%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA123^1 : 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 : n017.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 1.46s 1.29s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 9 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 26 ( 6 ~; 0 |; 0 &; 20 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 11 ( 8 ^; 3 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/realax/real': $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'const/trivia/I':
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_2,type,
'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
thf(f16,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f12,f15]) ).
thf(f15,plain,
( ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : Y0 )
!= $true ),
inference(definition_unfolding,[status(thm)],[f13,f14]) ).
thf(f14,plain,
! [X0: $tType] :
( 'const/trivia/I'
@ ( X0
= ( ^ [Y0: X0] : Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $tType] :
( 'const/trivia/I'
@ ( X0
= ( ^ [Y0: X0] : Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType] :
( 'const/trivia/I'
@ ( X0
= ( ^ [X1: X0] : X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5AcFHivnCJ/DTF2THF_32644.p','thm/trivia/I_DEF_') ).
thf(f13,plain,
( ( 'const/iterate/polynomial_function' @ 'const/trivia/I' @ 'type/realax/real' )
!= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( 'const/iterate/polynomial_function' @ 'const/trivia/I' @ 'type/realax/real' )
!= $true ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
( ( 'const/iterate/polynomial_function' @ 'const/trivia/I' @ 'type/realax/real' )
!= $true ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( 'const/iterate/polynomial_function' @ 'const/trivia/I' @ 'type/realax/real' ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( 'const/iterate/polynomial_function' @ 'const/trivia/I' @ 'type/realax/real' ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
'const/iterate/polynomial_function' @ 'const/trivia/I' @ 'type/realax/real',
file('/export/starexec/sandbox/tmp/tmp.5AcFHivnCJ/DTF2THF_32644.p','thm/iterate/POLYNOMIAL_FUNCTION_I_') ).
thf(f12,plain,
( ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : Y0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : Y0 )
= $true ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( 'const/iterate/polynomial_function'
@ ^ [X0: 'type/realax/real'] : X0 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( 'const/iterate/polynomial_function'
@ ^ [X0: 'type/realax/real'] : X0 ),
file('/export/starexec/sandbox/tmp/tmp.5AcFHivnCJ/DTF2THF_32644.p','thm/iterate/POLYNOMIAL_FUNCTION_ID_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ANA123^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n017.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 03:50:26 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : ANA123^1 : TPTP v9.2.1. Released v7.0.0.
% 0.29/0.45 % Domain : Analysis
% 0.29/0.45 % Problem : POLYNOMIAL_FUNCTION_I
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Kal16]
% 0.29/0.45 % Names : POLYNOMIAL_FUNCTION_I_.p [Kal16]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.00 v7.5.0, 0.33 v7.2.0, 0.50 v7.1.0
% 0.29/0.45 % Syntax : Number of formulae : 6 ( 3 unt; 3 typ; 1 def)
% 0.29/0.45 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 1 ( 1 avg)
% 0.29/0.45 % Number of connectives : 4 ( 0 ~; 0 |; 0 &; 4 @)
% 0.29/0.45 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 3 ( 3 avg)
% 0.29/0.45 % Number of types : 2 ( 1 usr)
% 0.29/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.29/0.45 % Number of variables : 4 ( 2 ^; 1 !; 0 ?; 4 :)
% 0.29/0.45 % ( 1 !>; 0 ?*; 0 @-; 0 @+)
% 0.29/0.45 % SPC : TH1_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : Exported from core HOL Light.
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf('thf_type_type/realax/real',type,
% 0.29/0.45 'type/realax/real': $tType ).
% 0.29/0.45
% 0.29/0.45 thf('thf_const_const/trivia/I',type,
% 0.29/0.45 'const/trivia/I':
% 0.29/0.45 !>[A: $tType] : ( A > A ) ).
% 0.29/0.45
% 0.29/0.45 thf('thf_const_const/iterate/polynomial_function',type,
% 0.29/0.45 'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf('thm/iterate/POLYNOMIAL_FUNCTION_ID_',axiom,
% 0.29/0.45 ( 'const/iterate/polynomial_function'
% 0.29/0.45 @ ^ [A: 'type/realax/real'] : A ) ).
% 0.29/0.45
% 0.29/0.45 thf('thm/trivia/I_DEF_',definition,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( 'const/trivia/I' @ A )
% 0.29/0.45 = ( ^ [A0: A] : A0 ) ) ).
% 0.29/0.45
% 0.29/0.45 thf('thm/iterate/POLYNOMIAL_FUNCTION_I_',conjecture,
% 0.29/0.45 'const/iterate/polynomial_function' @ ( 'const/trivia/I' @ 'type/realax/real' ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.46/1.26 ---- Embedded in THF ---
% 1.46/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.27 %%% Generated on Tue Feb 24 03:50:26 EST 2026
% 1.46/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.27 %%% Logic specification used:
% 1.46/1.27 %%% thf(spec, logic, $$dhol).
% 1.46/1.27
% 1.46/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.5AcFHivnCJ/DTF2DTF32644.p
% See solution above
% 1.46/1.27 ------------------------
% 1.46/1.27 ---- Cleaned THF ---
% 1.46/1.28 thf('thf_type_type/realax/real',type,
% 1.46/1.28 'type/realax/real': $tType ).
% 1.46/1.28
% 1.46/1.28 thf('thf_const_const/trivia/I',type,
% 1.46/1.28 'const/trivia/I':
% 1.46/1.28 !>[A: $tType] : ( A > A ) ).
% 1.46/1.28
% 1.46/1.28 thf('thf_const_const/iterate/polynomial_function',type,
% 1.46/1.28 'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
% 1.46/1.28
% 1.46/1.28 thf('thm/iterate/POLYNOMIAL_FUNCTION_ID_',axiom,
% 1.46/1.28 ( 'const/iterate/polynomial_function'
% 1.46/1.28 @ ^ [A: 'type/realax/real'] : A ) ).
% 1.46/1.28
% 1.46/1.28 thf('thm/trivia/I_DEF_',definition,
% 1.46/1.28 ! [A: $tType] :
% 1.46/1.28 ( ( 'const/trivia/I' @ A )
% 1.46/1.28 = ( ^ [A0: A] : A0 ) ) ).
% 1.46/1.28
% 1.46/1.28 thf('thm/iterate/POLYNOMIAL_FUNCTION_I_',conjecture,
% 1.46/1.28 'const/iterate/polynomial_function' @ ( 'const/trivia/I' @ 'type/realax/real' ) ).
% 1.46/1.28 ------------------------
% 1.46/1.29 % (479)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32644 for (3000ds/18Mi)
% 1.46/1.29 % (479)First to succeed.
% 1.46/1.29 % (479)Refutation found. Thanks to Tanya!
% 1.46/1.29 % SZS status Theorem for DTF2THF_32644
% 1.46/1.29 % SZS output start Proof for DTF2THF_32644
% 1.46/1.29 thf(type_def_6, type, 'type/realax/real': $tType).
% 1.46/1.29 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.46/1.29 thf(func_def_1, type, 'const/trivia/I': !>[X0: $tType]:(X0 > X0)).
% 1.46/1.29 thf(func_def_2, type, 'const/iterate/polynomial_function': ('type/realax/real' > 'type/realax/real') > $o).
% 1.46/1.29 thf(f16,plain,(
% 1.46/1.29 $false),
% 1.46/1.29 inference(subsumption_resolution,[status(thm)],[f12,f15])).
% 1.46/1.29 thf(f15,plain,(
% 1.46/1.29 (('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: (Y0))) != $true)),
% 1.46/1.29 inference(definition_unfolding,[status(thm)],[f13,f14])).
% 1.46/1.29 thf(f14,plain,(
% 1.46/1.29 ( ! [X0 : $tType] : (('const/trivia/I' @ X0 = (^[Y0 : X0]: (Y0)))) )),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f6])).
% 1.46/1.29 thf(f6,plain,(
% 1.46/1.29 ! [X0 : $tType] : ('const/trivia/I' @ X0 = (^[Y0 : X0]: (Y0)))),
% 1.46/1.29 inference(fool_elimination,[status(thm)],[f2])).
% 1.46/1.29 thf(f2,axiom,(
% 1.46/1.29 ! [X0 : $tType] : ('const/trivia/I' @ X0 = (^[X1 : X0] : (X1)))),
% 1.46/1.29 file('/export/starexec/sandbox/tmp/tmp.5AcFHivnCJ/DTF2THF_32644.p','thm/trivia/I_DEF_')).
% 1.46/1.29 thf(f13,plain,(
% 1.46/1.29 (('const/iterate/polynomial_function' @ 'const/trivia/I' @ 'type/realax/real') != $true)),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.46/1.29 thf(f11,plain,(
% 1.46/1.29 (('const/iterate/polynomial_function' @ 'const/trivia/I' @ 'type/realax/real') != $true)),
% 1.46/1.29 inference(flattening,[status(thm)],[f8])).
% 1.46/1.29 thf(f8,plain,(
% 1.46/1.29 ~(('const/iterate/polynomial_function' @ 'const/trivia/I' @ 'type/realax/real') = $true)),
% 1.46/1.29 inference(fool_elimination,[status(thm)],[f7])).
% 1.46/1.29 thf(f7,plain,(
% 1.46/1.29 ~('const/iterate/polynomial_function' @ 'const/trivia/I' @ 'type/realax/real')),
% 1.46/1.29 inference(rectify,[status(thm)],[f4])).
% 1.46/1.29 thf(f4,negated_conjecture,(
% 1.46/1.29 ~('const/iterate/polynomial_function' @ 'const/trivia/I' @ 'type/realax/real')),
% 1.46/1.29 inference(negated_conjecture,[status(cth)],[f3])).
% 1.46/1.29 thf(f3,conjecture,(
% 1.46/1.29 ('const/iterate/polynomial_function' @ 'const/trivia/I' @ 'type/realax/real')),
% 1.46/1.29 file('/export/starexec/sandbox/tmp/tmp.5AcFHivnCJ/DTF2THF_32644.p','thm/iterate/POLYNOMIAL_FUNCTION_I_')).
% 1.46/1.29 thf(f12,plain,(
% 1.46/1.29 (('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: (Y0))) = $true)),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f10])).
% 1.46/1.29 thf(f10,plain,(
% 1.46/1.29 (('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: (Y0))) = $true)),
% 1.46/1.29 inference(fool_elimination,[status(thm)],[f9])).
% 1.46/1.29 thf(f9,plain,(
% 1.46/1.29 ('const/iterate/polynomial_function' @ (^[X0 : 'type/realax/real'] : (X0)))),
% 1.46/1.29 inference(rectify,[status(thm)],[f1])).
% 1.46/1.29 thf(f1,axiom,(
% 1.46/1.29 ('const/iterate/polynomial_function' @ (^[X0 : 'type/realax/real'] : (X0)))),
% 1.46/1.29 file('/export/starexec/sandbox/tmp/tmp.5AcFHivnCJ/DTF2THF_32644.p','thm/iterate/POLYNOMIAL_FUNCTION_ID_')).
% 1.46/1.29 % SZS output end Proof for DTF2THF_32644
% 1.46/1.29 % (479)------------------------------
% 1.46/1.29 % (479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (479)Termination reason: Refutation
% 1.46/1.29
% 1.46/1.29 % (479)Memory used [KB]: 5373
% 1.46/1.29 % (479)Time elapsed: 0.002 s
% 1.46/1.29 % (479)------------------------------
% 1.46/1.29 % (479)------------------------------
% 1.46/1.29 % (471)Success in time 0.012 s
%------------------------------------------------------------------------------