%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA126^1 : 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 08:38:56 AM UTC 2026
% Result : Theorem 1.59s 1.39s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 14 unt; 0 typ; 4 def)
% Number of atoms : 200 ( 56 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 378 ( 76 ~; 59 |; 0 &; 235 @)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 9 con; 0-2 aty)
% Number of variables : 75 ( 35 ^; 38 !; 2 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/nums/num': $tType ).
thf(type_def_6,type,
'type/realax/real': $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_of_num': 'type/nums/num' > 'type/realax/real' ).
thf(func_def_3,type,
'const/realax/real_neg': 'type/realax/real' > '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/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
thf(func_def_14,type,
sK0: 'type/realax/real' > 'type/realax/real' ).
thf(func_def_16,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK3: 'type/realax/real' ).
thf(func_def_18,type,
sK4: 'type/realax/real' > 'type/realax/real' ).
thf(func_def_19,type,
sK5: 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_20,type,
sK6: 'type/realax/real' ).
thf(func_def_21,type,
sK7: 'type/realax/real' > 'type/realax/real' ).
thf(f127,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f31,f40,f78,f82,f85,f124]) ).
thf(f124,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f123]) ).
thf(f123,plain,
( $false
| ~ spl1_1
| ~ spl1_4 ),
inference(trivial_inequality_removal,[status(thm)],[f121]) ).
thf(f121,plain,
( ( ( 'const/realax/real_neg' @ ( sK0 @ ( sK7 @ ( 'const/realax/real_neg' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
!= ( 'const/realax/real_neg' @ ( sK0 @ ( sK7 @ ( 'const/realax/real_neg' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ) )
| ~ spl1_1
| ~ spl1_4 ),
inference(superposition,[status(thm)],[f119,f18]) ).
thf(f18,plain,
! [X0: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ X0 )
= X0 ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ X0 )
= X0 ),
file('/export/starexec/sandbox/tmp/tmp.N6oo7ynJnf/DTF2THF_3481.p','thm/realax/REAL_MUL_LID_') ).
thf(f119,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ X0 @ ( sK0 @ ( sK7 @ ( 'const/realax/real_neg' @ X0 ) ) ) ) )
!= ( 'const/realax/real_neg' @ ( sK0 @ ( sK7 @ ( 'const/realax/real_neg' @ X0 ) ) ) ) )
| ~ spl1_1
| ~ spl1_4 ),
inference(superposition,[status(thm)],[f117,f19]) ).
thf(f19,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ X1 ) @ X0 )
= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ X1 ) @ X0 )
= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: 'type/realax/real',X0: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ X0 ) @ X1 )
= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.N6oo7ynJnf/DTF2THF_3481.p','thm/calc_int/REAL_MUL_LNEG_') ).
thf(f117,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( sK0 @ ( sK7 @ X0 ) ) )
!= ( 'const/realax/real_mul' @ X0 @ ( sK0 @ ( sK7 @ X0 ) ) ) )
| ~ spl1_1
| ~ spl1_4 ),
inference(beta_eta_normalization,[status(thm)],[f116]) ).
thf(f116,plain,
( ! [X0: 'type/realax/real'] :
( ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK0 @ Y0 ) )
@ ( sK7 @ X0 ) )
!= ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( sK0 @ Y0 ) )
@ ( sK7 @ X0 ) ) )
| ~ spl1_1
| ~ spl1_4 ),
inference(negative_extensionality,[status(thm)],[f107]) ).
thf(f107,plain,
( ! [X0: 'type/realax/real'] :
( ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK0 @ Y0 ) ) ) )
| ~ spl1_1
| ~ spl1_4 ),
inference(trivial_inequality_removal,[status(thm)],[f100]) ).
thf(f100,plain,
( ! [X0: 'type/realax/real'] :
( ( $true = $false )
| ( ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK0 @ Y0 ) ) ) ) )
| ~ spl1_1
| ~ spl1_4 ),
inference(constrained_superposition,[status(thm)],[f88,f39]) ).
thf(f39,plain,
( ( $false
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK0 @ Y0 ) ) ) )
| ~ spl1_4 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f37,definition,
( spl1_4
<=> ( $false
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK0 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition]) ).
thf(f88,plain,
( ! [X0: 'type/realax/real'] :
( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( sK0 @ Y0 ) ) ) )
| ~ spl1_1 ),
inference(trivial_inequality_removal,[status(thm)],[f87]) ).
thf(f87,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( sK0 @ Y0 ) ) ) )
| ( $true != $true ) )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f16,f26]) ).
thf(f26,plain,
( ( $true
= ( 'const/iterate/polynomial_function' @ sK0 ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f24,definition,
( spl1_1
<=> ( $true
= ( 'const/iterate/polynomial_function' @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f16,plain,
! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X0 )
!= $true )
| ( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X1 @ ( X0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X0 )
!= $true )
| ( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X1 @ ( X0 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X0 )
= $true )
=> ( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X1 @ ( X0 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ X0 )
=> ( 'const/iterate/polynomial_function'
@ ^ [X2: 'type/realax/real'] : ( 'const/realax/real_mul' @ X1 @ ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ X0 )
=> ( 'const/iterate/polynomial_function'
@ ^ [X2: 'type/realax/real'] : ( 'const/realax/real_mul' @ X1 @ ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.N6oo7ynJnf/DTF2THF_3481.p','thm/iterate/POLYNOMIAL_FUNCTION_LMUL_') ).
thf(f85,plain,
( ~ spl1_2
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f84]) ).
thf(f84,plain,
( $false
| ~ spl1_2
| ~ spl1_4 ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
( ( $true = $false )
| ~ spl1_2
| ~ spl1_4 ),
inference(forward_demodulation,[status(thm)],[f30,f39]) ).
thf(f30,plain,
( ( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK0 @ Y0 ) ) ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f28]) ).
thf(f28,definition,
( spl1_2
<=> ( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK0 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f82,plain,
( ~ spl1_1
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f81]) ).
thf(f81,plain,
( $false
| ~ spl1_1
| ~ spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
( ( $true = $false )
| ~ spl1_1
| ~ spl1_3 ),
inference(forward_demodulation,[status(thm)],[f26,f35]) ).
thf(f35,plain,
( ( $false
= ( 'const/iterate/polynomial_function' @ sK0 ) )
| ~ spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl1_3
<=> ( $false
= ( 'const/iterate/polynomial_function' @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition]) ).
thf(f78,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f77]) ).
thf(f77,plain,
( $false
| ~ spl1_2
| ~ spl1_3 ),
inference(subsumption_resolution,[status(thm)],[f74,f20]) ).
thf(f20,plain,
! [X0: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_neg' @ X0 ) )
= X0 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_neg' @ X0 ) )
= X0 ),
file('/export/starexec/sandbox/tmp/tmp.N6oo7ynJnf/DTF2THF_3481.p','thm/calc_int/REAL_NEG_NEG_') ).
thf(f74,plain,
( ( ( 'const/realax/real_neg' @ ( 'const/realax/real_neg' @ ( sK0 @ ( sK4 @ ( 'const/realax/real_neg' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ) )
!= ( sK0 @ ( sK4 @ ( 'const/realax/real_neg' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ~ spl1_2
| ~ spl1_3 ),
inference(superposition,[status(thm)],[f70,f18]) ).
thf(f70,plain,
( ! [X0: 'type/realax/real'] :
( ( sK0 @ ( sK4 @ ( 'const/realax/real_neg' @ X0 ) ) )
!= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ X0 @ ( 'const/realax/real_neg' @ ( sK0 @ ( sK4 @ ( 'const/realax/real_neg' @ X0 ) ) ) ) ) ) )
| ~ spl1_2
| ~ spl1_3 ),
inference(superposition,[status(thm)],[f61,f19]) ).
thf(f61,plain,
( ! [X0: 'type/realax/real'] :
( ( sK0 @ ( sK4 @ X0 ) )
!= ( 'const/realax/real_mul' @ X0 @ ( 'const/realax/real_neg' @ ( sK0 @ ( sK4 @ X0 ) ) ) ) )
| ~ spl1_2
| ~ spl1_3 ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
( ! [X0: 'type/realax/real'] :
( ( sK0 @ ( sK4 @ X0 ) )
!= ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( 'const/realax/real_neg' @ ( sK0 @ Y0 ) ) )
@ ( sK4 @ X0 ) ) )
| ~ spl1_2
| ~ spl1_3 ),
inference(negative_extensionality,[status(thm)],[f59]) ).
thf(f59,plain,
( ! [X0: 'type/realax/real'] :
( sK0
!= ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( 'const/realax/real_neg' @ ( sK0 @ Y0 ) ) ) ) )
| ~ spl1_2
| ~ spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
( ! [X0: 'type/realax/real'] :
( ( $true = $false )
| ( sK0
!= ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( 'const/realax/real_neg' @ ( sK0 @ Y0 ) ) ) ) ) )
| ~ spl1_2
| ~ spl1_3 ),
inference(constrained_superposition,[status(thm)],[f35,f52]) ).
thf(f52,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( 'const/realax/real_neg' @ ( sK0 @ Y0 ) ) ) )
= $true )
| ~ spl1_2 ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
( ! [X0: 'type/realax/real'] :
( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] :
( 'const/realax/real_mul' @ X0
@ ( ^ [Y1: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK0 @ Y1 ) )
@ Y0 ) ) ) )
| ~ spl1_2 ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] :
( 'const/realax/real_mul' @ X0
@ ( ^ [Y1: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK0 @ Y1 ) )
@ Y0 ) ) ) )
| ( $true != $true ) )
| ~ spl1_2 ),
inference(superposition,[status(thm)],[f16,f30]) ).
thf(f40,plain,
( spl1_3
| spl1_4 ),
inference(avatar_split_clause,[status(thm)],[f22,f37,f33]) ).
thf(f22,plain,
( ( $false
= ( 'const/iterate/polynomial_function' @ sK0 ) )
| ( $false
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK0 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK0 @ Y0 ) ) )
!= ( 'const/iterate/polynomial_function' @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK0 @ Y0 ) ) )
!= ( 'const/iterate/polynomial_function' @ sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14]) ).
thf(f14,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 ) ) ) )
=> ( ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK0 @ Y0 ) ) )
!= ( 'const/iterate/polynomial_function' @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,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(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,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)],[f6]) ).
thf(f6,negated_conjecture,
~ ! [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 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
! [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.N6oo7ynJnf/DTF2THF_3481.p','thm/iterate/POLYNOMIAL_FUNCTION_NEG_') ).
thf(f31,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f21,f28,f24]) ).
thf(f21,plain,
( ( $true
= ( 'const/iterate/polynomial_function' @ sK0 ) )
| ( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( sK0 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ANA126^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.29 % Computer : n022.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Feb 24 03:51:36 EST 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.38 ---- Original DTF file ---
% 0.15/0.38 thf(spec,logic,$$dhol).
% 0.15/0.38 %------------------------------------------------------------------------------
% 0.15/0.38 % File : ANA126^1 : TPTP v9.2.1. Released v7.0.0.
% 0.15/0.38 % Domain : Analysis
% 0.15/0.38 % Problem : POLYNOMIAL_FUNCTION_NEG
% 0.15/0.38 % Version : Especial.
% 0.15/0.38 % English :
% 0.15/0.38
% 0.15/0.38 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.15/0.38 % Source : [Kal16]
% 0.15/0.38 % Names : POLYNOMIAL_FUNCTION_NEG_.p [Kal16]
% 0.15/0.38
% 0.15/0.38 % Status : Theorem
% 0.15/0.38 % Rating : 0.56 v9.1.0, 0.50 v9.0.0, 0.60 v8.2.0, 0.62 v8.1.0, 0.64 v7.5.0, 0.57 v7.4.0, 0.67 v7.2.0, 0.62 v7.1.0, 0.75 v7.0.0
% 0.15/0.38 % Syntax : Number of formulae : 14 ( 4 unt; 9 typ; 0 def)
% 0.15/0.38 % Number of atoms : 8 ( 4 equ; 0 cnn)
% 0.15/0.38 % Maximal formula atoms : 2 ( 1 avg)
% 0.15/0.38 % Number of connectives : 23 ( 0 ~; 0 |; 0 &; 22 @)
% 0.15/0.38 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.15/0.38 % Maximal formula depth : 8 ( 3 avg)
% 0.15/0.38 % Number of types : 3 ( 2 usr)
% 0.15/0.38 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.15/0.38 % Number of symbols : 8 ( 7 usr; 1 con; 0-2 aty)
% 0.15/0.38 % Number of variables : 9 ( 2 ^; 7 !; 0 ?; 9 :)
% 0.15/0.38 % SPC : TH0_THM_EQU_NAR
% 0.15/0.38
% 0.15/0.38 % Comments : Exported from core HOL Light.
% 0.15/0.38 %------------------------------------------------------------------------------
% 0.15/0.38 thf('thf_type_type/realax/real',type,
% 0.15/0.38 'type/realax/real': $tType ).
% 0.15/0.38
% 0.15/0.38 thf('thf_type_type/nums/num',type,
% 0.15/0.38 'type/nums/num': $tType ).
% 0.15/0.38
% 0.15/0.38 thf('thf_const_const/realax/real_of_num',type,
% 0.15/0.38 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
% 0.15/0.38
% 0.15/0.38 thf('thf_const_const/realax/real_neg',type,
% 0.15/0.38 'const/realax/real_neg': 'type/realax/real' > 'type/realax/real' ).
% 0.15/0.38
% 0.15/0.38 thf('thf_const_const/realax/real_mul',type,
% 0.15/0.38 'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 0.15/0.38
% 0.15/0.38 thf('thf_const_const/nums/NUMERAL',type,
% 0.15/0.38 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 0.15/0.38
% 0.15/0.38 thf('thf_const_const/nums/BIT1',type,
% 0.15/0.38 'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
% 0.15/0.38
% 0.15/0.38 thf('thf_const_const/nums/_0',type,
% 0.15/0.38 'const/nums/_0': 'type/nums/num' ).
% 0.15/0.38
% 0.15/0.38 thf('thf_const_const/iterate/polynomial_function',type,
% 0.15/0.38 'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
% 0.15/0.38
% 0.15/0.38 thf('thm/realax/REAL_MUL_LID_',axiom,
% 0.15/0.38 ! [A: 'type/realax/real'] :
% 0.15/0.38 ( ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A )
% 0.15/0.38 = A ) ).
% 0.15/0.38
% 0.15/0.38 thf('thm/calc_int/REAL_MUL_LNEG_',axiom,
% 0.15/0.38 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 0.15/0.38 ( ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ A ) @ A0 )
% 0.15/0.38 = ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ A @ A0 ) ) ) ).
% 0.15/0.38
% 0.15/0.38 thf('thm/iterate/POLYNOMIAL_FUNCTION_LMUL_',axiom,
% 0.15/0.38 ! [A: 'type/realax/real' > 'type/realax/real',A0: 'type/realax/real'] :
% 0.15/0.38 ( ( 'const/iterate/polynomial_function' @ A )
% 0.15/0.38 => ( 'const/iterate/polynomial_function'
% 0.15/0.38 @ ^ [A1: 'type/realax/real'] : ( 'const/realax/real_mul' @ A0 @ ( A @ A1 ) ) ) ) ).
% 0.15/0.38
% 0.15/0.38 thf('thm/calc_int/REAL_NEG_NEG_',axiom,
% 0.15/0.38 ! [A: 'type/realax/real'] :
% 0.15/0.38 ( ( 'const/realax/real_neg' @ ( 'const/realax/real_neg' @ A ) )
% 0.15/0.38 = A ) ).
% 0.15/0.38
% 0.15/0.38 thf('thm/iterate/POLYNOMIAL_FUNCTION_NEG_',conjecture,
% 0.15/0.38 ! [A: 'type/realax/real' > 'type/realax/real'] :
% 0.15/0.38 ( ( 'const/iterate/polynomial_function'
% 0.15/0.38 @ ^ [A0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( A @ A0 ) ) )
% 0.15/0.38 = ( 'const/iterate/polynomial_function' @ A ) ) ).
% 0.15/0.38
% 0.15/0.38 %------------------------------------------------------------------------------
% 0.15/0.38 ------------------------
% 1.38/1.29 ---- Embedded in THF ---
% 1.38/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.38/1.29 %%% Generated on Tue Feb 24 03:51:37 EST 2026
% 1.38/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.38/1.29 %%% Logic specification used:
% 1.38/1.29 %%% thf(spec, logic, $$dhol).
% 1.38/1.29
% 1.38/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.N6oo7ynJnf/DTF2DTF3481.p
% See solution above
% 1.38/1.29 ------------------------
% 1.38/1.30 ---- Cleaned THF ---
% 1.59/1.30 thf('thf_type_type/realax/real',type,
% 1.59/1.30 'type/realax/real': $tType ).
% 1.59/1.30
% 1.59/1.30 thf('thf_type_type/nums/num',type,
% 1.59/1.30 'type/nums/num': $tType ).
% 1.59/1.30
% 1.59/1.30 thf('thf_const_const/realax/real_of_num',type,
% 1.59/1.30 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
% 1.59/1.30
% 1.59/1.30 thf('thf_const_const/realax/real_neg',type,
% 1.59/1.30 'const/realax/real_neg': 'type/realax/real' > 'type/realax/real' ).
% 1.59/1.30
% 1.59/1.30 thf('thf_const_const/realax/real_mul',type,
% 1.59/1.30 'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 1.59/1.30
% 1.59/1.30 thf('thf_const_const/nums/NUMERAL',type,
% 1.59/1.30 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 1.59/1.30
% 1.59/1.30 thf('thf_const_const/nums/BIT1',type,
% 1.59/1.30 'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
% 1.59/1.30
% 1.59/1.30 thf('thf_const_const/nums/_0',type,
% 1.59/1.30 'const/nums/_0': 'type/nums/num' ).
% 1.59/1.30
% 1.59/1.30 thf('thf_const_const/iterate/polynomial_function',type,
% 1.59/1.30 'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
% 1.59/1.30
% 1.59/1.30 thf('thm/realax/REAL_MUL_LID_',axiom,
% 1.59/1.30 ! [A: 'type/realax/real'] :
% 1.59/1.30 ( ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A )
% 1.59/1.30 = A ) ).
% 1.59/1.30
% 1.59/1.30 thf('thm/calc_int/REAL_MUL_LNEG_',axiom,
% 1.59/1.30 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 1.59/1.30 ( ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ A ) @ A0 )
% 1.59/1.30 = ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ A @ A0 ) ) ) ).
% 1.59/1.30
% 1.59/1.30 thf('thm/iterate/POLYNOMIAL_FUNCTION_LMUL_',axiom,
% 1.59/1.30 ! [A: 'type/realax/real' > 'type/realax/real',A0: 'type/realax/real'] :
% 1.59/1.30 ( ( 'const/iterate/polynomial_function' @ A )
% 1.59/1.30 => ( 'const/iterate/polynomial_function'
% 1.59/1.30 @ ^ [A1: 'type/realax/real'] : ( 'const/realax/real_mul' @ A0 @ ( A @ A1 ) ) ) ) ).
% 1.59/1.30
% 1.59/1.30 thf('thm/calc_int/REAL_NEG_NEG_',axiom,
% 1.59/1.30 ! [A: 'type/realax/real'] :
% 1.59/1.30 ( ( 'const/realax/real_neg' @ ( 'const/realax/real_neg' @ A ) )
% 1.59/1.30 = A ) ).
% 1.59/1.30
% 1.59/1.30 thf('thm/iterate/POLYNOMIAL_FUNCTION_NEG_',conjecture,
% 1.59/1.30 ! [A: 'type/realax/real' > 'type/realax/real'] :
% 1.59/1.30 ( ( 'const/iterate/polynomial_function'
% 1.59/1.30 @ ^ [A0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( A @ A0 ) ) )
% 1.59/1.30 = ( 'const/iterate/polynomial_function' @ A ) ) ).
% 1.59/1.30 ------------------------
% 1.59/1.32 % (3578)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3481 for (2999ds/183Mi)
% 1.59/1.32 % (3582)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_3481 for (2999ds/2Mi)
% 1.59/1.32 % (3581)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3481 for (2999ds/2Mi)
% 1.59/1.32 % (3580)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_3481 for (2999ds/27Mi)
% 1.59/1.32 % (3579)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_3481 for (2999ds/4Mi)
% 1.59/1.32 % (3584)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3481 for (2999ds/18Mi)
% 1.59/1.32 % (3583)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_3481 for (2999ds/275Mi)
% 1.59/1.32 % (3581)Instruction limit reached!
% 1.59/1.32 % (3581)------------------------------
% 1.59/1.32 % (3581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (3581)Termination reason: Unknown
% 1.59/1.32 % (3582)Instruction limit reached!
% 1.59/1.32 % (3582)------------------------------
% 1.59/1.32 % (3582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (3582)Termination reason: Unknown
% 1.59/1.32 % (3582)Termination phase: Saturation
% 1.59/1.32
% 1.59/1.32 % (3582)Memory used [KB]: 5500
% 1.59/1.32 % (3582)Time elapsed: 0.003 s
% 1.59/1.32 % (3582)Instructions burned: 2 (million)
% 1.59/1.32 % (3582)------------------------------
% 1.59/1.32 % (3582)------------------------------
% 1.59/1.32 % (3581)Termination phase: Saturation
% 1.59/1.32
% 1.59/1.32 % (3581)Memory used [KB]: 5500
% 1.59/1.32 % (3581)Time elapsed: 0.003 s
% 1.59/1.32 % (3581)Instructions burned: 2 (million)
% 1.59/1.32 % (3581)------------------------------
% 1.59/1.32 % (3581)------------------------------
% 1.59/1.32 % (3583)Refutation not found, incomplete strategy
% 1.59/1.32 % (3583)------------------------------
% 1.59/1.32 % (3583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (3583)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.32
% 1.59/1.32
% 1.59/1.32 % (3583)Memory used [KB]: 5500
% 1.59/1.32 % (3583)Time elapsed: 0.003 s
% 1.59/1.32 % (3583)Instructions burned: 2 (million)
% 1.59/1.32 % (3583)------------------------------
% 1.59/1.32 % (3583)------------------------------
% 1.59/1.32 % (3579)Instruction limit reached!
% 1.59/1.32 % (3579)------------------------------
% 1.59/1.32 % (3579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (3579)Termination reason: Unknown
% 1.59/1.32 % (3579)Termination phase: Saturation
% 1.59/1.32
% 1.59/1.32 % (3579)Memory used [KB]: 5500
% 1.59/1.32 % (3579)Time elapsed: 0.004 s
% 1.59/1.32 % (3579)Instructions burned: 4 (million)
% 1.59/1.32 % (3579)------------------------------
% 1.59/1.32 % (3579)------------------------------
% 1.59/1.33 % (3584)Instruction limit reached!
% 1.59/1.33 % (3584)------------------------------
% 1.59/1.33 % (3584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.33 % (3584)Termination reason: Unknown
% 1.59/1.33 % (3584)Termination phase: Saturation
% 1.59/1.33
% 1.59/1.33 % (3584)Memory used [KB]: 5628
% 1.59/1.33 % (3584)Time elapsed: 0.012 s
% 1.59/1.33 % (3584)Instructions burned: 19 (million)
% 1.59/1.33 % (3584)------------------------------
% 1.59/1.33 % (3584)------------------------------
% 1.59/1.33 % (3580)Instruction limit reached!
% 1.59/1.33 % (3580)------------------------------
% 1.59/1.33 % (3580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.33 % (3580)Termination reason: Unknown
% 1.59/1.33 % (3580)Termination phase: Saturation
% 1.59/1.33
% 1.59/1.33 % (3580)Memory used [KB]: 5628
% 1.59/1.33 % (3580)Time elapsed: 0.016 s
% 1.59/1.33 % (3580)Instructions burned: 28 (million)
% 1.59/1.33 % (3580)------------------------------
% 1.59/1.33 % (3580)------------------------------
% 1.59/1.33 % (3585)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3481 for (2999ds/3Mi)
% 1.59/1.33 % (3586)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_3481 for (2999ds/37Mi)
% 1.59/1.33 % (3587)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_3481 for (2999ds/15Mi)
% 1.59/1.33 % (3588)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_3481 for (2999ds/3Mi)
% 1.59/1.34 % (3585)Instruction limit reached!
% 1.59/1.34 % (3585)------------------------------
% 1.59/1.34 % (3585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.34 % (3585)Termination reason: Unknown
% 1.59/1.34 % (3585)Termination phase: Saturation
% 1.59/1.34
% 1.59/1.34 % (3585)Memory used [KB]: 5500
% 1.59/1.34 % (3585)Time elapsed: 0.003 s
% 1.59/1.34 % (3585)Instructions burned: 3 (million)
% 1.59/1.34 % (3585)------------------------------
% 1.59/1.34 % (3585)------------------------------
% 1.59/1.34 % (3588)Instruction limit reached!
% 1.59/1.34 % (3588)------------------------------
% 1.59/1.34 % (3588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.34 % (3588)Termination reason: Unknown
% 1.59/1.34 % (3588)Termination phase: Saturation
% 1.59/1.34
% 1.59/1.34 % (3588)Memory used [KB]: 5500
% 1.59/1.34 % (3588)Time elapsed: 0.004 s
% 1.59/1.34 % (3588)Instructions burned: 4 (million)
% 1.59/1.34 % (3588)------------------------------
% 1.59/1.34 % (3588)------------------------------
% 1.59/1.34 % (3589)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_3481 for (2999ds/1041Mi)
% 1.59/1.34 % (3587)Instruction limit reached!
% 1.59/1.34 % (3587)------------------------------
% 1.59/1.34 % (3587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.34 % (3587)Termination reason: Unknown
% 1.59/1.34 % (3587)Termination phase: Saturation
% 1.59/1.34
% 1.59/1.34 % (3587)Memory used [KB]: 5628
% 1.59/1.34 % (3587)Time elapsed: 0.010 s
% 1.59/1.34 % (3587)Instructions burned: 17 (million)
% 1.59/1.34 % (3587)------------------------------
% 1.59/1.34 % (3587)------------------------------
% 1.59/1.35 % (3590)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3481 for (2999ds/7Mi)
% 1.59/1.35 % (3590)Instruction limit reached!
% 1.59/1.35 % (3590)------------------------------
% 1.59/1.35 % (3590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (3590)Termination reason: Unknown
% 1.59/1.35 % (3590)Termination phase: Saturation
% 1.59/1.35
% 1.59/1.35 % (3590)Memory used [KB]: 1023
% 1.59/1.35 % (3590)Time elapsed: 0.006 s
% 1.59/1.35 % (3590)Instructions burned: 8 (million)
% 1.59/1.35 % (3590)------------------------------
% 1.59/1.35 % (3590)------------------------------
% 1.59/1.35 % (3591)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3481 for (2999ds/16Mi)
% 1.59/1.35 % (3592)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_3481 for (2999ds/3Mi)
% 1.59/1.35 % (3586)Instruction limit reached!
% 1.59/1.35 % (3586)------------------------------
% 1.59/1.35 % (3586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (3586)Termination reason: Unknown
% 1.59/1.35 % (3586)Termination phase: Saturation
% 1.59/1.35
% 1.59/1.35 % (3586)Memory used [KB]: 5756
% 1.59/1.35 % (3586)Time elapsed: 0.021 s
% 1.59/1.35 % (3586)Instructions burned: 38 (million)
% 1.59/1.35 % (3586)------------------------------
% 1.59/1.35 % (3586)------------------------------
% 1.59/1.35 % (3592)Instruction limit reached!
% 1.59/1.35 % (3592)------------------------------
% 1.59/1.35 % (3592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (3592)Termination reason: Unknown
% 1.59/1.35 % (3592)Termination phase: Saturation
% 1.59/1.35
% 1.59/1.35 % (3592)Memory used [KB]: 5500
% 1.59/1.35 % (3592)Time elapsed: 0.003 s
% 1.59/1.35 % (3592)Instructions burned: 3 (million)
% 1.59/1.35 % (3592)------------------------------
% 1.59/1.35 % (3592)------------------------------
% 1.59/1.36 % (3593)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_3481 for (2999ds/3Mi)
% 1.59/1.36 % (3593)Instruction limit reached!
% 1.59/1.36 % (3593)------------------------------
% 1.59/1.36 % (3593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.36 % (3593)Termination reason: Unknown
% 1.59/1.36 % (3593)Termination phase: Saturation
% 1.59/1.36
% 1.59/1.36 % (3593)Memory used [KB]: 1023
% 1.59/1.36 % (3593)Time elapsed: 0.003 s
% 1.59/1.36 % (3593)Instructions burned: 3 (million)
% 1.59/1.36 % (3593)------------------------------
% 1.59/1.36 % (3593)------------------------------
% 1.59/1.36 % (3591)Instruction limit reached!
% 1.59/1.36 % (3591)------------------------------
% 1.59/1.36 % (3591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.36 % (3591)Termination reason: Unknown
% 1.59/1.36 % (3591)Termination phase: Saturation
% 1.59/1.36
% 1.59/1.36 % (3591)Memory used [KB]: 5628
% 1.59/1.36 % (3591)Time elapsed: 0.011 s
% 1.59/1.36 % (3591)Instructions burned: 17 (million)
% 1.59/1.36 % (3591)------------------------------
% 1.59/1.36 % (3591)------------------------------
% 1.59/1.37 % (3594)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3481 for (2999ds/7Mi)
% 1.59/1.37 % (3594)Refutation not found, incomplete strategy
% 1.59/1.37 % (3594)------------------------------
% 1.59/1.37 % (3594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.37 % (3594)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.37
% 1.59/1.37
% 1.59/1.37 % (3594)Memory used [KB]: 5500
% 1.59/1.37 % (3594)Time elapsed: 0.002 s
% 1.59/1.37 % (3594)Instructions burned: 2 (million)
% 1.59/1.37 % (3594)------------------------------
% 1.59/1.37 % (3594)------------------------------
% 1.59/1.37 % (3595)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3481 for (2999ds/3Mi)
% 1.59/1.37 % (3596)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3481 for (2999ds/4Mi)
% 1.59/1.37 % (3595)Instruction limit reached!
% 1.59/1.37 % (3595)------------------------------
% 1.59/1.37 % (3595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.37 % (3595)Termination reason: Unknown
% 1.59/1.37 % (3595)Termination phase: Saturation
% 1.59/1.37
% 1.59/1.37 % (3595)Memory used [KB]: 5500
% 1.59/1.37 % (3595)Time elapsed: 0.003 s
% 1.59/1.37 % (3595)Instructions burned: 3 (million)
% 1.59/1.37 % (3595)------------------------------
% 1.59/1.37 % (3595)------------------------------
% 1.59/1.37 % (3596)Instruction limit reached!
% 1.59/1.37 % (3596)------------------------------
% 1.59/1.37 % (3596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.37 % (3596)Termination reason: Unknown
% 1.59/1.37 % (3596)Termination phase: Saturation
% 1.59/1.37
% 1.59/1.37 % (3596)Memory used [KB]: 5500
% 1.59/1.37 % (3596)Time elapsed: 0.004 s
% 1.59/1.37 % (3596)Instructions burned: 4 (million)
% 1.59/1.37 % (3596)------------------------------
% 1.59/1.37 % (3596)------------------------------
% 1.59/1.38 % (3597)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3481 for (2999ds/18Mi)
% 1.59/1.38 % (3598)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3481 for (2999ds/710Mi)
% 1.59/1.38 % (3597)Refutation not found, incomplete strategy
% 1.59/1.38 % (3597)------------------------------
% 1.59/1.38 % (3597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.38 % (3597)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.38
% 1.59/1.38
% 1.59/1.38 % (3597)Memory used [KB]: 5500
% 1.59/1.38 % (3597)Time elapsed: 0.003 s
% 1.59/1.38 % (3597)Instructions burned: 3 (million)
% 1.59/1.38 % (3597)------------------------------
% 1.59/1.38 % (3597)------------------------------
% 1.59/1.38 % (3599)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3481 for (2999ds/6Mi)
% 1.59/1.39 % (3600)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_3481 for (2999ds/902Mi)
% 1.59/1.39 % (3598)First to succeed.
% 1.59/1.39 % (3600)Refutation not found, incomplete strategy
% 1.59/1.39 % (3600)------------------------------
% 1.59/1.39 % (3600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.39 % (3600)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.39
% 1.59/1.39
% 1.59/1.39 % (3600)Memory used [KB]: 5500
% 1.59/1.39 % (3600)Time elapsed: 0.002 s
% 1.59/1.39 % (3600)Instructions burned: 2 (million)
% 1.59/1.39 % (3600)------------------------------
% 1.59/1.39 % (3600)------------------------------
% 1.59/1.39 % (3599)Instruction limit reached!
% 1.59/1.39 % (3599)------------------------------
% 1.59/1.39 % (3599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.39 % (3599)Termination reason: Unknown
% 1.59/1.39 % (3599)Termination phase: Saturation
% 1.59/1.39
% 1.59/1.39 % (3599)Memory used [KB]: 5500
% 1.59/1.39 % (3599)Time elapsed: 0.005 s
% 1.59/1.39 % (3599)Instructions burned: 6 (million)
% 1.59/1.39 % (3599)------------------------------
% 1.59/1.39 % (3599)------------------------------
% 1.59/1.39 % (3598)Refutation found. Thanks to Tanya!
% 1.59/1.39 % SZS status Theorem for DTF2THF_3481
% 1.59/1.39 % SZS output start Proof for DTF2THF_3481
% 1.59/1.39 thf(type_def_5, type, 'type/nums/num': $tType).
% 1.59/1.39 thf(type_def_6, type, 'type/realax/real': $tType).
% 1.59/1.39 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.59/1.39 thf(func_def_1, type, 'type/nums/num': $tType).
% 1.59/1.39 thf(func_def_2, type, 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real').
% 1.59/1.39 thf(func_def_3, type, 'const/realax/real_neg': 'type/realax/real' > 'type/realax/real').
% 1.59/1.39 thf(func_def_4, type, 'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real').
% 1.59/1.39 thf(func_def_5, type, 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num').
% 1.59/1.39 thf(func_def_6, type, 'const/nums/BIT1': 'type/nums/num' > 'type/nums/num').
% 1.59/1.39 thf(func_def_7, type, 'const/nums/_0': 'type/nums/num').
% 1.59/1.39 thf(func_def_8, type, 'const/iterate/polynomial_function': ('type/realax/real' > 'type/realax/real') > $o).
% 1.59/1.39 thf(func_def_14, type, sK0: 'type/realax/real' > 'type/realax/real').
% 1.59/1.39 thf(func_def_16, type, ph2: !>[X0: $tType]:(X0)).
% 1.59/1.39 thf(func_def_17, type, sK3: 'type/realax/real').
% 1.59/1.39 thf(func_def_18, type, sK4: 'type/realax/real' > 'type/realax/real').
% 1.59/1.39 thf(func_def_19, type, sK5: 'type/realax/real' > 'type/realax/real' > 'type/realax/real').
% 1.59/1.39 thf(func_def_20, type, sK6: 'type/realax/real').
% 1.59/1.39 thf(func_def_21, type, sK7: 'type/realax/real' > 'type/realax/real').
% 1.59/1.39 thf(f127,plain,(
% 1.59/1.39 $false),
% 1.59/1.39 inference(avatar_sat_refutation,[status(thm)],[f31,f40,f78,f82,f85,f124])).
% 1.59/1.39 thf(f124,plain,(
% 1.59/1.39 ~spl1_1 | ~spl1_4),
% 1.59/1.39 inference(avatar_contradiction_clause,[status(thm)],[f123])).
% 1.59/1.39 thf(f123,plain,(
% 1.59/1.39 $false | (~spl1_1 | ~spl1_4)),
% 1.59/1.39 inference(trivial_inequality_removal,[status(thm)],[f121])).
% 1.59/1.39 thf(f121,plain,(
% 1.59/1.39 (('const/realax/real_neg' @ (sK0 @ (sK7 @ ('const/realax/real_neg' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))))) != ('const/realax/real_neg' @ (sK0 @ (sK7 @ ('const/realax/real_neg' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))))) | (~spl1_1 | ~spl1_4)),
% 1.59/1.39 inference(superposition,[status(thm)],[f119,f18])).
% 1.59/1.39 thf(f18,plain,(
% 1.59/1.39 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ X0) = X0)) )),
% 1.59/1.39 inference(cnf_transformation,[status(thm)],[f1])).
% 1.59/1.39 thf(f1,axiom,(
% 1.59/1.39 ! [X0 : 'type/realax/real'] : (('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ X0) = X0)),
% 1.59/1.39 file('/export/starexec/sandbox/tmp/tmp.N6oo7ynJnf/DTF2THF_3481.p','thm/realax/REAL_MUL_LID_')).
% 1.59/1.39 thf(f119,plain,(
% 1.59/1.39 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_neg' @ ('const/realax/real_mul' @ X0 @ (sK0 @ (sK7 @ ('const/realax/real_neg' @ X0))))) != ('const/realax/real_neg' @ (sK0 @ (sK7 @ ('const/realax/real_neg' @ X0)))))) ) | (~spl1_1 | ~spl1_4)),
% 1.59/1.39 inference(superposition,[status(thm)],[f117,f19])).
% 1.59/1.39 thf(f19,plain,(
% 1.59/1.39 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_mul' @ ('const/realax/real_neg' @ X1) @ X0) = ('const/realax/real_neg' @ ('const/realax/real_mul' @ X1 @ X0)))) )),
% 1.59/1.39 inference(cnf_transformation,[status(thm)],[f11])).
% 1.59/1.39 thf(f11,plain,(
% 1.59/1.39 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_mul' @ ('const/realax/real_neg' @ X1) @ X0) = ('const/realax/real_neg' @ ('const/realax/real_mul' @ X1 @ X0)))),
% 1.59/1.39 inference(rectify,[status(thm)],[f2])).
% 1.59/1.39 thf(f2,axiom,(
% 1.59/1.39 ! [X1 : 'type/realax/real',X0 : 'type/realax/real'] : (('const/realax/real_mul' @ ('const/realax/real_neg' @ X0) @ X1) = ('const/realax/real_neg' @ ('const/realax/real_mul' @ X0 @ X1)))),
% 1.59/1.39 file('/export/starexec/sandbox/tmp/tmp.N6oo7ynJnf/DTF2THF_3481.p','thm/calc_int/REAL_MUL_LNEG_')).
% 1.59/1.39 thf(f117,plain,(
% 1.59/1.39 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_neg' @ (sK0 @ (sK7 @ X0))) != ('const/realax/real_mul' @ X0 @ (sK0 @ (sK7 @ X0))))) ) | (~spl1_1 | ~spl1_4)),
% 1.59/1.39 inference(beta_eta_normalization,[status(thm)],[f116])).
% 1.59/1.39 thf(f116,plain,(
% 1.59/1.39 ( ! [X0 : 'type/realax/real'] : ((((^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK0 @ Y0))) @ (sK7 @ X0)) != ((^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ X0 @ (sK0 @ Y0))) @ (sK7 @ X0)))) ) | (~spl1_1 | ~spl1_4)),
% 1.59/1.39 inference(negative_extensionality,[status(thm)],[f107])).
% 1.59/1.39 thf(f107,plain,(
% 1.59/1.39 ( ! [X0 : 'type/realax/real'] : (((^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ X0 @ (sK0 @ Y0))) != (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK0 @ Y0))))) ) | (~spl1_1 | ~spl1_4)),
% 1.59/1.39 inference(trivial_inequality_removal,[status(thm)],[f100])).
% 1.59/1.39 thf(f100,plain,(
% 1.59/1.39 ( ! [X0 : 'type/realax/real'] : (($true = $false) | ((^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ X0 @ (sK0 @ Y0))) != (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK0 @ Y0))))) ) | (~spl1_1 | ~spl1_4)),
% 1.59/1.39 inference(constrained_superposition,[status(thm)],[f88,f39])).
% 1.59/1.39 thf(f39,plain,(
% 1.59/1.39 ($false = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK0 @ Y0))))) | ~spl1_4),
% 1.59/1.39 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.59/1.39 thf(f37,definition,(
% 1.59/1.39 spl1_4 <=> ($false = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK0 @ Y0)))))),
% 1.59/1.39 introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition])).
% 1.59/1.39 thf(f88,plain,(
% 1.59/1.39 ( ! [X0 : 'type/realax/real'] : (($true = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ X0 @ (sK0 @ Y0)))))) ) | ~spl1_1),
% 1.59/1.39 inference(trivial_inequality_removal,[status(thm)],[f87])).
% 1.59/1.39 thf(f87,plain,(
% 1.59/1.39 ( ! [X0 : 'type/realax/real'] : (($true = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ X0 @ (sK0 @ Y0))))) | ($true != $true)) ) | ~spl1_1),
% 1.59/1.39 inference(superposition,[status(thm)],[f16,f26])).
% 1.59/1.39 thf(f26,plain,(
% 1.59/1.39 ($true = ('const/iterate/polynomial_function' @ sK0)) | ~spl1_1),
% 1.59/1.39 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.59/1.39 thf(f24,definition,(
% 1.59/1.39 spl1_1 <=> ($true = ('const/iterate/polynomial_function' @ sK0))),
% 1.59/1.39 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.59/1.39 thf(f16,plain,(
% 1.59/1.39 ( ! [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real'] : ((('const/iterate/polynomial_function' @ X0) != $true) | ($true = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ X1 @ (X0 @ Y0)))))) )),
% 1.59/1.39 inference(cnf_transformation,[status(thm)],[f12])).
% 1.59/1.39 thf(f12,plain,(
% 1.59/1.39 ! [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real'] : ((('const/iterate/polynomial_function' @ X0) != $true) | ($true = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ X1 @ (X0 @ Y0))))))),
% 1.59/1.39 inference(ennf_transformation,[status(thm)],[f9])).
% 1.59/1.39 thf(f9,plain,(
% 1.59/1.39 ! [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real'] : ((('const/iterate/polynomial_function' @ X0) = $true) => ($true = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ X1 @ (X0 @ Y0))))))),
% 1.59/1.39 inference(fool_elimination,[status(thm)],[f8])).
% 1.59/1.39 thf(f8,plain,(
% 1.59/1.39 ! [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real'] : (('const/iterate/polynomial_function' @ X0) => ('const/iterate/polynomial_function' @ (^[X2 : 'type/realax/real'] : ('const/realax/real_mul' @ X1 @ (X0 @ X2)))))),
% 1.59/1.39 inference(rectify,[status(thm)],[f3])).
% 1.59/1.39 thf(f3,axiom,(
% 1.59/1.39 ! [X0 : 'type/realax/real' > 'type/realax/real',X1 : 'type/realax/real'] : (('const/iterate/polynomial_function' @ X0) => ('const/iterate/polynomial_function' @ (^[X2 : 'type/realax/real'] : ('const/realax/real_mul' @ X1 @ (X0 @ X2)))))),
% 1.59/1.39 file('/export/starexec/sandbox/tmp/tmp.N6oo7ynJnf/DTF2THF_3481.p','thm/iterate/POLYNOMIAL_FUNCTION_LMUL_')).
% 1.59/1.39 thf(f85,plain,(
% 1.59/1.39 ~spl1_2 | ~spl1_4),
% 1.59/1.39 inference(avatar_contradiction_clause,[status(thm)],[f84])).
% 1.59/1.39 thf(f84,plain,(
% 1.59/1.39 $false | (~spl1_2 | ~spl1_4)),
% 1.59/1.39 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.59/1.39 thf(f83,plain,(
% 1.59/1.39 ($true = $false) | (~spl1_2 | ~spl1_4)),
% 1.59/1.39 inference(forward_demodulation,[status(thm)],[f30,f39])).
% 1.59/1.39 thf(f30,plain,(
% 1.59/1.39 ($true = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK0 @ Y0))))) | ~spl1_2),
% 1.59/1.39 inference(avatar_component_clause,[status(thm)],[f28])).
% 1.59/1.39 thf(f28,definition,(
% 1.59/1.39 spl1_2 <=> ($true = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK0 @ Y0)))))),
% 1.59/1.39 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.59/1.39 thf(f82,plain,(
% 1.59/1.39 ~spl1_1 | ~spl1_3),
% 1.59/1.39 inference(avatar_contradiction_clause,[status(thm)],[f81])).
% 1.59/1.39 thf(f81,plain,(
% 1.59/1.39 $false | (~spl1_1 | ~spl1_3)),
% 1.59/1.39 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.59/1.39 thf(f80,plain,(
% 1.59/1.39 ($true = $false) | (~spl1_1 | ~spl1_3)),
% 1.59/1.39 inference(forward_demodulation,[status(thm)],[f26,f35])).
% 1.59/1.39 thf(f35,plain,(
% 1.59/1.39 ($false = ('const/iterate/polynomial_function' @ sK0)) | ~spl1_3),
% 1.59/1.39 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.59/1.39 thf(f33,definition,(
% 1.59/1.39 spl1_3 <=> ($false = ('const/iterate/polynomial_function' @ sK0))),
% 1.59/1.39 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 1.59/1.39 thf(f78,plain,(
% 1.59/1.39 ~spl1_2 | ~spl1_3),
% 1.59/1.39 inference(avatar_contradiction_clause,[status(thm)],[f77])).
% 1.59/1.39 thf(f77,plain,(
% 1.59/1.39 $false | (~spl1_2 | ~spl1_3)),
% 1.59/1.39 inference(subsumption_resolution,[status(thm)],[f74,f20])).
% 1.59/1.39 thf(f20,plain,(
% 1.59/1.39 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_neg' @ ('const/realax/real_neg' @ X0)) = X0)) )),
% 1.59/1.39 inference(cnf_transformation,[status(thm)],[f4])).
% 1.59/1.39 thf(f4,axiom,(
% 1.59/1.39 ! [X0 : 'type/realax/real'] : (('const/realax/real_neg' @ ('const/realax/real_neg' @ X0)) = X0)),
% 1.59/1.39 file('/export/starexec/sandbox/tmp/tmp.N6oo7ynJnf/DTF2THF_3481.p','thm/calc_int/REAL_NEG_NEG_')).
% 1.59/1.39 thf(f74,plain,(
% 1.59/1.39 (('const/realax/real_neg' @ ('const/realax/real_neg' @ (sK0 @ (sK4 @ ('const/realax/real_neg' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))))) != (sK0 @ (sK4 @ ('const/realax/real_neg' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))))) | (~spl1_2 | ~spl1_3)),
% 1.59/1.39 inference(superposition,[status(thm)],[f70,f18])).
% 1.59/1.39 thf(f70,plain,(
% 1.59/1.39 ( ! [X0 : 'type/realax/real'] : (((sK0 @ (sK4 @ ('const/realax/real_neg' @ X0))) != ('const/realax/real_neg' @ ('const/realax/real_mul' @ X0 @ ('const/realax/real_neg' @ (sK0 @ (sK4 @ ('const/realax/real_neg' @ X0)))))))) ) | (~spl1_2 | ~spl1_3)),
% 1.59/1.39 inference(superposition,[status(thm)],[f61,f19])).
% 1.59/1.39 thf(f61,plain,(
% 1.59/1.39 ( ! [X0 : 'type/realax/real'] : (((sK0 @ (sK4 @ X0)) != ('const/realax/real_mul' @ X0 @ ('const/realax/real_neg' @ (sK0 @ (sK4 @ X0)))))) ) | (~spl1_2 | ~spl1_3)),
% 1.59/1.39 inference(beta_eta_normalization,[status(thm)],[f60])).
% 1.59/1.39 thf(f60,plain,(
% 1.59/1.39 ( ! [X0 : 'type/realax/real'] : (((sK0 @ (sK4 @ X0)) != ((^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ X0 @ ('const/realax/real_neg' @ (sK0 @ Y0)))) @ (sK4 @ X0)))) ) | (~spl1_2 | ~spl1_3)),
% 1.59/1.39 inference(negative_extensionality,[status(thm)],[f59])).
% 1.59/1.39 thf(f59,plain,(
% 1.59/1.39 ( ! [X0 : 'type/realax/real'] : ((sK0 != (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ X0 @ ('const/realax/real_neg' @ (sK0 @ Y0)))))) ) | (~spl1_2 | ~spl1_3)),
% 1.59/1.39 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 1.59/1.39 thf(f54,plain,(
% 1.59/1.39 ( ! [X0 : 'type/realax/real'] : (($true = $false) | (sK0 != (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ X0 @ ('const/realax/real_neg' @ (sK0 @ Y0)))))) ) | (~spl1_2 | ~spl1_3)),
% 1.59/1.39 inference(constrained_superposition,[status(thm)],[f35,f52])).
% 1.59/1.39 thf(f52,plain,(
% 1.59/1.39 ( ! [X0 : 'type/realax/real'] : ((('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ X0 @ ('const/realax/real_neg' @ (sK0 @ Y0))))) = $true)) ) | ~spl1_2),
% 1.59/1.39 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.59/1.39 thf(f51,plain,(
% 1.59/1.39 ( ! [X0 : 'type/realax/real'] : (($true = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ X0 @ ((^[Y1 : 'type/realax/real']: ('const/realax/real_neg' @ (sK0 @ Y1))) @ Y0)))))) ) | ~spl1_2),
% 1.59/1.39 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.59/1.39 thf(f49,plain,(
% 1.59/1.39 ( ! [X0 : 'type/realax/real'] : (($true = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_mul' @ X0 @ ((^[Y1 : 'type/realax/real']: ('const/realax/real_neg' @ (sK0 @ Y1))) @ Y0))))) | ($true != $true)) ) | ~spl1_2),
% 1.59/1.39 inference(superposition,[status(thm)],[f16,f30])).
% 1.59/1.39 thf(f40,plain,(
% 1.59/1.39 spl1_3 | spl1_4),
% 1.59/1.39 inference(avatar_split_clause,[status(thm)],[f22,f37,f33])).
% 1.59/1.39 thf(f22,plain,(
% 1.59/1.39 ($false = ('const/iterate/polynomial_function' @ sK0)) | ($false = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK0 @ Y0)))))),
% 1.59/1.39 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.59/1.39 thf(f17,plain,(
% 1.59/1.39 (('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK0 @ Y0)))) != ('const/iterate/polynomial_function' @ sK0))),
% 1.59/1.39 inference(cnf_transformation,[status(thm)],[f15])).
% 1.59/1.39 thf(f15,plain,(
% 1.59/1.39 (('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK0 @ Y0)))) != ('const/iterate/polynomial_function' @ sK0))),
% 1.59/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14])).
% 1.59/1.39 thf(f14,plain,(
% 1.59/1.39 ? [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))))) => (('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK0 @ Y0)))) != ('const/iterate/polynomial_function' @ sK0))),
% 1.59/1.39 introduced(definition,[],[choice_axiom])).
% 1.59/1.39 thf(f13,plain,(
% 1.59/1.39 ? [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)))))),
% 1.59/1.39 inference(ennf_transformation,[status(thm)],[f10])).
% 1.59/1.39 thf(f10,plain,(
% 1.59/1.39 ~! [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)))))),
% 1.59/1.39 inference(fool_elimination,[status(thm)],[f6])).
% 1.59/1.39 thf(f6,negated_conjecture,(
% 1.59/1.39 ~! [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))),
% 1.59/1.39 inference(negated_conjecture,[status(cth)],[f5])).
% 1.59/1.39 thf(f5,conjecture,(
% 1.59/1.39 ! [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))),
% 1.59/1.39 file('/export/starexec/sandbox/tmp/tmp.N6oo7ynJnf/DTF2THF_3481.p','thm/iterate/POLYNOMIAL_FUNCTION_NEG_')).
% 1.59/1.39 thf(f31,plain,(
% 1.59/1.39 spl1_1 | spl1_2),
% 1.59/1.39 inference(avatar_split_clause,[status(thm)],[f21,f28,f24])).
% 1.59/1.39 thf(f21,plain,(
% 1.59/1.39 ($true = ('const/iterate/polynomial_function' @ sK0)) | ($true = ('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: ('const/realax/real_neg' @ (sK0 @ Y0)))))),
% 1.59/1.39 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.59/1.39 % SZS output end Proof for DTF2THF_3481
% 1.59/1.39 % (3598)------------------------------
% 1.59/1.39 % (3598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.39 % (3598)Termination reason: Refutation
% 1.59/1.39
% 1.59/1.39 % (3598)Memory used [KB]: 5628
% 1.59/1.39 % (3598)Time elapsed: 0.012 s
% 1.59/1.39 % (3598)Instructions burned: 18 (million)
% 1.59/1.39 % (3598)------------------------------
% 1.59/1.39 % (3598)------------------------------
% 1.59/1.39 % (3577)Success in time 0.08 s
%------------------------------------------------------------------------------