%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA115^1 : 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 : n024.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 08:38:54 AM UTC 2026
% Result : Theorem 0.86s 0.88s
% Output : Refutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 64 ( 21 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 214 ( 12 ~; 3 |; 0 &; 195 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 51 ( 13 ^; 32 !; 6 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(type_def_7,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/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
thf(func_def_4,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_5,type,
'const/iterate/nsum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/nums/num' ) > 'type/nums/num' ) ).
thf(func_def_6,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_12,type,
sK0: 'type/nums/num' > 'type/nums/num' ).
thf(func_def_13,type,
sK1: 'type/nums/num' ).
thf(func_def_14,type,
sK2: 'type/nums/num' ).
thf(func_def_16,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f20,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f19,f15]) ).
thf(f15,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: 'type/nums/num',X1: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.7GupvXpVwo/DTF2THF_30808.p','thm/iterate/FINITE_NUMSEG_') ).
thf(f19,plain,
( $true
!= ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $true
!= ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) ) )
| ( ( 'const/realax/real_of_num' @ ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 ) )
!= ( 'const/realax/real_of_num' @ ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 ) ) ) ),
inference(superposition,[status(thm)],[f16,f17]) ).
thf(f17,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > 'type/nums/num'] :
( ( ( 'const/realax/real_of_num' @ ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) )
= ( 'const/iterate/sum' @ X0 @ X2
@ ^ [Y0: X0] : ( 'const/realax/real_of_num' @ ( X1 @ Y0 ) ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $tType,X1: X0 > 'type/nums/num',X2: X0 > $o] :
( ( ( 'const/realax/real_of_num' @ ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) )
= ( 'const/iterate/sum' @ X0 @ X2
@ ^ [Y0: X0] : ( 'const/realax/real_of_num' @ ( X1 @ Y0 ) ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $tType,X1: X0 > 'type/nums/num',X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
=> ( ( 'const/realax/real_of_num' @ ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) )
= ( 'const/iterate/sum' @ X0 @ X2
@ ^ [Y0: X0] : ( 'const/realax/real_of_num' @ ( X1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $tType,X1: X0 > 'type/nums/num',X2: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X2 )
=> ( ( 'const/realax/real_of_num' @ ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) )
= ( 'const/iterate/sum' @ X0 @ X2
@ ^ [X3: X0] : ( 'const/realax/real_of_num' @ ( X1 @ X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > 'type/nums/num',X2: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X2 )
=> ( ( 'const/realax/real_of_num' @ ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) )
= ( 'const/iterate/sum' @ X0 @ X2
@ ^ [X3: X0] : ( 'const/realax/real_of_num' @ ( X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7GupvXpVwo/DTF2THF_30808.p','thm/iterate/REAL_OF_NUM_SUM_') ).
thf(f16,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_of_num' @ ( sK0 @ Y0 ) ) )
!= ( 'const/realax/real_of_num' @ ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_of_num' @ ( sK0 @ Y0 ) ) )
!= ( 'const/realax/real_of_num' @ ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f11,f13]) ).
thf(f13,plain,
( ? [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( 'const/realax/real_of_num' @ ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_of_num' @ ( X0 @ Y0 ) ) ) )
=> ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_of_num' @ ( sK0 @ Y0 ) ) )
!= ( 'const/realax/real_of_num' @ ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
? [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( 'const/realax/real_of_num' @ ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_of_num' @ ( X0 @ Y0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
~ ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( 'const/realax/real_of_num' @ ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 ) )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_of_num' @ ( X0 @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( 'const/realax/real_of_num' @ ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 ) )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 )
@ ^ [X3: 'type/nums/num'] : ( 'const/realax/real_of_num' @ ( X0 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( 'const/realax/real_of_num' @ ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 ) )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 )
@ ^ [X3: 'type/nums/num'] : ( 'const/realax/real_of_num' @ ( X0 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7GupvXpVwo/DTF2THF_30808.p','thm/iterate/REAL_OF_NUM_SUM_NUMSEG_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : ANA115^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon Feb 23 22:50:25 EST 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.24 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.06/0.31 ---- Original DTF file ---
% 0.06/0.31 thf(spec,logic,$$dhol).
% 0.06/0.31 %------------------------------------------------------------------------------
% 0.06/0.31 % File : ANA115^1 : TPTP v9.2.1. Released v7.0.0.
% 0.06/0.31 % Domain : Analysis
% 0.06/0.31 % Problem : REAL_OF_NUM_SUM_NUMSEG
% 0.06/0.31 % Version : Especial.
% 0.06/0.31 % English :
% 0.06/0.31
% 0.06/0.31 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.06/0.31 % Source : [Kal16]
% 0.06/0.31 % Names : REAL_OF_NUM_SUM_NUMSEG_.p [Kal16]
% 0.06/0.31
% 0.06/0.31 % Status : Theorem
% 0.06/0.31 % Rating : 0.00 v7.1.0
% 0.06/0.31 % Syntax : Number of formulae : 10 ( 1 unt; 7 typ; 0 def)
% 0.06/0.31 % Number of atoms : 7 ( 2 equ; 0 cnn)
% 0.06/0.31 % Maximal formula atoms : 2 ( 2 avg)
% 0.06/0.31 % Number of connectives : 29 ( 0 ~; 0 |; 0 &; 28 @)
% 0.06/0.31 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.06/0.31 % Maximal formula depth : 7 ( 6 avg)
% 0.06/0.31 % Number of types : 3 ( 2 usr)
% 0.06/0.31 % Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% 0.06/0.31 % Number of symbols : 6 ( 5 usr; 0 con; 1-3 aty)
% 0.06/0.31 % Number of variables : 13 ( 2 ^; 8 !; 0 ?; 13 :)
% 0.06/0.31 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.06/0.31 % SPC : TH1_THM_EQU_NAR
% 0.06/0.31
% 0.06/0.31 % Comments : Exported from core HOL Light.
% 0.06/0.31 %------------------------------------------------------------------------------
% 0.06/0.31 thf('thf_type_type/realax/real',type,
% 0.06/0.31 'type/realax/real': $tType ).
% 0.06/0.31
% 0.06/0.31 thf('thf_type_type/nums/num',type,
% 0.06/0.31 'type/nums/num': $tType ).
% 0.06/0.31
% 0.06/0.31 thf('thf_const_const/sets/FINITE',type,
% 0.06/0.31 'const/sets/FINITE':
% 0.06/0.31 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.06/0.31
% 0.06/0.31 thf('thf_const_const/realax/real_of_num',type,
% 0.06/0.31 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
% 0.06/0.31
% 0.06/0.31 thf('thf_const_const/iterate/sum',type,
% 0.06/0.31 'const/iterate/sum':
% 0.06/0.31 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 0.06/0.31
% 0.06/0.31 thf('thf_const_const/iterate/nsum',type,
% 0.06/0.31 'const/iterate/nsum':
% 0.06/0.31 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/nums/num' ) > 'type/nums/num' ) ).
% 0.06/0.31
% 0.06/0.31 thf('thf_const_const/iterate/..',type,
% 0.06/0.31 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
% 0.06/0.31
% 0.06/0.31 thf('thm/iterate/REAL_OF_NUM_SUM_',axiom,
% 0.06/0.31 ! [A: $tType,A0: A > 'type/nums/num',A1: A > $o] :
% 0.06/0.31 ( ( 'const/sets/FINITE' @ A @ A1 )
% 0.06/0.31 => ( ( 'const/realax/real_of_num' @ ( 'const/iterate/nsum' @ A @ A1 @ A0 ) )
% 0.06/0.31 = ( 'const/iterate/sum' @ A @ A1
% 0.06/0.31 @ ^ [A2: A] : ( 'const/realax/real_of_num' @ ( A0 @ A2 ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf('thm/iterate/FINITE_NUMSEG_',axiom,
% 0.06/0.31 ! [A: 'type/nums/num',A0: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ A0 ) ) ).
% 0.06/0.31
% 0.06/0.31 thf('thm/iterate/REAL_OF_NUM_SUM_NUMSEG_',conjecture,
% 0.06/0.31 ! [A: 'type/nums/num' > 'type/nums/num',A0: 'type/nums/num',A1: 'type/nums/num'] :
% 0.06/0.31 ( ( 'const/realax/real_of_num' @ ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A0 @ A1 ) @ A ) )
% 0.06/0.31 = ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A0 @ A1 )
% 0.06/0.31 @ ^ [A2: 'type/nums/num'] : ( 'const/realax/real_of_num' @ ( A @ A2 ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 %------------------------------------------------------------------------------
% 0.06/0.31 ------------------------
% 0.86/0.86 ---- Embedded in THF ---
% 0.86/0.86 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.86/0.86 %%% Generated on Mon Feb 23 22:50:26 EST 2026
% 0.86/0.86 %%% using '$$dhol' embedding, version 1.3.0.
% 0.86/0.86 %%% Logic specification used:
% 0.86/0.86 %%% thf(spec, logic, $$dhol).
% 0.86/0.86
% 0.86/0.86 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.7GupvXpVwo/DTF2DTF30808.p
% See solution above
% 0.86/0.86 ------------------------
% 0.86/0.86 ---- Cleaned THF ---
% 0.86/0.87 thf('thf_type_type/realax/real',type,
% 0.86/0.87 'type/realax/real': $tType ).
% 0.86/0.87
% 0.86/0.87 thf('thf_type_type/nums/num',type,
% 0.86/0.87 'type/nums/num': $tType ).
% 0.86/0.87
% 0.86/0.87 thf('thf_const_const/sets/FINITE',type,
% 0.86/0.87 'const/sets/FINITE':
% 0.86/0.87 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.86/0.87
% 0.86/0.87 thf('thf_const_const/realax/real_of_num',type,
% 0.86/0.87 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
% 0.86/0.87
% 0.86/0.87 thf('thf_const_const/iterate/sum',type,
% 0.86/0.87 'const/iterate/sum':
% 0.86/0.87 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 0.86/0.87
% 0.86/0.87 thf('thf_const_const/iterate/nsum',type,
% 0.86/0.87 'const/iterate/nsum':
% 0.86/0.87 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/nums/num' ) > 'type/nums/num' ) ).
% 0.86/0.87
% 0.86/0.87 thf('thf_const_const/iterate/..',type,
% 0.86/0.87 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
% 0.86/0.87
% 0.86/0.87 thf('thm/iterate/REAL_OF_NUM_SUM_',axiom,
% 0.86/0.87 ! [A: $tType,A0: A > 'type/nums/num',A1: A > $o] :
% 0.86/0.87 ( ( 'const/sets/FINITE' @ A @ A1 )
% 0.86/0.87 => ( ( 'const/realax/real_of_num' @ ( 'const/iterate/nsum' @ A @ A1 @ A0 ) )
% 0.86/0.87 = ( 'const/iterate/sum' @ A @ A1
% 0.86/0.87 @ ^ [A2: A] : ( 'const/realax/real_of_num' @ ( A0 @ A2 ) ) ) ) ) ).
% 0.86/0.87
% 0.86/0.87 thf('thm/iterate/FINITE_NUMSEG_',axiom,
% 0.86/0.87 ! [A: 'type/nums/num',A0: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ A0 ) ) ).
% 0.86/0.87
% 0.86/0.87 thf('thm/iterate/REAL_OF_NUM_SUM_NUMSEG_',conjecture,
% 0.86/0.87 ! [A: 'type/nums/num' > 'type/nums/num',A0: 'type/nums/num',A1: 'type/nums/num'] :
% 0.86/0.87 ( ( 'const/realax/real_of_num' @ ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A0 @ A1 ) @ A ) )
% 0.86/0.87 = ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A0 @ A1 )
% 0.86/0.87 @ ^ [A2: 'type/nums/num'] : ( 'const/realax/real_of_num' @ ( A @ A2 ) ) ) ) ).
% 0.86/0.87 ------------------------
% 0.86/0.88 % (31012)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_30808 for (3000ds/4Mi)
% 0.86/0.88 % (31014)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30808 for (3000ds/2Mi)
% 0.86/0.88 % (31016)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_30808 for (3000ds/275Mi)
% 0.86/0.88 % (31011)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30808 for (3000ds/183Mi)
% 0.86/0.88 % (31015)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_30808 for (3000ds/2Mi)
% 0.86/0.88 % (31013)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_30808 for (3000ds/27Mi)
% 0.86/0.88 % (31017)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30808 for (3000ds/18Mi)
% 0.86/0.88 % (31014)Instruction limit reached!
% 0.86/0.88 % (31014)------------------------------
% 0.86/0.88 % (31014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.86/0.88 % (31014)Termination reason: Unknown
% 0.86/0.88 % (31014)Termination phase: Saturation
% 0.86/0.88
% 0.86/0.88 % (31014)Memory used [KB]: 5373
% 0.86/0.88 % (31014)Time elapsed: 0.002 s
% 0.86/0.88 % (31014)Instructions burned: 2 (million)
% 0.86/0.88 % (31014)------------------------------
% 0.86/0.88 % (31014)------------------------------
% 0.86/0.88 % (31015)Instruction limit reached!
% 0.86/0.88 % (31015)------------------------------
% 0.86/0.88 % (31015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.86/0.88 % (31015)Termination reason: Unknown
% 0.86/0.88 % (31015)Termination phase: Saturation
% 0.86/0.88
% 0.86/0.88 % (31015)Memory used [KB]: 1023
% 0.86/0.88 % (31015)Time elapsed: 0.002 s
% 0.86/0.88 % (31015)Instructions burned: 2 (million)
% 0.86/0.88 % (31015)------------------------------
% 0.86/0.88 % (31015)------------------------------
% 0.86/0.88 % (31016)First to succeed.
% 0.86/0.88 % (31012)Instruction limit reached!
% 0.86/0.88 % (31012)------------------------------
% 0.86/0.88 % (31012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.86/0.88 % (31012)Termination reason: Unknown
% 0.86/0.88 % (31012)Termination phase: Saturation
% 0.86/0.88
% 0.86/0.88 % (31012)Memory used [KB]: 5500
% 0.86/0.88 % (31012)Time elapsed: 0.003 s
% 0.86/0.88 % (31012)Instructions burned: 4 (million)
% 0.86/0.88 % (31012)------------------------------
% 0.86/0.88 % (31012)------------------------------
% 0.86/0.88 % (31013)Also succeeded, but the first one will report.
% 0.86/0.88 % (31016)Refutation found. Thanks to Tanya!
% 0.86/0.88 % SZS status Theorem for DTF2THF_30808
% 0.86/0.88 % SZS output start Proof for DTF2THF_30808
% 0.86/0.88 thf(type_def_6, type, 'type/nums/num': $tType).
% 0.86/0.88 thf(type_def_7, type, 'type/realax/real': $tType).
% 0.86/0.88 thf(func_def_0, type, 'type/realax/real': $tType).
% 0.86/0.88 thf(func_def_1, type, 'type/nums/num': $tType).
% 0.86/0.88 thf(func_def_2, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 0.86/0.88 thf(func_def_3, type, 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real').
% 0.86/0.88 thf(func_def_4, type, 'const/iterate/sum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real')).
% 0.86/0.88 thf(func_def_5, type, 'const/iterate/nsum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/nums/num') > 'type/nums/num')).
% 0.86/0.88 thf(func_def_6, type, 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o).
% 0.86/0.88 thf(func_def_12, type, sK0: 'type/nums/num' > 'type/nums/num').
% 0.86/0.88 thf(func_def_13, type, sK1: 'type/nums/num').
% 0.86/0.88 thf(func_def_14, type, sK2: 'type/nums/num').
% 0.86/0.88 thf(func_def_16, type, ph4: !>[X0: $tType]:(X0)).
% 0.86/0.88 thf(f20,plain,(
% 0.86/0.88 $false),
% 0.86/0.88 inference(subsumption_resolution,[status(thm)],[f19,f15])).
% 0.86/0.88 thf(f15,plain,(
% 0.86/0.88 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ((('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1)) = $true)) )),
% 0.86/0.88 inference(cnf_transformation,[status(thm)],[f9])).
% 0.86/0.88 thf(f9,plain,(
% 0.86/0.88 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1)) = $true)),
% 0.86/0.88 inference(fool_elimination,[status(thm)],[f8])).
% 0.86/0.88 thf(f8,plain,(
% 0.86/0.88 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1))),
% 0.86/0.88 inference(rectify,[status(thm)],[f2])).
% 0.86/0.88 thf(f2,axiom,(
% 0.86/0.88 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1))),
% 0.86/0.88 file('/export/starexec/sandbox2/tmp/tmp.7GupvXpVwo/DTF2THF_30808.p','thm/iterate/FINITE_NUMSEG_')).
% 0.86/0.88 thf(f19,plain,(
% 0.86/0.88 ($true != ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2)))),
% 0.86/0.88 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 0.86/0.88 thf(f18,plain,(
% 0.86/0.88 ($true != ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2))) | (('const/realax/real_of_num' @ ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0)) != ('const/realax/real_of_num' @ ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0)))),
% 0.86/0.88 inference(superposition,[status(thm)],[f16,f17])).
% 0.86/0.88 thf(f17,plain,(
% 0.86/0.88 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > 'type/nums/num'] : ((('const/realax/real_of_num' @ ('const/iterate/nsum' @ X0 @ X2 @ X1)) = ('const/iterate/sum' @ X0 @ X2 @ (^[Y0 : X0]: ('const/realax/real_of_num' @ (X1 @ Y0))))) | (('const/sets/FINITE' @ X0 @ X2) != $true)) )),
% 0.86/0.88 inference(cnf_transformation,[status(thm)],[f12])).
% 0.86/0.88 thf(f12,plain,(
% 0.86/0.88 ! [X0 : $tType,X1 : X0 > 'type/nums/num',X2 : X0 > $o] : ((('const/realax/real_of_num' @ ('const/iterate/nsum' @ X0 @ X2 @ X1)) = ('const/iterate/sum' @ X0 @ X2 @ (^[Y0 : X0]: ('const/realax/real_of_num' @ (X1 @ Y0))))) | (('const/sets/FINITE' @ X0 @ X2) != $true))),
% 0.86/0.88 inference(ennf_transformation,[status(thm)],[f7])).
% 0.86/0.88 thf(f7,plain,(
% 0.86/0.88 ! [X0 : $tType,X1 : X0 > 'type/nums/num',X2 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X2) = $true) => (('const/realax/real_of_num' @ ('const/iterate/nsum' @ X0 @ X2 @ X1)) = ('const/iterate/sum' @ X0 @ X2 @ (^[Y0 : X0]: ('const/realax/real_of_num' @ (X1 @ Y0))))))),
% 0.86/0.88 inference(fool_elimination,[status(thm)],[f6])).
% 0.86/0.88 thf(f6,plain,(
% 0.86/0.88 ! [X0 : $tType,X1 : X0 > 'type/nums/num',X2 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X2) => (('const/realax/real_of_num' @ ('const/iterate/nsum' @ X0 @ X2 @ X1)) = ('const/iterate/sum' @ X0 @ X2 @ (^[X3 : X0] : ('const/realax/real_of_num' @ (X1 @ X3))))))),
% 0.86/0.88 inference(rectify,[status(thm)],[f1])).
% 0.86/0.88 thf(f1,axiom,(
% 0.86/0.88 ! [X0 : $tType,X1 : X0 > 'type/nums/num',X2 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X2) => (('const/realax/real_of_num' @ ('const/iterate/nsum' @ X0 @ X2 @ X1)) = ('const/iterate/sum' @ X0 @ X2 @ (^[X3 : X0] : ('const/realax/real_of_num' @ (X1 @ X3))))))),
% 0.86/0.88 file('/export/starexec/sandbox2/tmp/tmp.7GupvXpVwo/DTF2THF_30808.p','thm/iterate/REAL_OF_NUM_SUM_')).
% 0.86/0.88 thf(f16,plain,(
% 0.86/0.88 (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_of_num' @ (sK0 @ Y0)))) != ('const/realax/real_of_num' @ ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0)))),
% 0.86/0.88 inference(cnf_transformation,[status(thm)],[f14])).
% 0.86/0.88 thf(f14,plain,(
% 0.86/0.88 (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_of_num' @ (sK0 @ Y0)))) != ('const/realax/real_of_num' @ ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0)))),
% 0.86/0.88 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f11,f13])).
% 0.86/0.88 thf(f13,plain,(
% 0.86/0.88 ? [X0 : 'type/nums/num' > 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : (('const/realax/real_of_num' @ ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)) != ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_of_num' @ (X0 @ Y0))))) => (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_of_num' @ (sK0 @ Y0)))) != ('const/realax/real_of_num' @ ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0)))),
% 0.86/0.88 introduced(definition,[],[choice_axiom])).
% 0.86/0.88 thf(f11,plain,(
% 0.86/0.88 ? [X0 : 'type/nums/num' > 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : (('const/realax/real_of_num' @ ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)) != ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_of_num' @ (X0 @ Y0)))))),
% 0.86/0.88 inference(ennf_transformation,[status(thm)],[f10])).
% 0.86/0.88 thf(f10,plain,(
% 0.86/0.88 ~! [X0 : 'type/nums/num' > 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : (('const/realax/real_of_num' @ ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_of_num' @ (X0 @ Y0)))))),
% 0.86/0.88 inference(fool_elimination,[status(thm)],[f4])).
% 0.86/0.88 thf(f4,negated_conjecture,(
% 0.86/0.88 ~! [X0 : 'type/nums/num' > 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : (('const/realax/real_of_num' @ ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ (^[X3 : 'type/nums/num'] : ('const/realax/real_of_num' @ (X0 @ X3)))))),
% 0.86/0.88 inference(negated_conjecture,[status(cth)],[f3])).
% 0.86/0.88 thf(f3,conjecture,(
% 0.86/0.88 ! [X0 : 'type/nums/num' > 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : (('const/realax/real_of_num' @ ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ (^[X3 : 'type/nums/num'] : ('const/realax/real_of_num' @ (X0 @ X3)))))),
% 0.86/0.88 file('/export/starexec/sandbox2/tmp/tmp.7GupvXpVwo/DTF2THF_30808.p','thm/iterate/REAL_OF_NUM_SUM_NUMSEG_')).
% 0.86/0.88 % SZS output end Proof for DTF2THF_30808
% 0.86/0.88 % (31016)------------------------------
% 0.86/0.88 % (31016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.86/0.88 % (31016)Termination reason: Refutation
% 0.86/0.88
% 0.86/0.88 % (31016)Memory used [KB]: 5500
% 0.86/0.88 % (31016)Time elapsed: 0.002 s
% 0.86/0.88 % (31016)Instructions burned: 2 (million)
% 0.86/0.88 % (31016)------------------------------
% 0.86/0.88 % (31016)------------------------------
% 0.86/0.88 % (31010)Success in time 0.01 s
%------------------------------------------------------------------------------