@ X0 ) ) )
| ( ( 'const/iterate/polynomial_function' @ X0 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f197]) ).
thf(f197,plain,
! [X0: 'type/realax/real' > 'type/realax/real'] :
( ( $true
!= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] :
( 'const/realax/real_neg'
@ ( ^ [Y1: 'type/realax/real'] :
( sK1
@ ( ^ [Y2: 'type/realax/real'] : Y2
@ Y1 ) )
@ Y0 ) ) ) )
| ( ( 'const/iterate/polynomial_function' @ X0 )
!= $true )
| ( ( sK0
@ ( sK10
@ ^ [Y0: 'type/realax/real'] :
( 'const/realax/real_neg'
@ ( ^ [Y1: 'type/realax/real'] :
( sK1
@ ( ^ [Y2: 'type/realax/real'] : Y2
@ Y1 ) )
@ Y0 ) )
@ X0 ) )
!= ( X0
@ ( sK10
@ ^ [Y0: 'type/realax/real'] :
( 'const/realax/real_neg'
@ ( ^ [Y1: 'type/realax/real'] :
( sK1
@ ( ^ [Y2: 'type/realax/real'] : Y2
@ Y1 ) )
@ Y0 ) )
@ X0 ) ) ) ),
inference(equality_resolution,[status(thm)],[f191]) ).
thf(f191,plain,
! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( ( sK1
@ ( sK10
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( X1 @ Y0 ) )
@ X0 ) )
!= ( X1
@ ( sK10
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( X1 @ Y0 ) )
@ X0 ) ) )
| ( ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( X1 @ Y0 ) ) )
!= $true )
| ( ( X0
@ ( sK10
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( X1 @ Y0 ) )
@ X0 ) )
!= ( sK0
@ ( sK10
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( X1 @ Y0 ) )
@ X0 ) ) )
| ( ( 'const/iterate/polynomial_function' @ X0 )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f119]) ).
thf(f119,plain,
! [X2: 'type/realax/real',X3: 'type/realax/real',X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/realax/real_sub'
@ ( sK0
@ ( sK10
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( X1 @ Y0 ) )
@ X0 ) )
@ ( sK1
@ ( sK10
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( X1 @ Y0 ) )
@ X0 ) ) )
!= ( 'const/realax/real_sub' @ X2 @ X3 ) )
| ( ( 'const/iterate/polynomial_function' @ X0 )
!= $true )
| ( ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( X1 @ Y0 ) ) )
!= $true )
| ( ( X0
@ ( sK10
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( X1 @ Y0 ) )
@ X0 ) )
!= X2 )
| ( ( X1
@ ( sK10
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( X1 @ Y0 ) )
@ X0 ) )
!= X3 ) ),
inference(constrained_superposition,[status(thm)],[f72,f21]) ).
thf(f21,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_sub' @ X0 @ X1 )
= ( 'const/realax/real_add' @ X0 @ ( 'const/realax/real_neg' @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_sub' @ X0 @ X1 )
= ( 'const/realax/real_add' @ X0 @ ( 'const/realax/real_neg' @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PRKencDl8S/DTF2THF_23358.p','thm/realax/real_sub_') ).
thf(f72,plain,
! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/realax/real_add' @ ( X0 @ ( sK10 @ X1 @ X0 ) ) @ ( X1 @ ( sK10 @ X1 @ X0 ) ) )
!= ( 'const/realax/real_sub' @ ( sK0 @ ( sK10 @ X1 @ X0 ) ) @ ( sK1 @ ( sK10 @ X1 @ X0 ) ) ) )
| ( ( 'const/iterate/polynomial_function' @ X1 )
!= $true )
| ( ( 'const/iterate/polynomial_function' @ X0 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f71]) ).
thf(f71,plain,
! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X1 )
!= $true )
| ( ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_add' @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) )
@ ( sK10 @ X1 @ X0 ) )
!= ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_sub' @ ( sK0 @ Y0 ) @ ( sK1 @ Y0 ) )
@ ( sK10 @ X1 @ X0 ) ) )
| ( ( 'const/iterate/polynomial_function' @ X0 )
!= $true ) ),
inference(negative_extensionality,[status(thm)],[f58]) ).
thf(f58,plain,
! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_sub' @ ( sK0 @ Y0 ) @ ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_add' @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) )
| ( ( 'const/iterate/polynomial_function' @ X0 )
!= $true )
| ( ( 'const/iterate/polynomial_function' @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/iterate/polynomial_function' @ X0 )
!= $true )
| ( ( 'const/iterate/polynomial_function' @ X1 )
!= $true )
| ( ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_sub' @ ( sK0 @ Y0 ) @ ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_add' @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) ),
inference(constrained_superposition,[status(thm)],[f20,f23]) ).
thf(f23,plain,
! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_add' @ ( X1 @ Y0 ) @ ( X0 @ Y0 ) ) ) )
| ( ( 'const/iterate/polynomial_function' @ X1 )
!= $true )
| ( ( 'const/iterate/polynomial_function' @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X0 )
!= $true )
| ( ( 'const/iterate/polynomial_function' @ X1 )
!= $true )
| ( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_add' @ ( X1 @ Y0 ) @ ( X0 @ Y0 ) ) ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_add' @ ( X1 @ Y0 ) @ ( X0 @ Y0 ) ) ) )
| ( ( 'const/iterate/polynomial_function' @ X1 )
!= $true )
| ( ( 'const/iterate/polynomial_function' @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( ( ( 'const/iterate/polynomial_function' @ X1 )
= $true )
& ( ( 'const/iterate/polynomial_function' @ X0 )
= $true ) )
=> ( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_add' @ ( X1 @ Y0 ) @ ( X0 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X1 )
& ( 'const/iterate/polynomial_function' @ X0 ) )
=> ( 'const/iterate/polynomial_function'
@ ^ [X2: 'type/realax/real'] : ( 'const/realax/real_add' @ ( X1 @ X2 ) @ ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: 'type/realax/real' > 'type/realax/real',X0: 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X0 )
& ( 'const/iterate/polynomial_function' @ X1 ) )
=> ( 'const/iterate/polynomial_function'
@ ^ [X2: 'type/realax/real'] : ( 'const/realax/real_add' @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PRKencDl8S/DTF2THF_23358.p','thm/iterate/POLYNOMIAL_FUNCTION_ADD_') ).
thf(f20,plain,
( $true
!= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_sub' @ ( sK0 @ Y0 ) @ ( sK1 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA127^1 : TPTP v9.2.1. Released v7.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n026.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 03:51:40 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.48 ---- Original DTF file ---
% 0.20/0.48 thf(spec,logic,$$dhol).
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 % File : ANA127^1 : TPTP v9.2.1. Released v7.0.0.
% 0.20/0.48 % Domain : Analysis
% 0.20/0.48 % Problem : POLYNOMIAL_FUNCTION_SUB
% 0.20/0.48 % Version : Especial.
% 0.20/0.48 % English :
% 0.20/0.48
% 0.20/0.48 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.20/0.48 % Source : [Kal16]
% 0.20/0.48 % Names : POLYNOMIAL_FUNCTION_SUB_.p [Kal16]
% 0.20/0.48
% 0.20/0.48 % Status : Theorem
% 0.20/0.48 % Rating : 0.56 v9.1.0, 0.50 v8.2.0, 0.54 v8.1.0, 0.55 v7.5.0, 0.43 v7.4.0, 0.44 v7.3.0, 0.56 v7.2.0, 0.50 v7.1.0, 0.62 v7.0.0
% 0.20/0.48 % Syntax : Number of formulae : 9 ( 2 unt; 5 typ; 0 def)
% 0.20/0.48 % Number of atoms : 10 ( 2 equ; 0 cnn)
% 0.20/0.48 % Maximal formula atoms : 3 ( 2 avg)
% 0.20/0.48 % Number of connectives : 27 ( 0 ~; 0 |; 2 &; 23 @)
% 0.20/0.48 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.20/0.48 % Maximal formula depth : 9 ( 6 avg)
% 0.20/0.48 % Number of types : 2 ( 1 usr)
% 0.20/0.48 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.20/0.48 % Number of symbols : 5 ( 4 usr; 0 con; 1-2 aty)
% 0.20/0.48 % Number of variables : 10 ( 3 ^; 7 !; 0 ?; 10 :)
% 0.20/0.48 % SPC : TH0_THM_EQU_NAR
% 0.20/0.48
% 0.20/0.48 % Comments : Exported from core HOL Light.
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 thf('thf_type_type/realax/real',type,
% 0.20/0.48 'type/realax/real': $tType ).
% 0.20/0.48
% 0.20/0.48 thf('thf_const_const/realax/real_sub',type,
% 0.20/0.48 'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 0.20/0.48
% 0.20/0.48 thf('thf_const_const/realax/real_neg',type,
% 0.20/0.48 'const/realax/real_neg': 'type/realax/real' > 'type/realax/real' ).
% 0.20/0.48
% 0.20/0.48 thf('thf_const_const/realax/real_add',type,
% 0.20/0.48 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 0.20/0.48
% 0.20/0.48 thf('thf_const_const/iterate/polynomial_function',type,
% 0.20/0.48 'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
% 0.20/0.48
% 0.20/0.48 thf('thm/iterate/POLYNOMIAL_FUNCTION_ADD_',axiom,
% 0.20/0.48 ! [A: 'type/realax/real' > 'type/realax/real',A0: 'type/realax/real' > 'type/realax/real'] :
% 0.20/0.48 ( ( ( 'const/iterate/polynomial_function' @ A )
% 0.20/0.48 & ( 'const/iterate/polynomial_function' @ A0 ) )
% 0.20/0.48 => ( 'const/iterate/polynomial_function'
% 0.20/0.48 @ ^ [A1: 'type/realax/real'] : ( 'const/realax/real_add' @ ( A @ A1 ) @ ( A0 @ A1 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf('thm/iterate/POLYNOMIAL_FUNCTION_NEG_',axiom,
% 0.20/0.48 ! [A: 'type/realax/real' > 'type/realax/real'] :
% 0.20/0.48 ( ( 'const/iterate/polynomial_function'
% 0.20/0.48 @ ^ [A0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( A @ A0 ) ) )
% 0.20/0.48 = ( 'const/iterate/polynomial_function' @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf('thm/realax/real_sub_',axiom,
% 0.20/0.48 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 0.20/0.48 ( ( 'const/realax/real_sub' @ A @ A0 )
% 0.20/0.48 = ( 'const/realax/real_add' @ A @ ( 'const/realax/real_neg' @ A0 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf('thm/iterate/POLYNOMIAL_FUNCTION_SUB_',conjecture,
% 0.20/0.48 ! [A: 'type/realax/real' > 'type/realax/real',A0: 'type/realax/real' > 'type/realax/real'] :
% 0.20/0.48 ( ( ( 'const/iterate/polynomial_function' @ A )
% 0.20/0.48 & ( 'const/iterate/polynomial_function' @ A0 ) )
% 0.20/0.48 => ( 'const/iterate/polynomial_function'
% 0.20/0.48 @ ^ [A1: 'type/realax/real'] : ( 'const/realax/real_sub' @ ( A @ A1 ) @ ( A0 @ A1 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 ------------------------
% 1.70/1.41 ---- Embedded in THF ---
% 1.70/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.70/1.41 %%% Generated on Tue Feb 24 03:51:41 EST 2026
% 1.70/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.70/1.41 %%% Logic specification used:
% 1.70/1.41 %%% thf(spec, logic, $$dhol).
% 1.70/1.41
% 1.70/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.PRKencDl8S/DTF2DTF23358.p
% See solution above
% 1.70/1.41 ------------------------
% 1.70/1.42 ---- Cleaned THF ---
% 1.70/1.42 thf('thf_type_type/realax/real',type,
% 1.70/1.42 'type/realax/real': $tType ).
% 1.70/1.42
% 1.70/1.42 thf('thf_const_const/realax/real_sub',type,
% 1.70/1.42 'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 1.70/1.42
% 1.70/1.42 thf('thf_const_const/realax/real_neg',type,
% 1.70/1.42 'const/realax/real_neg': 'type/realax/real' > 'type/realax/real' ).
% 1.70/1.42
% 1.70/1.42 thf('thf_const_const/realax/real_add',type,
% 1.70/1.42 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 1.70/1.42
% 1.70/1.42 thf('thf_const_const/iterate/polynomial_function',type,
% 1.70/1.42 'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
% 1.70/1.42
% 1.70/1.42 thf('thm/iterate/POLYNOMIAL_FUNCTION_ADD_',axiom,
% 1.70/1.42 ! [A: 'type/realax/real' > 'type/realax/real',A0: 'type/realax/real' > 'type/realax/real'] :
% 1.70/1.42 ( ( ( 'const/iterate/polynomial_function' @ A )
% 1.70/1.42 & ( 'const/iterate/polynomial_function' @ A0 ) )
% 1.70/1.42 => ( 'const/iterate/polynomial_function'
% 1.70/1.42 @ ^ [A1: 'type/realax/real'] : ( 'const/realax/real_add' @ ( A @ A1 ) @ ( A0 @ A1 ) ) ) ) ).
% 1.70/1.42
% 1.70/1.42 thf('thm/iterate/POLYNOMIAL_FUNCTION_NEG_',axiom,
% 1.70/1.42 ! [A: 'type/realax/real' > 'type/realax/real'] :
% 1.70/1.42 ( ( 'const/iterate/polynomial_function'
% 1.70/1.42 @ ^ [A0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( A @ A0 ) ) )
% 1.70/1.42 = ( 'const/iterate/polynomial_function' @ A ) ) ).
% 1.70/1.42
% 1.70/1.42 thf('thm/realax/real_sub_',axiom,
% 1.70/1.42 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 1.70/1.42 ( ( 'const/realax/real_sub' @ A @ A0 )
% 1.70/1.42 = ( 'const/realax/real_add' @ A @ ( 'const/realax/real_neg' @ A0 ) ) ) ).
% 1.70/1.42
% 1.70/1.42 thf('thm/iterate/POLYNOMIAL_FUNCTION_SUB_',conjecture,
% 1.70/1.42 ! [A: 'type/realax/real' > 'type/realax/real',A0: 'type/realax/real' > 'type/realax/real'] :
% 1.70/1.42 ( ( ( 'const/iterate/polynomial_function' @ A )
% 1.70/1.42 & ( 'const/iterate/polynomial_function' @ A0 ) )
% 1.70/1.42 => ( 'const/iterate/polynomial_function'
% 1.70/1.42 @ ^ [A1: 'type/realax/real'] : ( 'const/realax/real_sub' @ ( A @ A1 ) @ ( A0 @ A1 ) ) ) ) ).
% 1.70/1.42 ------------------------
% 1.70/1.44 % (23461)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23358 for (2999ds/18Mi)
% 1.70/1.44 % (23455)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23358 for (2999ds/183Mi)
% 1.70/1.44 % (23456)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_23358 for (2999ds/4Mi)
% 1.70/1.44 % (23460)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_23358 for (2999ds/275Mi)
% 1.70/1.44 % (23459)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_23358 for (2999ds/2Mi)
% 1.70/1.44 % (23457)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_23358 for (2999ds/27Mi)
% 1.70/1.44 % (23458)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23358 for (2999ds/2Mi)
% 1.70/1.44 % (23458)Instruction limit reached!
% 1.70/1.44 % (23458)------------------------------
% 1.70/1.44 % (23458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.44 % (23458)Termination reason: Unknown
% 1.70/1.44 % (23458)Termination phase: Saturation
% 1.70/1.44
% 1.70/1.44 % (23458)Memory used [KB]: 5373
% 1.70/1.44 % (23458)Time elapsed: 0.003 s
% 1.70/1.44 % (23458)Instructions burned: 2 (million)
% 1.70/1.44 % (23458)------------------------------
% 1.70/1.44 % (23458)------------------------------
% 1.70/1.44 % (23459)Instruction limit reached!
% 1.70/1.44 % (23459)------------------------------
% 1.70/1.44 % (23459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.44 % (23459)Termination reason: Unknown
% 1.70/1.44 % (23459)Termination phase: Saturation
% 1.70/1.44
% 1.70/1.44 % (23459)Memory used [KB]: 1023
% 1.70/1.44 % (23459)Time elapsed: 0.003 s
% 1.70/1.44 % (23459)Instructions burned: 2 (million)
% 1.70/1.44 % (23459)------------------------------
% 1.70/1.44 % (23459)------------------------------
% 1.70/1.44 % (23456)Instruction limit reached!
% 1.70/1.44 % (23456)------------------------------
% 1.70/1.44 % (23456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.44 % (23456)Termination reason: Unknown
% 1.70/1.44 % (23456)Termination phase: Saturation
% 1.70/1.44
% 1.70/1.44 % (23456)Memory used [KB]: 5500
% 1.70/1.44 % (23456)Time elapsed: 0.004 s
% 1.70/1.44 % (23460)Refutation not found, incomplete strategy
% 1.70/1.44 % (23460)------------------------------
% 1.70/1.44 % (23460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.44 % (23456)Instructions burned: 4 (million)
% 1.70/1.44 % (23456)------------------------------
% 1.70/1.44 % (23456)------------------------------
% 1.70/1.44 % (23460)Termination reason: Refutation not found, incomplete strategy
% 1.70/1.44
% 1.70/1.44
% 1.70/1.44 % (23460)Memory used [KB]: 5500
% 1.70/1.44 % (23460)Time elapsed: 0.003 s
% 1.70/1.44 % (23460)Instructions burned: 2 (million)
% 1.70/1.44 % (23460)------------------------------
% 1.70/1.44 % (23460)------------------------------
% 1.70/1.45 % (23461)Instruction limit reached!
% 1.70/1.45 % (23461)------------------------------
% 1.70/1.45 % (23461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.45 % (23461)Termination reason: Unknown
% 1.70/1.45 % (23461)Termination phase: Saturation
% 1.70/1.45
% 1.70/1.45 % (23461)Memory used [KB]: 5628
% 1.70/1.45 % (23461)Time elapsed: 0.013 s
% 1.70/1.45 % (23461)Instructions burned: 18 (million)
% 1.70/1.45 % (23461)------------------------------
% 1.70/1.45 % (23461)------------------------------
% 1.70/1.45 % (23457)Instruction limit reached!
% 1.70/1.45 % (23457)------------------------------
% 1.70/1.45 % (23457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.45 % (23457)Termination reason: Unknown
% 1.70/1.45 % (23457)Termination phase: Saturation
% 1.70/1.45
% 1.70/1.45 % (23457)Memory used [KB]: 5628
% 1.70/1.45 % (23457)Time elapsed: 0.017 s
% 1.70/1.45 % (23457)Instructions burned: 28 (million)
% 1.70/1.45 % (23457)------------------------------
% 1.70/1.45 % (23457)------------------------------
% 1.70/1.46 % (23462)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23358 for (2999ds/3Mi)
% 1.70/1.46 % (23463)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_23358 for (2999ds/37Mi)
% 1.70/1.46 % (23464)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_23358 for (2999ds/15Mi)
% 1.70/1.46 % (23465)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_23358 for (2999ds/3Mi)
% 1.70/1.46 % (23462)Instruction limit reached!
% 1.70/1.46 % (23462)------------------------------
% 1.70/1.46 % (23462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.46 % (23462)Termination reason: Unknown
% 1.70/1.46 % (23462)Termination phase: Saturation
% 1.70/1.46
% 1.70/1.46 % (23462)Memory used [KB]: 5500
% 1.70/1.46 % (23462)Time elapsed: 0.003 s
% 1.70/1.46 % (23462)Instructions burned: 3 (million)
% 1.70/1.46 % (23462)------------------------------
% 1.70/1.46 % (23462)------------------------------
% 1.70/1.46 % (23465)Instruction limit reached!
% 1.70/1.46 % (23465)------------------------------
% 1.70/1.46 % (23465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.46 % (23465)Termination reason: Unknown
% 1.70/1.46 % (23465)Termination phase: Saturation
% 1.70/1.46
% 1.70/1.46 % (23465)Memory used [KB]: 5500
% 1.70/1.46 % (23465)Time elapsed: 0.004 s
% 1.70/1.46 % (23465)Instructions burned: 4 (million)
% 1.70/1.46 % (23465)------------------------------
% 1.70/1.46 % (23465)------------------------------
% 1.70/1.46 % (23464)Instruction limit reached!
% 1.70/1.46 % (23464)------------------------------
% 1.70/1.46 % (23464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.46 % (23464)Termination reason: Unknown
% 1.70/1.46 % (23464)Termination phase: Saturation
% 1.70/1.46
% 1.70/1.46 % (23464)Memory used [KB]: 5628
% 1.70/1.46 % (23464)Time elapsed: 0.010 s
% 1.70/1.46 % (23464)Instructions burned: 16 (million)
% 1.70/1.46 % (23464)------------------------------
% 1.70/1.46 % (23464)------------------------------
% 1.70/1.47 % (23466)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_23358 for (2999ds/1041Mi)
% 1.70/1.47 % (23467)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_23358 for (2999ds/7Mi)
% 1.70/1.47 % (23468)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_23358 for (2999ds/16Mi)
% 1.70/1.47 % (23467)Instruction limit reached!
% 1.70/1.47 % (23467)------------------------------
% 1.70/1.47 % (23467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.47 % (23467)Termination reason: Unknown
% 1.70/1.47 % (23467)Termination phase: Saturation
% 1.70/1.47
% 1.70/1.47 % (23467)Memory used [KB]: 1023
% 1.70/1.47 % (23467)Time elapsed: 0.006 s
% 1.70/1.47 % (23467)Instructions burned: 8 (million)
% 1.70/1.47 % (23467)------------------------------
% 1.70/1.47 % (23467)------------------------------
% 1.70/1.48 % (23463)Instruction limit reached!
% 1.70/1.48 % (23463)------------------------------
% 1.70/1.48 % (23463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.48 % (23463)Termination reason: Unknown
% 1.70/1.48 % (23463)Termination phase: Saturation
% 1.70/1.48
% 1.70/1.48 % (23463)Memory used [KB]: 5756
% 1.70/1.48 % (23463)Time elapsed: 0.021 s
% 1.70/1.48 % (23463)Instructions burned: 39 (million)
% 1.70/1.48 % (23463)------------------------------
% 1.70/1.48 % (23463)------------------------------
% 1.70/1.48 % (23469)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_23358 for (2999ds/3Mi)
% 1.70/1.48 % (23469)Instruction limit reached!
% 1.70/1.48 % (23469)------------------------------
% 1.70/1.48 % (23469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.48 % (23469)Termination reason: Unknown
% 1.70/1.48 % (23469)Termination phase: Saturation
% 1.70/1.48
% 1.70/1.48 % (23469)Memory used [KB]: 5500
% 1.70/1.48 % (23469)Time elapsed: 0.003 s
% 1.70/1.48 % (23469)Instructions burned: 3 (million)
% 1.70/1.48 % (23469)------------------------------
% 1.70/1.48 % (23469)------------------------------
% 1.70/1.48 % (23470)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_23358 for (2999ds/3Mi)
% 1.70/1.48 % (23455)First to succeed.
% 1.70/1.48 % (23470)Instruction limit reached!
% 1.70/1.48 % (23470)------------------------------
% 1.70/1.48 % (23470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.48 % (23470)Termination reason: Unknown
% 1.70/1.48 % (23470)Termination phase: Saturation
% 1.70/1.48
% 1.70/1.48 % (23470)Memory used [KB]: 1023
% 1.70/1.48 % (23470)Time elapsed: 0.003 s
% 1.70/1.48 % (23470)Instructions burned: 3 (million)
% 1.70/1.48 % (23470)------------------------------
% 1.70/1.48 % (23470)------------------------------
% 1.70/1.48 % (23468)Instruction limit reached!
% 1.70/1.48 % (23468)------------------------------
% 1.70/1.48 % (23468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.48 % (23468)Termination reason: Unknown
% 1.70/1.48 % (23468)Termination phase: Saturation
% 1.70/1.48
% 1.70/1.48 % (23468)Memory used [KB]: 5628
% 1.70/1.48 % (23468)Time elapsed: 0.011 s
% 1.70/1.48 % (23468)Instructions burned: 17 (million)
% 1.70/1.48 % (23468)------------------------------
% 1.70/1.48 % (23468)------------------------------
% 1.70/1.48 % (23455)Refutation found. Thanks to Tanya!
% 1.70/1.48 % SZS status Theorem for DTF2THF_23358
% 1.70/1.48 % SZS output start Proof for DTF2THF_23358
% 1.70/1.48 thf(type_def_5, type, 'type/realax/real': $tType).
% 1.70/1.48 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.70/1.48 thf(func_def_1, type, 'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > 'type/realax/real').
% 1.70/1.48 thf(func_def_2, type, 'const/realax/real_neg': 'type/realax/real' > 'type/realax/real').
% 1.70/1.48 thf(func_def_3, type, 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real').
% 1.70/1.48 thf(func_def_4, type, 'const/iterate/polynomial_function': ('type/realax/real' > 'type/realax/real') > $o).
% 1.70/1.48 thf(func_def_10, type, sK0: 'type/realax/real' > 'type/realax/real').
% 1.70/1.48 thf(func_def_11, type, sK1: 'type/realax/real' > 'type/realax/real').
% 1.70/1.48 thf(func_def_13, type, ph3: !>[X0: $tType]:(X0)).
% 1.70/1.48 thf(func_def_14, type, sK4: ('type/realax/real' > 'type/realax/real') > 'type/realax/real').
% 1.70/1.48 thf(func_def_15, type, sK5: ('type/realax/real' > 'type/realax/real') > 'type/realax/real').
% 1.70/1.48 thf(func_def_16, type, sK6: 'type/realax/real').
% 1.70/1.48 thf(func_def_17, type, sK7: 'type/realax/real').
% 1.70/1.48 thf(func_def_18, type, sK8: ('type/realax/real' > 'type/realax/real') > ('type/realax/real' > 'type/realax/real') > 'type/realax/real').
% 1.70/1.48 thf(func_def_19, type, sK9: ('type/realax/real' > 'type/realax/real') > 'type/realax/real').
% 1.70/1.48 thf(func_def_20, type, sK10: ('type/realax/real' > 'type/realax/real') > ('type/realax/real' > 'type/realax/real') > 'type/realax/real').
% 1.70/1.48 thf(func_def_21, type, sK11: ('type/realax/real' > 'type/realax/real') > ('type/realax/real' > 'type/realax/real') > ('type/realax/real' > 'type/realax/real') > 'type/realax/real').
% 1.70/1.48 thf(func_def_22, type, sK12: ('type/realax/real' > 'type/realax/real') > ('type/realax/real' > 'type/realax/real') > 'type/realax/real').
% 1.70/1.48 thf(func_def_23, type, sK13: ('type/realax/real' > 'type/realax/real') > 'type/realax/real').
% 1.70/1.48 thf(func_def_24, type, sK14: 'type/realax/real').
% 1.70/1.48 thf(func_def_25, type, sK15: 'type/realax/real').
% 1.70/1.48 thf(func_def_26, type, sK16: ('type/realax/real' > 'type/realax/real') > 'type/realax/real').
% 1.70/1.48 thf(func_def_27, type, sK17: ('type/realax/real' > 'type/realax/real') > 'type/realax/real').
% 1.70/1.48 thf(func_def_28, type, sK18: 'type/realax/real').
% 1.70/1.48 thf(f291,plain,(
% 1.70/1.48 $false),
% 1.70/1.48 inference(avatar_sat_refutation,[status(thm)],[f207,f251,f290])).
% 1.70/1.48 thf(f290,plain,(
% 1.70/1.48 ~spl2_2),
% 1.70/1.48 inference(avatar_contradiction_clause,[status(thm)],[f289])).
% 1.70/1.48 thf(f289,plain,(
% 1.70/1.48 $false | ~spl2_2),
% 1.70/1.48 inference(subsumption_resolution,[status(thm)],[f287,f18])).
% 1.70/1.48 thf(f18,plain,(
% 1.70/1.48 ($true = ('const/iterate/polynomial_function' @ sK0))),
% 1.70/1.48 inference(cnf_transformation,[status(thm)],[f17])).
% 1.70/1.48 thf(f17,plain,(
% 1.70/1.48 ($true != ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_sub' @ (sK0 @ Y0) @ (sK1 @ Y0))))) & (('const/iterate/polynomial_function' @ sK1) = $true) & ($true = ('const/iterate/polynomial_function' @ sK0))),
% 1.70/1.48 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f15,f16])).
% 1.70/1.48 thf(f16,plain,(
% 1.70/1.48 ? [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : (($true != ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_sub' @ (X0 @ Y0) @ (X1 @ Y0))))) & (('const/iterate/polynomial_function' @ X1) = $true) & (('const/iterate/polynomial_function' @ X0) = $true)) => (($true != ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_sub' @ (sK0 @ Y0) @ (sK1 @ Y0))))) & (('const/iterate/polynomial_function' @ sK1) = $true) & ($true = ('const/iterate/polynomial_function' @ sK0)))),
% 1.70/1.48 introduced(definition,[],[choice_axiom])).
% 1.70/1.48 thf(f15,plain,(
% 1.70/1.48 ? [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : (($true != ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_sub' @ (X0 @ Y0) @ (X1 @ Y0))))) & (('const/iterate/polynomial_function' @ X1) = $true) & (('const/iterate/polynomial_function' @ X0) = $true))),
% 1.70/1.48 inference(flattening,[status(thm)],[f14])).
% 1.70/1.48 thf(f14,plain,(
% 1.70/1.48 ? [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : (($true != ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_sub' @ (X0 @ Y0) @ (X1 @ Y0))))) & ((('const/iterate/polynomial_function' @ X0) = $true) & (('const/iterate/polynomial_function' @ X1) = $true)))),
% 1.70/1.48 inference(ennf_transformation,[status(thm)],[f10])).
% 1.70/1.48 thf(f10,plain,(
% 1.70/1.48 ~! [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : (((('const/iterate/polynomial_function' @ X0) = $true) & (('const/iterate/polynomial_function' @ X1) = $true)) => ($true = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_sub' @ (X0 @ Y0) @ (X1 @ Y0))))))),
% 1.70/1.48 inference(fool_elimination,[status(thm)],[f9])).
% 1.70/1.48 thf(f9,plain,(
% 1.70/1.48 ~! [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : ((('const/iterate/polynomial_function' @ X0) & ('const/iterate/polynomial_function' @ X1)) => ('const/iterate/polynomial_function' @ (^[X2 : 'type/realax/real'] : ('const/realax/real_sub' @ (X0 @ X2) @ (X1 @ X2)))))),
% 1.70/1.48 inference(rectify,[status(thm)],[f5])).
% 1.70/1.48 thf(f5,negated_conjecture,(
% 1.70/1.48 ~! [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : ((('const/iterate/polynomial_function' @ X0) & ('const/iterate/polynomial_function' @ X1)) => ('const/iterate/polynomial_function' @ (^[X2 : 'type/realax/real'] : ('const/realax/real_sub' @ (X0 @ X2) @ (X1 @ X2)))))),
% 1.70/1.48 inference(negated_conjecture,[status(cth)],[f4])).
% 1.70/1.48 thf(f4,conjecture,(
% 1.70/1.48 ! [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : ((('const/iterate/polynomial_function' @ X0) & ('const/iterate/polynomial_function' @ X1)) => ('const/iterate/polynomial_function' @ (^[X2 : 'type/realax/real'] : ('const/realax/real_sub' @ (X0 @ X2) @ (X1 @ X2)))))),
% 1.70/1.48 file('/export/starexec/sandbox/tmp/tmp.PRKencDl8S/DTF2THF_23358.p','thm/iterate/POLYNOMIAL_FUNCTION_SUB_')).
% 1.70/1.48 thf(f287,plain,(
% 1.70/1.48 ($true != ('const/iterate/polynomial_function' @ sK0)) | ~spl2_2),
% 1.70/1.48 inference(beta_eta_normalization,[status(thm)],[f286])).
% 1.70/1.48 thf(f286,plain,(
% 1.70/1.48 ($true != ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: (sK0 @ ((^[Y1 : 'type/realax/real']: (Y1)) @ Y0))))) | ~spl2_2),
% 1.70/1.48 inference(equality_resolution,[status(thm)],[f206])).
% 1.70/1.48 thf(f206,plain,(
% 1.70/1.48 ( ! [X0 : 'type/realax/real' > 'type/realax/real'] : (((X0 @ (sK10 @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK1 @ Y0))) @ X0)) != (sK0 @ (sK10 @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK1 @ Y0))) @ X0))) | (('const/iterate/polynomial_function' @ X0) != $true)) ) | ~spl2_2),
% 1.70/1.48 inference(avatar_component_clause,[status(thm)],[f205])).
% 1.70/1.48 thf(f205,definition,(
% 1.70/1.48 spl2_2 <=> ! [X0 : 'type/realax/real' > 'type/realax/real'] : (((X0 @ (sK10 @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK1 @ Y0))) @ X0)) != (sK0 @ (sK10 @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK1 @ Y0))) @ X0))) | (('const/iterate/polynomial_function' @ X0) != $true))),
% 1.70/1.48 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.70/1.48 thf(f251,plain,(
% 1.70/1.48 spl2_1),
% 1.70/1.48 inference(avatar_contradiction_clause,[status(thm)],[f250])).
% 1.70/1.48 thf(f250,plain,(
% 1.70/1.48 $false | spl2_1),
% 1.70/1.48 inference(trivial_inequality_removal,[status(thm)],[f241])).
% 1.70/1.48 thf(f241,plain,(
% 1.70/1.48 ($false = $true) | spl2_1),
% 1.70/1.48 inference(superposition,[status(thm)],[f19,f233])).
% 1.70/1.48 thf(f233,plain,(
% 1.70/1.48 (('const/iterate/polynomial_function' @ sK1) = $false) | spl2_1),
% 1.70/1.48 inference(beta_eta_normalization,[status(thm)],[f232])).
% 1.70/1.48 thf(f232,plain,(
% 1.70/1.48 ($false = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: (sK1 @ ((^[Y1 : 'type/realax/real']: (Y1)) @ Y0))))) | spl2_1),
% 1.70/1.48 inference(equality_resolution,[status(thm)],[f228])).
% 1.70/1.48 thf(f228,plain,(
% 1.70/1.48 ( ! [X0 : 'type/realax/real' > 'type/realax/real'] : ((('const/realax/real_neg' @ (X0 @ (sK16 @ X0))) != ('const/realax/real_neg' @ (sK1 @ (sK16 @ X0)))) | (('const/iterate/polynomial_function' @ X0) = $false)) ) | spl2_1),
% 1.70/1.48 inference(beta_eta_normalization,[status(thm)],[f227])).
% 1.70/1.48 thf(f227,plain,(
% 1.70/1.48 ( ! [X0 : 'type/realax/real' > 'type/realax/real'] : ((((^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK1 @ Y0))) @ (sK16 @ X0)) != ((^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (X0 @ Y0))) @ (sK16 @ X0))) | (('const/iterate/polynomial_function' @ X0) = $false)) ) | spl2_1),
% 1.70/1.48 inference(negative_extensionality,[status(thm)],[f222])).
% 1.70/1.48 thf(f222,plain,(
% 1.70/1.48 ( ! [X0 : 'type/realax/real' > 'type/realax/real'] : (((^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (X0 @ Y0))) != (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK1 @ Y0)))) | (('const/iterate/polynomial_function' @ X0) = $false)) ) | spl2_1),
% 1.70/1.48 inference(trivial_inequality_removal,[status(thm)],[f210])).
% 1.70/1.48 thf(f210,plain,(
% 1.70/1.48 ( ! [X0 : 'type/realax/real' > 'type/realax/real'] : ((('const/iterate/polynomial_function' @ X0) = $false) | ((^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (X0 @ Y0))) != (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK1 @ Y0)))) | ($true != $true)) ) | spl2_1),
% 1.70/1.48 inference(constrained_superposition,[status(thm)],[f203,f25])).
% 1.70/1.48 thf(f25,plain,(
% 1.70/1.48 ( ! [X0 : 'type/realax/real' > 'type/realax/real'] : (($true = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (X0 @ Y0))))) | (('const/iterate/polynomial_function' @ X0) = $false)) )),
% 1.70/1.48 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.70/1.48 thf(f22,plain,(
% 1.70/1.48 ( ! [X0 : 'type/realax/real' > 'type/realax/real'] : ((('const/iterate/polynomial_function' @ X0) = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (X0 @ Y0)))))) )),
% 1.70/1.48 inference(cnf_transformation,[status(thm)],[f11])).
% 1.70/1.48 thf(f11,plain,(
% 1.70/1.48 ! [X0 : 'type/realax/real' > 'type/realax/real'] : (('const/iterate/polynomial_function' @ X0) = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (X0 @ Y0)))))),
% 1.70/1.48 inference(fool_elimination,[status(thm)],[f2])).
% 1.70/1.48 thf(f2,axiom,(
% 1.70/1.48 ! [X0 : 'type/realax/real' > 'type/realax/real'] : (('const/iterate/polynomial_function' @ (^[X1 : 'type/realax/real'] : ('const/realax/real_neg' @ (X0 @ X1)))) = ('const/iterate/polynomial_function' @ X0))),
% 1.70/1.48 file('/export/starexec/sandbox/tmp/tmp.PRKencDl8S/DTF2THF_23358.p','thm/iterate/POLYNOMIAL_FUNCTION_NEG_')).
% 1.70/1.48 thf(f203,plain,(
% 1.70/1.48 ($true != ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK1 @ Y0))))) | spl2_1),
% 1.70/1.48 inference(avatar_component_clause,[status(thm)],[f201])).
% 1.70/1.48 thf(f201,definition,(
% 1.70/1.48 spl2_1 <=> ($true = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK1 @ Y0)))))),
% 1.70/1.48 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.70/1.48 thf(f19,plain,(
% 1.70/1.48 (('const/iterate/polynomial_function' @ sK1) = $true)),
% 1.70/1.48 inference(cnf_transformation,[status(thm)],[f17])).
% 1.70/1.48 thf(f207,plain,(
% 1.70/1.48 ~spl2_1 | spl2_2),
% 1.70/1.48 inference(avatar_split_clause,[status(thm)],[f198,f205,f201])).
% 1.70/1.48 thf(f198,plain,(
% 1.70/1.48 ( ! [X0 : 'type/realax/real' > 'type/realax/real'] : (($true != ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK1 @ Y0))))) | ((X0 @ (sK10 @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK1 @ Y0))) @ X0)) != (sK0 @ (sK10 @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK1 @ Y0))) @ X0))) | (('const/iterate/polynomial_function' @ X0) != $true)) )),
% 1.70/1.48 inference(beta_eta_normalization,[status(thm)],[f197])).
% 1.70/1.48 thf(f197,plain,(
% 1.70/1.48 ( ! [X0 : 'type/realax/real' > 'type/realax/real'] : (($true != ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ ((^[Y1 : 'type/realax/real']: (sK1 @ ((^[Y2 : 'type/realax/real']: (Y2)) @ Y1))) @ Y0))))) | (('const/iterate/polynomial_function' @ X0) != $true) | ((sK0 @ (sK10 @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ ((^[Y1 : 'type/realax/real']: (sK1 @ ((^[Y2 : 'type/realax/real']: (Y2)) @ Y1))) @ Y0))) @ X0)) != (X0 @ (sK10 @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ ((^[Y1 : 'type/realax/real']: (sK1 @ ((^[Y2 : 'type/realax/real']: (Y2)) @ Y1))) @ Y0))) @ X0)))) )),
% 1.70/1.48 inference(equality_resolution,[status(thm)],[f191])).
% 1.70/1.48 thf(f191,plain,(
% 1.70/1.48 ( ! [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : (((sK1 @ (sK10 @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (X1 @ Y0))) @ X0)) != (X1 @ (sK10 @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (X1 @ Y0))) @ X0))) | (('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (X1 @ Y0)))) != $true) | ((X0 @ (sK10 @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (X1 @ Y0))) @ X0)) != (sK0 @ (sK10 @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (X1 @ Y0))) @ X0))) | (('const/iterate/polynomial_function' @ X0) != $true)) )),
% 1.70/1.48 inference(equality_resolution,[status(thm)],[f119])).
% 1.70/1.48 thf(f119,plain,(
% 1.70/1.48 ( ! [X2 : 'type/realax/real',X3 : 'type/realax/real',X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : ((('const/realax/real_sub' @ (sK0 @ (sK10 @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (X1 @ Y0))) @ X0)) @ (sK1 @ (sK10 @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (X1 @ Y0))) @ X0))) != ('const/realax/real_sub' @ X2 @ X3)) | (('const/iterate/polynomial_function' @ X0) != $true) | (('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (X1 @ Y0)))) != $true) | ((X0 @ (sK10 @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (X1 @ Y0))) @ X0)) != X2) | ((X1 @ (sK10 @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (X1 @ Y0))) @ X0)) != X3)) )),
% 1.70/1.48 inference(constrained_superposition,[status(thm)],[f72,f21])).
% 1.70/1.48 thf(f21,plain,(
% 1.70/1.48 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_sub' @ X0 @ X1) = ('const/realax/real_add' @ X0 @ ('const/realax/real_neg' @ X1)))) )),
% 1.70/1.48 inference(cnf_transformation,[status(thm)],[f3])).
% 1.70/1.48 thf(f3,axiom,(
% 1.70/1.48 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_sub' @ X0 @ X1) = ('const/realax/real_add' @ X0 @ ('const/realax/real_neg' @ X1)))),
% 1.70/1.48 file('/export/starexec/sandbox/tmp/tmp.PRKencDl8S/DTF2THF_23358.p','thm/realax/real_sub_')).
% 1.70/1.48 thf(f72,plain,(
% 1.70/1.48 ( ! [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : ((('const/realax/real_add' @ (X0 @ (sK10 @ X1 @ X0)) @ (X1 @ (sK10 @ X1 @ X0))) != ('const/realax/real_sub' @ (sK0 @ (sK10 @ X1 @ X0)) @ (sK1 @ (sK10 @ X1 @ X0)))) | (('const/iterate/polynomial_function' @ X1) != $true) | (('const/iterate/polynomial_function' @ X0) != $true)) )),
% 1.70/1.48 inference(beta_eta_normalization,[status(thm)],[f71])).
% 1.70/1.48 thf(f71,plain,(
% 1.70/1.48 ( ! [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : ((('const/iterate/polynomial_function' @ X1) != $true) | (((^[Y0 : 'type/realax/real']: ('const/realax/real_add' @ (X0 @ Y0) @ (X1 @ Y0))) @ (sK10 @ X1 @ X0)) != ((^[Y0 : 'type/realax/real']: ('const/realax/real_sub' @ (sK0 @ Y0) @ (sK1 @ Y0))) @ (sK10 @ X1 @ X0))) | (('const/iterate/polynomial_function' @ X0) != $true)) )),
% 1.70/1.48 inference(negative_extensionality,[status(thm)],[f58])).
% 1.70/1.48 thf(f58,plain,(
% 1.70/1.48 ( ! [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : (((^[Y0 : 'type/realax/real']: ('const/realax/real_sub' @ (sK0 @ Y0) @ (sK1 @ Y0))) != (^[Y0 : 'type/realax/real']: ('const/realax/real_add' @ (X0 @ Y0) @ (X1 @ Y0)))) | (('const/iterate/polynomial_function' @ X0) != $true) | (('const/iterate/polynomial_function' @ X1) != $true)) )),
% 1.70/1.48 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.70/1.48 thf(f56,plain,(
% 1.70/1.48 ( ! [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : (($true != $true) | (('const/iterate/polynomial_function' @ X0) != $true) | (('const/iterate/polynomial_function' @ X1) != $true) | ((^[Y0 : 'type/realax/real']: ('const/realax/real_sub' @ (sK0 @ Y0) @ (sK1 @ Y0))) != (^[Y0 : 'type/realax/real']: ('const/realax/real_add' @ (X0 @ Y0) @ (X1 @ Y0))))) )),
% 1.70/1.48 inference(constrained_superposition,[status(thm)],[f20,f23])).
% 1.70/1.48 thf(f23,plain,(
% 1.70/1.48 ( ! [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : (($true = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_add' @ (X1 @ Y0) @ (X0 @ Y0))))) | (('const/iterate/polynomial_function' @ X1) != $true) | (('const/iterate/polynomial_function' @ X0) != $true)) )),
% 1.70/1.48 inference(cnf_transformation,[status(thm)],[f13])).
% 1.70/1.48 thf(f13,plain,(
% 1.70/1.48 ! [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : ((('const/iterate/polynomial_function' @ X0) != $true) | (('const/iterate/polynomial_function' @ X1) != $true) | ($true = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_add' @ (X1 @ Y0) @ (X0 @ Y0))))))),
% 1.70/1.48 inference(flattening,[status(thm)],[f12])).
% 1.70/1.48 thf(f12,plain,(
% 1.70/1.48 ! [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : (($true = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_add' @ (X1 @ Y0) @ (X0 @ Y0))))) | ((('const/iterate/polynomial_function' @ X1) != $true) | (('const/iterate/polynomial_function' @ X0) != $true)))),
% 1.70/1.48 inference(ennf_transformation,[status(thm)],[f8])).
% 1.70/1.48 thf(f8,plain,(
% 1.70/1.48 ! [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : (((('const/iterate/polynomial_function' @ X1) = $true) & (('const/iterate/polynomial_function' @ X0) = $true)) => ($true = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_add' @ (X1 @ Y0) @ (X0 @ Y0))))))),
% 1.70/1.48 inference(fool_elimination,[status(thm)],[f7])).
% 1.70/1.48 thf(f7,plain,(
% 1.70/1.48 ! [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real' > 'type/realax/real'] : ((('const/iterate/polynomial_function' @ X1) & ('const/iterate/polynomial_function' @ X0)) => ('const/iterate/polynomial_function' @ (^[X2 : 'type/realax/real'] : ('const/realax/real_add' @ (X1 @ X2) @ (X0 @ X2)))))),
% 1.70/1.48 inference(rectify,[status(thm)],[f1])).
% 1.70/1.48 thf(f1,axiom,(
% 1.70/1.48 ! [X1 : 'type/realax/real' > 'type/realax/real',X0 : 'type/realax/real' > 'type/realax/real'] : ((('const/iterate/polynomial_function' @ X0) & ('const/iterate/polynomial_function' @ X1)) => ('const/iterate/polynomial_function' @ (^[X2 : 'type/realax/real'] : ('const/realax/real_add' @ (X0 @ X2) @ (X1 @ X2)))))),
% 1.70/1.48 file('/export/starexec/sandbox/tmp/tmp.PRKencDl8S/DTF2THF_23358.p','thm/iterate/POLYNOMIAL_FUNCTION_ADD_')).
% 1.70/1.48 thf(f20,plain,(
% 1.70/1.48 ($true != ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_sub' @ (sK0 @ Y0) @ (sK1 @ Y0)))))),
% 1.70/1.48 inference(cnf_transformation,[status(thm)],[f17])).
% 1.70/1.48 % SZS output end Proof for DTF2THF_23358
% 1.70/1.48 % (23455)------------------------------
% 1.70/1.48 % (23455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.48 % (23455)Termination reason: Refutation
% 1.70/1.48
% 1.70/1.48 % (23455)Memory used [KB]: 6012
% 1.70/1.48 % (23455)Time elapsed: 0.046 s
% 1.70/1.48 % (23455)Instructions burned: 85 (million)
% 1.70/1.48 % (23455)------------------------------
% 1.70/1.48 % (23455)------------------------------
% 1.70/1.48 % (23454)Success in time 0.055 s
%------------------------------------------------------------------------------