%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUN051^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n021.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 09:27:15 AM UTC 2026
% Result : Theorem 1.66s 1.31s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 90 ( 34 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 325 ( 13 ~; 3 |; 4 &; 297 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 58 ( 13 ^; 39 !; 6 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/nums/num': $tType ).
thf(func_def_0,type,
'type/nums/num': $tType ).
thf(func_def_1,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_2,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_3,type,
'const/iterate/nsum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/nums/num' ) > 'type/nums/num' ) ).
thf(func_def_4,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_5,type,
'const/arith/+': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_6,type,
'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_7,type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_9,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_14,type,
sK0: 'type/nums/num' > 'type/nums/num' ).
thf(func_def_15,type,
sK1: 'type/nums/num' ).
thf(func_def_16,type,
sK2: 'type/nums/num' ).
thf(func_def_18,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f33,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 )
!= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 ) ),
inference(forward_demodulation,[status(thm)],[f31,f22]) ).
thf(f22,plain,
( sK2
= ( 'const/arith/+' @ ( 'const/arith/-' @ sK2 @ sK1 ) @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $true != $true )
| ( sK2
= ( 'const/arith/+' @ ( 'const/arith/-' @ sK2 @ sK1 ) @ sK1 ) ) ),
inference(superposition,[status(thm)],[f16,f17]) ).
thf(f17,plain,
( ( 'const/arith/<=' @ sK1 @ sK2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 )
!= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sK2 @ sK1 ) )
@ ^ [Y0: 'type/nums/num'] : ( sK0 @ ( 'const/arith/+' @ Y0 @ sK1 ) ) ) )
& ( ( 'const/arith/<=' @ sK1 @ sK2 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f14]) ).
thf(f14,plain,
( ? [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 )
!= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X2 @ X1 ) )
@ ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ X1 ) ) ) )
& ( ( 'const/arith/<=' @ X1 @ X2 )
= $true ) )
=> ( ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 )
!= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sK2 @ sK1 ) )
@ ^ [Y0: 'type/nums/num'] : ( sK0 @ ( 'const/arith/+' @ Y0 @ sK1 ) ) ) )
& ( ( 'const/arith/<=' @ sK1 @ sK2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
? [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 )
!= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X2 @ X1 ) )
@ ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ X1 ) ) ) )
& ( ( 'const/arith/<=' @ X1 @ X2 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X1 @ X2 )
= $true )
=> ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X2 @ X1 ) )
@ ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ X1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( 'const/arith/<=' @ X1 @ X2 )
=> ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X2 @ X1 ) )
@ ^ [X3: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ X3 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( 'const/arith/<=' @ X1 @ X2 )
=> ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X2 @ X1 ) )
@ ^ [X3: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ X3 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( 'const/arith/<=' @ X1 @ X2 )
=> ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X2 @ X1 ) )
@ ^ [X3: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ X3 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nYCkmnUWTq/DTF2THF_8960.p','thm/iterate/NSUM_OFFSET_0_') ).
thf(f16,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X1 @ X0 )
!= $true )
| ( ( 'const/arith/+' @ ( 'const/arith/-' @ X0 @ X1 ) @ X1 )
= X0 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X1 @ X0 )
!= $true )
| ( ( 'const/arith/+' @ ( 'const/arith/-' @ X0 @ X1 ) @ X1 )
= X0 ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X1 @ X0 )
= $true )
=> ( ( 'const/arith/+' @ ( 'const/arith/-' @ X0 @ X1 ) @ X1 )
= X0 ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ X1 @ X0 )
=> ( ( 'const/arith/+' @ ( 'const/arith/-' @ X0 @ X1 ) @ X1 )
= X0 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ X1 @ X0 )
=> ( ( 'const/arith/+' @ ( 'const/arith/-' @ X0 @ X1 ) @ X1 )
= X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.nYCkmnUWTq/DTF2THF_8960.p','thm/arith/SUB_ADD_') ).
thf(f31,plain,
( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 )
!= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ ( 'const/arith/+' @ ( 'const/arith/-' @ sK2 @ sK1 ) @ sK1 ) ) @ sK0 ) ),
inference(superposition,[status(thm)],[f18,f25]) ).
thf(f25,plain,
! [X2: 'type/nums/num' > 'type/nums/num',X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ ( 'const/arith/+' @ X1 @ X0 ) ) @ X2 )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ X1 )
@ ^ [Y0: 'type/nums/num'] : ( X2 @ ( 'const/arith/+' @ Y0 @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f20,f19]) ).
thf(f19,plain,
! [X0: 'type/nums/num'] :
( ( 'const/arith/+' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ X0 )
= X0 ),
inference(cnf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: 'type/nums/num'] :
( ( 'const/arith/+' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ X0 )
= X0 ),
file('/export/starexec/sandbox2/tmp/tmp.nYCkmnUWTq/DTF2THF_8960.p','thm/arith/ADD_CLAUSES_0') ).
thf(f20,plain,
! [X2: 'type/nums/num',X3: 'type/nums/num',X0: 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num'] :
( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/arith/+' @ X2 @ X0 ) @ ( 'const/arith/+' @ X3 @ X0 ) ) @ X1 )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/arith/+' @ X2 @ X0 ) @ ( 'const/arith/+' @ X3 @ X0 ) ) @ X1 )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [X4: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ X4 @ X0 ) ) )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/arith/+' @ X2 @ X0 ) @ ( 'const/arith/+' @ X3 @ X0 ) ) @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.nYCkmnUWTq/DTF2THF_8960.p','thm/iterate/NSUM_OFFSET_') ).
thf(f18,plain,
( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 )
!= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sK2 @ sK1 ) )
@ ^ [Y0: 'type/nums/num'] : ( sK0 @ ( 'const/arith/+' @ Y0 @ sK1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN051^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n021.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 11:19:54 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : NUN051^1 : TPTP v9.2.1. Released v7.0.0.
% 0.30/0.46 % Domain : Number theory
% 0.30/0.46 % Problem : NSUM_OFFSET_0
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Kal16]
% 0.30/0.46 % Names : NSUM_OFFSET_0_.p [Kal16]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v7.1.0
% 0.30/0.46 % Syntax : Number of formulae : 12 ( 2 unt; 8 typ; 0 def)
% 0.30/0.46 % Number of atoms : 10 ( 4 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.30/0.46 % Number of connectives : 46 ( 0 ~; 0 |; 0 &; 44 @)
% 0.30/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 7 ( 5 avg)
% 0.30/0.46 % Number of types : 2 ( 1 usr)
% 0.30/0.46 % Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 8 ( 7 usr; 1 con; 0-3 aty)
% 0.30/0.46 % Number of variables : 13 ( 2 ^; 10 !; 0 ?; 13 :)
% 0.30/0.46 % ( 1 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.46 % SPC : TH1_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : Exported from core HOL Light.
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf('thf_type_type/nums/num',type,
% 0.30/0.46 'type/nums/num': $tType ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/nums/NUMERAL',type,
% 0.30/0.46 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/nums/_0',type,
% 0.30/0.46 'const/nums/_0': 'type/nums/num' ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/iterate/nsum',type,
% 0.30/0.46 'const/iterate/nsum':
% 0.30/0.46 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/nums/num' ) > 'type/nums/num' ) ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/iterate/..',type,
% 0.30/0.46 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/arith/+',type,
% 0.30/0.46 'const/arith/+': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/arith/-',type,
% 0.30/0.46 'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/arith/<=',type,
% 0.30/0.46 'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
% 0.30/0.46
% 0.30/0.46 thf('thm/arith/SUB_ADD_',axiom,
% 0.30/0.46 ! [A: 'type/nums/num',A0: 'type/nums/num'] :
% 0.30/0.46 ( ( 'const/arith/<=' @ A0 @ A )
% 0.30/0.46 => ( ( 'const/arith/+' @ ( 'const/arith/-' @ A @ A0 ) @ A0 )
% 0.30/0.46 = A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf('thm/arith/ADD_CLAUSES_0',axiom,
% 0.30/0.46 ! [A: 'type/nums/num'] :
% 0.30/0.46 ( ( 'const/arith/+' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ A )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 thf('thm/iterate/NSUM_OFFSET_',axiom,
% 0.30/0.46 ! [A: 'type/nums/num',A0: 'type/nums/num' > 'type/nums/num',A1: 'type/nums/num',A2: 'type/nums/num'] :
% 0.30/0.46 ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/arith/+' @ A1 @ A ) @ ( 'const/arith/+' @ A2 @ A ) ) @ A0 )
% 0.30/0.46 = ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A1 @ A2 )
% 0.30/0.46 @ ^ [A3: 'type/nums/num'] : ( A0 @ ( 'const/arith/+' @ A3 @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf('thm/iterate/NSUM_OFFSET_0_',conjecture,
% 0.30/0.46 ! [A: 'type/nums/num' > 'type/nums/num',A0: 'type/nums/num',A1: 'type/nums/num'] :
% 0.30/0.46 ( ( 'const/arith/<=' @ A0 @ A1 )
% 0.30/0.46 => ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A0 @ A1 ) @ A )
% 0.30/0.46 = ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ A1 @ A0 ) )
% 0.30/0.46 @ ^ [A2: 'type/nums/num'] : ( A @ ( 'const/arith/+' @ A2 @ A0 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.52/1.27 ---- Embedded in THF ---
% 1.52/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.27 %%% Generated on Tue Feb 24 11:19:54 EST 2026
% 1.52/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.27 %%% Logic specification used:
% 1.52/1.27 %%% thf(spec, logic, $$dhol).
% 1.52/1.27
% 1.52/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.nYCkmnUWTq/DTF2DTF8960.p
% See solution above
% 1.52/1.27 ------------------------
% 1.52/1.28 ---- Cleaned THF ---
% 1.52/1.28 thf('thf_type_type/nums/num',type,
% 1.52/1.28 'type/nums/num': $tType ).
% 1.52/1.28
% 1.52/1.28 thf('thf_const_const/nums/NUMERAL',type,
% 1.52/1.28 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 1.52/1.28
% 1.52/1.28 thf('thf_const_const/nums/_0',type,
% 1.52/1.28 'const/nums/_0': 'type/nums/num' ).
% 1.52/1.28
% 1.52/1.28 thf('thf_const_const/iterate/nsum',type,
% 1.52/1.28 'const/iterate/nsum':
% 1.52/1.28 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/nums/num' ) > 'type/nums/num' ) ).
% 1.52/1.28
% 1.52/1.28 thf('thf_const_const/iterate/..',type,
% 1.52/1.28 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
% 1.52/1.28
% 1.52/1.28 thf('thf_const_const/arith/+',type,
% 1.52/1.28 'const/arith/+': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
% 1.52/1.28
% 1.52/1.28 thf('thf_const_const/arith/-',type,
% 1.52/1.28 'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
% 1.52/1.28
% 1.52/1.28 thf('thf_const_const/arith/<=',type,
% 1.52/1.28 'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
% 1.52/1.28
% 1.52/1.28 thf('thm/arith/SUB_ADD_',axiom,
% 1.52/1.28 ! [A: 'type/nums/num',A0: 'type/nums/num'] :
% 1.52/1.28 ( ( 'const/arith/<=' @ A0 @ A )
% 1.52/1.28 => ( ( 'const/arith/+' @ ( 'const/arith/-' @ A @ A0 ) @ A0 )
% 1.52/1.28 = A ) ) ).
% 1.52/1.28
% 1.52/1.28 thf('thm/arith/ADD_CLAUSES_0',axiom,
% 1.52/1.28 ! [A: 'type/nums/num'] :
% 1.52/1.28 ( ( 'const/arith/+' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ A )
% 1.52/1.28 = A ) ).
% 1.52/1.28
% 1.52/1.28 thf('thm/iterate/NSUM_OFFSET_',axiom,
% 1.52/1.28 ! [A: 'type/nums/num',A0: 'type/nums/num' > 'type/nums/num',A1: 'type/nums/num',A2: 'type/nums/num'] :
% 1.52/1.28 ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/arith/+' @ A1 @ A ) @ ( 'const/arith/+' @ A2 @ A ) ) @ A0 )
% 1.52/1.28 = ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A1 @ A2 )
% 1.52/1.28 @ ^ [A3: 'type/nums/num'] : ( A0 @ ( 'const/arith/+' @ A3 @ A ) ) ) ) ).
% 1.52/1.28
% 1.52/1.28 thf('thm/iterate/NSUM_OFFSET_0_',conjecture,
% 1.52/1.28 ! [A: 'type/nums/num' > 'type/nums/num',A0: 'type/nums/num',A1: 'type/nums/num'] :
% 1.52/1.28 ( ( 'const/arith/<=' @ A0 @ A1 )
% 1.52/1.28 => ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A0 @ A1 ) @ A )
% 1.52/1.28 = ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ A1 @ A0 ) )
% 1.52/1.28 @ ^ [A2: 'type/nums/num'] : ( A @ ( 'const/arith/+' @ A2 @ A0 ) ) ) ) ) ).
% 1.52/1.28 ------------------------
% 1.52/1.30 % (9236)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_8960 for (3000ds/4Mi)
% 1.66/1.30 % (9236)Instruction limit reached!
% 1.66/1.30 % (9236)------------------------------
% 1.66/1.30 % (9236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.30 % (9236)Termination reason: Unknown
% 1.66/1.30 % (9236)Termination phase: Saturation
% 1.66/1.30
% 1.66/1.30 % (9236)Memory used [KB]: 5500
% 1.66/1.30 % (9236)Time elapsed: 0.003 s
% 1.66/1.30 % (9236)Instructions burned: 5 (million)
% 1.66/1.30 % (9236)------------------------------
% 1.66/1.30 % (9236)------------------------------
% 1.66/1.30 % (9235)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8960 for (3000ds/183Mi)
% 1.66/1.30 % (9238)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8960 for (3000ds/2Mi)
% 1.66/1.30 % (9237)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_8960 for (3000ds/27Mi)
% 1.66/1.30 % (9239)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_8960 for (3000ds/2Mi)
% 1.66/1.30 % (9240)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_8960 for (3000ds/275Mi)
% 1.66/1.30 % (9241)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8960 for (3000ds/18Mi)
% 1.66/1.30 % (9238)Instruction limit reached!
% 1.66/1.30 % (9238)------------------------------
% 1.66/1.30 % (9238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.30 % (9238)Termination reason: Unknown
% 1.66/1.30 % (9238)Termination phase: Property scanning
% 1.66/1.30
% 1.66/1.30 % (9238)Memory used [KB]: 895
% 1.66/1.30 % (9238)Time elapsed: 0.003 s
% 1.66/1.30 % (9238)Instructions burned: 2 (million)
% 1.66/1.30 % (9238)------------------------------
% 1.66/1.30 % (9238)------------------------------
% 1.66/1.30 % (9239)Instruction limit reached!
% 1.66/1.30 % (9239)------------------------------
% 1.66/1.30 % (9239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.30 % (9239)Termination reason: Unknown
% 1.66/1.30 % (9239)Termination phase: Property scanning
% 1.66/1.30
% 1.66/1.30 % (9239)Memory used [KB]: 895
% 1.66/1.30 % (9239)Time elapsed: 0.003 s
% 1.66/1.30 % (9239)Instructions burned: 2 (million)
% 1.66/1.30 % (9239)------------------------------
% 1.66/1.30 % (9239)------------------------------
% 1.66/1.31 % (9240)Refutation not found, incomplete strategy
% 1.66/1.31 % (9240)------------------------------
% 1.66/1.31 % (9240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.31 % (9240)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.31
% 1.66/1.31
% 1.66/1.31 % (9240)Memory used [KB]: 5500
% 1.66/1.31 % (9240)Time elapsed: 0.004 s
% 1.66/1.31 % (9240)Instructions burned: 3 (million)
% 1.66/1.31 % (9240)------------------------------
% 1.66/1.31 % (9240)------------------------------
% 1.66/1.31 % (9242)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8960 for (2999ds/3Mi)
% 1.66/1.31 % (9242)Instruction limit reached!
% 1.66/1.31 % (9242)------------------------------
% 1.66/1.31 % (9242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.31 % (9242)Termination reason: Unknown
% 1.66/1.31 % (9242)Termination phase: Saturation
% 1.66/1.31
% 1.66/1.31 % (9242)Memory used [KB]: 5500
% 1.66/1.31 % (9242)Time elapsed: 0.003 s
% 1.66/1.31 % (9242)Instructions burned: 3 (million)
% 1.66/1.31 % (9242)------------------------------
% 1.66/1.31 % (9242)------------------------------
% 1.66/1.31 % (9237)First to succeed.
% 1.66/1.31 % (9237)Refutation found. Thanks to Tanya!
% 1.66/1.31 % SZS status Theorem for DTF2THF_8960
% 1.66/1.31 % SZS output start Proof for DTF2THF_8960
% 1.66/1.31 thf(type_def_5, type, 'type/nums/num': $tType).
% 1.66/1.31 thf(func_def_0, type, 'type/nums/num': $tType).
% 1.66/1.31 thf(func_def_1, type, 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num').
% 1.66/1.31 thf(func_def_2, type, 'const/nums/_0': 'type/nums/num').
% 1.66/1.31 thf(func_def_3, type, 'const/iterate/nsum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/nums/num') > 'type/nums/num')).
% 1.66/1.31 thf(func_def_4, type, 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o).
% 1.66/1.31 thf(func_def_5, type, 'const/arith/+': 'type/nums/num' > 'type/nums/num' > 'type/nums/num').
% 1.66/1.31 thf(func_def_6, type, 'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num').
% 1.66/1.31 thf(func_def_7, type, 'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o).
% 1.66/1.31 thf(func_def_9, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.66/1.31 thf(func_def_14, type, sK0: 'type/nums/num' > 'type/nums/num').
% 1.66/1.31 thf(func_def_15, type, sK1: 'type/nums/num').
% 1.66/1.31 thf(func_def_16, type, sK2: 'type/nums/num').
% 1.66/1.31 thf(func_def_18, type, ph4: !>[X0: $tType]:(X0)).
% 1.66/1.31 thf(f33,plain,(
% 1.66/1.31 $false),
% 1.66/1.31 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.66/1.31 thf(f32,plain,(
% 1.66/1.31 (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0) != ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0))),
% 1.66/1.31 inference(forward_demodulation,[status(thm)],[f31,f22])).
% 1.66/1.31 thf(f22,plain,(
% 1.66/1.31 (sK2 = ('const/arith/+' @ ('const/arith/-' @ sK2 @ sK1) @ sK1))),
% 1.66/1.31 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.66/1.31 thf(f21,plain,(
% 1.66/1.31 ($true != $true) | (sK2 = ('const/arith/+' @ ('const/arith/-' @ sK2 @ sK1) @ sK1))),
% 1.66/1.31 inference(superposition,[status(thm)],[f16,f17])).
% 1.66/1.31 thf(f17,plain,(
% 1.66/1.31 (('const/arith/<=' @ sK1 @ sK2) = $true)),
% 1.66/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.66/1.31 thf(f15,plain,(
% 1.66/1.31 (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0) != ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ sK2 @ sK1)) @ (^[Y0 : 'type/nums/num']: (sK0 @ ('const/arith/+' @ Y0 @ sK1))))) & (('const/arith/<=' @ sK1 @ sK2) = $true)),
% 1.66/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f14])).
% 1.66/1.31 thf(f14,plain,(
% 1.66/1.31 ? [X0 : 'type/nums/num' > 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : ((('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0) != ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ X2 @ X1)) @ (^[Y0 : 'type/nums/num']: (X0 @ ('const/arith/+' @ Y0 @ X1))))) & (('const/arith/<=' @ X1 @ X2) = $true)) => ((('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0) != ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ sK2 @ sK1)) @ (^[Y0 : 'type/nums/num']: (sK0 @ ('const/arith/+' @ Y0 @ sK1))))) & (('const/arith/<=' @ sK1 @ sK2) = $true))),
% 1.66/1.31 introduced(definition,[],[choice_axiom])).
% 1.66/1.31 thf(f13,plain,(
% 1.66/1.31 ? [X0 : 'type/nums/num' > 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : ((('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0) != ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ X2 @ X1)) @ (^[Y0 : 'type/nums/num']: (X0 @ ('const/arith/+' @ Y0 @ X1))))) & (('const/arith/<=' @ X1 @ X2) = $true))),
% 1.66/1.31 inference(ennf_transformation,[status(thm)],[f8])).
% 1.66/1.31 thf(f8,plain,(
% 1.66/1.31 ~! [X0 : 'type/nums/num' > 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : ((('const/arith/<=' @ X1 @ X2) = $true) => (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0) = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ X2 @ X1)) @ (^[Y0 : 'type/nums/num']: (X0 @ ('const/arith/+' @ Y0 @ X1))))))),
% 1.66/1.31 inference(fool_elimination,[status(thm)],[f7])).
% 1.66/1.31 thf(f7,plain,(
% 1.66/1.31 ~! [X0 : 'type/nums/num' > 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : (('const/arith/<=' @ X1 @ X2) => (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0) = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ X2 @ X1)) @ (^[X3 : 'type/nums/num'] : (X0 @ ('const/arith/+' @ X3 @ X1))))))),
% 1.66/1.31 inference(rectify,[status(thm)],[f5])).
% 1.66/1.31 thf(f5,negated_conjecture,(
% 1.66/1.31 ~! [X0 : 'type/nums/num' > 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : (('const/arith/<=' @ X1 @ X2) => (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0) = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ X2 @ X1)) @ (^[X3 : 'type/nums/num'] : (X0 @ ('const/arith/+' @ X3 @ X1))))))),
% 1.66/1.31 inference(negated_conjecture,[status(cth)],[f4])).
% 1.66/1.31 thf(f4,conjecture,(
% 1.66/1.31 ! [X0 : 'type/nums/num' > 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : (('const/arith/<=' @ X1 @ X2) => (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0) = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ X2 @ X1)) @ (^[X3 : 'type/nums/num'] : (X0 @ ('const/arith/+' @ X3 @ X1))))))),
% 1.66/1.31 file('/export/starexec/sandbox2/tmp/tmp.nYCkmnUWTq/DTF2THF_8960.p','thm/iterate/NSUM_OFFSET_0_')).
% 1.66/1.31 thf(f16,plain,(
% 1.66/1.31 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ((('const/arith/<=' @ X1 @ X0) != $true) | (('const/arith/+' @ ('const/arith/-' @ X0 @ X1) @ X1) = X0)) )),
% 1.66/1.31 inference(cnf_transformation,[status(thm)],[f12])).
% 1.66/1.31 thf(f12,plain,(
% 1.66/1.31 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ((('const/arith/<=' @ X1 @ X0) != $true) | (('const/arith/+' @ ('const/arith/-' @ X0 @ X1) @ X1) = X0))),
% 1.66/1.31 inference(ennf_transformation,[status(thm)],[f11])).
% 1.66/1.31 thf(f11,plain,(
% 1.66/1.31 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ((('const/arith/<=' @ X1 @ X0) = $true) => (('const/arith/+' @ ('const/arith/-' @ X0 @ X1) @ X1) = X0))),
% 1.66/1.31 inference(fool_elimination,[status(thm)],[f10])).
% 1.66/1.31 thf(f10,plain,(
% 1.66/1.31 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (('const/arith/<=' @ X1 @ X0) => (('const/arith/+' @ ('const/arith/-' @ X0 @ X1) @ X1) = X0))),
% 1.66/1.31 inference(rectify,[status(thm)],[f1])).
% 1.66/1.31 thf(f1,axiom,(
% 1.66/1.31 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (('const/arith/<=' @ X1 @ X0) => (('const/arith/+' @ ('const/arith/-' @ X0 @ X1) @ X1) = X0))),
% 1.66/1.31 file('/export/starexec/sandbox2/tmp/tmp.nYCkmnUWTq/DTF2THF_8960.p','thm/arith/SUB_ADD_')).
% 1.66/1.31 thf(f31,plain,(
% 1.66/1.31 (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0) != ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ ('const/arith/+' @ ('const/arith/-' @ sK2 @ sK1) @ sK1)) @ sK0))),
% 1.66/1.31 inference(superposition,[status(thm)],[f18,f25])).
% 1.66/1.31 thf(f25,plain,(
% 1.66/1.31 ( ! [X2 : 'type/nums/num' > 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num'] : ((('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ ('const/arith/+' @ X1 @ X0)) @ X2) = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X1) @ (^[Y0 : 'type/nums/num']: (X2 @ ('const/arith/+' @ Y0 @ X0)))))) )),
% 1.66/1.31 inference(superposition,[status(thm)],[f20,f19])).
% 1.66/1.31 thf(f19,plain,(
% 1.66/1.31 ( ! [X0 : 'type/nums/num'] : ((('const/arith/+' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X0) = X0)) )),
% 1.66/1.31 inference(cnf_transformation,[status(thm)],[f2])).
% 1.66/1.31 thf(f2,axiom,(
% 1.66/1.31 ! [X0 : 'type/nums/num'] : (('const/arith/+' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X0) = X0)),
% 1.66/1.31 file('/export/starexec/sandbox2/tmp/tmp.nYCkmnUWTq/DTF2THF_8960.p','thm/arith/ADD_CLAUSES_0')).
% 1.66/1.31 thf(f20,plain,(
% 1.66/1.31 ( ! [X2 : 'type/nums/num',X3 : 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num' > 'type/nums/num'] : ((('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/arith/+' @ X2 @ X0) @ ('const/arith/+' @ X3 @ X0)) @ X1) = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X2 @ X3) @ (^[Y0 : 'type/nums/num']: (X1 @ ('const/arith/+' @ Y0 @ X0)))))) )),
% 1.66/1.31 inference(cnf_transformation,[status(thm)],[f9])).
% 1.66/1.31 thf(f9,plain,(
% 1.66/1.31 ! [X0 : 'type/nums/num',X1 : 'type/nums/num' > 'type/nums/num',X2 : 'type/nums/num',X3 : 'type/nums/num'] : (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/arith/+' @ X2 @ X0) @ ('const/arith/+' @ X3 @ X0)) @ X1) = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X2 @ X3) @ (^[Y0 : 'type/nums/num']: (X1 @ ('const/arith/+' @ Y0 @ X0)))))),
% 1.66/1.31 inference(fool_elimination,[status(thm)],[f3])).
% 1.66/1.31 thf(f3,axiom,(
% 1.66/1.31 ! [X0 : 'type/nums/num',X1 : 'type/nums/num' > 'type/nums/num',X2 : 'type/nums/num',X3 : 'type/nums/num'] : (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X2 @ X3) @ (^[X4 : 'type/nums/num'] : (X1 @ ('const/arith/+' @ X4 @ X0)))) = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/arith/+' @ X2 @ X0) @ ('const/arith/+' @ X3 @ X0)) @ X1))),
% 1.66/1.31 file('/export/starexec/sandbox2/tmp/tmp.nYCkmnUWTq/DTF2THF_8960.p','thm/iterate/NSUM_OFFSET_')).
% 1.66/1.31 thf(f18,plain,(
% 1.66/1.31 (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0) != ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ ('const/arith/-' @ sK2 @ sK1)) @ (^[Y0 : 'type/nums/num']: (sK0 @ ('const/arith/+' @ Y0 @ sK1)))))),
% 1.66/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.66/1.31 % SZS output end Proof for DTF2THF_8960
% 1.66/1.31 % (9237)------------------------------
% 1.66/1.31 % (9237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.31 % (9237)Termination reason: Refutation
% 1.66/1.31
% 1.66/1.31 % (9237)Memory used [KB]: 5500
% 1.66/1.31 % (9237)Time elapsed: 0.011 s
% 1.66/1.31 % (9237)Instructions burned: 11 (million)
% 1.66/1.31 % (9237)------------------------------
% 1.66/1.31 % (9237)------------------------------
% 1.66/1.31 % (9234)Success in time 0.025 s
%------------------------------------------------------------------------------